A new rotation period and longitude system for Uranus

A new rotation period and longitude system for Uranus | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A new rotation period and longitude system for Uranus Laurent Lamy, Renee Prange, Jerome Berthier, Chihiro Tao, Tae Kim, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3876131/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Apr, 2025 Read the published version in Nature Astronomy → Version 1 posted You are reading this latest preprint version Abstract In the absence of any visible solid surface, the rotation period of the giant planets has been inferred from periodic phenomena tied to the magnetic field produced in their deep interior. The main method relied on remote radio auroral observations, sometimes complemented by in situ magnetic measurements. For Uranus, such measurements acquired during the Voyager 2 flyby in 1986 yielded a rotation period of 17.24±0.01h 1 . This fundamental planetary parameter, referenced since then by the International Astronomical Union, is the basis of the Uranian longitude model 2 . Still, the period uncertainty limits its validity to a few years, after which the orientation of the magnetic axis was lost. Here, we use a novel approach, based on the long term (2011-2022) tracking of Uranus’ magnetic poles from Hubble Space Telescope images of its ultraviolet aurorae, to achieve a new rotation period of 17.247864±0.000010h. It is consistent with, although 28s longer than, the Voyager 2 period. This much more precise determination leads to a new longitude model now valid over decades, from before the Voyager 2 epoch up to the arrival of any future Uranus mission. It also has strong direct implications on formation scenarios, interior models, dynamo theories and studies of the magnetosphere. This novel approach stands as an alternate method to determine the rotation rate of any object hosting a magnetosphere and rotationally modulated aurorae, in our solar system and beyond. Physical sciences/Astronomy and planetary science/Planetary science/Giant planets Physical sciences/Astronomy and planetary science/Space physics/Aurora Physical sciences/Astronomy and planetary science/Space physics/Magnetospheric physics Physical sciences/Astronomy and planetary science/Space physics/Astronomical instrumentation Figures Figure 1 Figure 2 Figure 3 Context Unlike the telluric planets, the central part of the giant planets is embedded within a large gaseous envelope subject to strong zonal winds, which prevent one from measuring directly its rotation period. This has been instead inferred by observing periodic phenomena tied to the magnetic field anchored in, and rigidly rotating with, the planetary core-mantle. Two main methods have been used so far for this purpose. The main one relies on long-term remote observations of auroral radio emissions produced near the magnetic poles. A second, complimentary, method consists of tracking in situ the oscillations produced by the rotating magnetic field with spacecraft exploring the inner magnetosphere. The rotation rate of the giant planets’ interior stands as a fundamental planetary parameter referenced by the International Astronomical Union (IAU) and bases the definition of their System III (SIII) longitude system 2 . The Voyager 2 flyby of Uranus, with a closest approach (CA) on January 24 th , 1986, 18:00 during northern summer solstice, yielded the discovery of a highly tilted (59°) and offset (-0.3 Uranian radii, 1 R U = 25559 km) magnetic field 3 . The rotation axis is inclined by 98° from the celestial north, and it carves out a highly asymmetric magnetosphere whose auroral emissions were detected at radio and ultraviolet (UV) wavelengths 4-6 . A 17.24±0.01h rotation period of Uranus was determined by comparing remote radio and in situ magnetic measurements. More precisely, monitoring the Uranian Kilometric Radiation (UKR) during a 1 month-long post-encounter interval (42 planetary rotations) revealed a radio period of 17.239±0.009h, while the independent analysis of magnetic oscillations measured during a 6h-long interval near the CA with a simple magnetic field model provided a coarser magnetic period of 17.29±0.2h. The 17.24h value retained as the rotation period was used to define both the westward Uranian Longitude System (ULS) and the IAU SIII eastward longitude model (hereafter IAU 17.24h ), described in the Methods section. The northern and southern magnetic poles of an Offset/Tilted Dipole (OTD) simple model were located at (+15.2°,47.7°) and (-44.2°,227.5°) ULS latitude and longitude, respectively 3 . This period finally served to build up the Q 3 (3 rd order) Uranus internal magnetic field model from the spherical analysis of in situ magnetic field measurements 7 . Overall, the ±0.01h period uncertainty transposes into a ±180° error on longitudes in only ~1.7 years, so that the orientation of the magnetic axis was completely lost only a few years after the Voyager 2 flyby. In 2009, a third approach, based on the direct localization of the magnetic poles through the re-analysis of the UV aurorae mapped by the Voyager 2 Ultraviolet Spectrometer (UVS), was explored to further constrain the radio period. Despite the UVS limitations (partial and time variable slit coverage of the disc, lack of spatial resolution), the authors could reconstruct cylindrical maps of the UV aurorae observed over a few days before/after the flyby 8-9 . They achieved a UV period of 17.212+0.0/-0.04h, whose low degree of confidence results from the limited time period analyzed and UVS imaging capabilities. Assuming a north/south spatial magnetic conjugacy of the UV aurorae on average, the authors could further constrain the magnetic field data to build up the AH 5 (5 th order) most recent magnetic field model 9 . In 2011, 25 years after the Voyager 2 flyby, the Hubble Space Telescope (HST) unambiguously redetected the Uranian UV aurorae from Earth 10 with the Space Telescope Imaging Spectrograph (STIS), providing the first reported auroral images and opening a new window to remotely study the Uranian magnetosphere on the long term. HST then subsequently observed the Uranian UV aurorae in 2012, 2014, 2017, 2020 and 2022. These observing campaigns, sampling various solar wind conditions while the magnetospheric configuration gradually shifted from equinox to southern summer solstice, revealed a diversity of auroral signatures gradually switching from scarce, transient, spot-like, signatures to more frequent, elongated, arc-like, emissions 10-12 . By fitting a model auroral oval to the average cylindrical map of the aurorae observed in 2014, we retrieved the position the OTD southern magnetic pole in the ULS system, with a 104±26° longitude inconsistent with the Voyager 2 reference. In this study, we take advantage of HST/STIS high resolution images of Uranus’ UV aurorae collected between 2011 and 2022 to constrain the position of the magnetic poles and achieve a new, independent, rotation period. We then combine HST results and the Voyager 2 reference position of the magnetic poles to determine the most precise period possible. We use this new rotation period to provide a corrected SIII longitude system together with the longitude of the magnetic poles. We finally discuss the broader implications of these results. Results Unlike the spot-like emissions observed across the disc from 2011 to 2014, the aurorae imaged late 2017 unexpectedly revealed an elongated, well localized, northern auroral arc observed twice, 3 weeks apart 6 . By cross-correlating in longitude the cylindrical projections of the September 30 th and October 21 st images (Figure S1), we determined a 304±12° phase shift between the two auroral arcs, yielding pairs of solutions (rotation period, number of rotations). The only period matching the Voyager 2 estimate was 17.247±0.010h, with 28 rotations separating both images. This value, slightly longer than the Voyager 2 period, stands as the first independent measurement of the rotation period since 1986. It only assumes a similar emission region in the two images. The uncertainty, similar to that on the Voyager 2 estimate, demonstrates the value-added of Earth-based auroral observations for an independent period determination. To achieve a more precise period, we extended the temporal coverage and statistically analyzed the auroral images acquired from 2011 to 2022. To this end, we selected six reference images, one per HST observing campaign, displayed in Figure 1. The image processing is described in the Methods section. Whenever possible, we favoured observations where both the northern and southern auroral regions were simultaneously visible, which strongly constrain the orientation of the magnetic axis, as in 2017 12 and 2022. The aurorae were then individually fitted for each of the 6 references images with two families of model auroral ovals, defined by the footprints at 1100 km altitude of magnetic shells (M-shell)of 5 R U and20 R U , using the Q 3 and AH 5 internal magnetic field models (see Methods and Figure S2 for details). Importantly, we chose to fit auroral emissions as observed in the HST field-of-view (rather than in cylindrical projections) in order not to exclude any high altitude emission from beyond the limb. The best-fit Q 3 (top) and AH 5 (bottom) northern (blue) and southern (red) model auroral ovals are superimposed to the aurorae in Figure 1. Table 1 provides the IAU 17.24h HST Central Meridian Longitude (CML) and the best-fit longitude (and uncertainty range) of the OTD northern magnetic pole at mid-exposure. The Q 3 ovals are more extended and less asymmetric than the AH 5 ones, so that the inferred longitude of the OTD magnetic poles is slightly less constrained. We then performed a χ 2 minimization analysis between (i) the observed best-fit longitude of the northern magnetic pole for each model oval and (ii) the longitude of the northern magnetic pole modeled for a set of rotation periods P i sampling the 17h-17.5h range. The computation of IAU longitudes for a given P i is described in the Methods section : for observations well separated in time, such as those dealt with here, it requires to account for the proper motion of Uranus along its orbit according to equations of celestial mechanics 2,14 . For each tested P i , we computed the χ 2 values for all possible longitudes of the northern magnetic pole (sampled with a 1° step) and retained the minimal value. The final χ 2 curves displayed in Figure S3 minimize in both the AH 5 and Q 3 cases for very close periods, only 5x10 -5 h apart. The inferred average period is 17.2478±0.0001h. This value, based on HST auroral observations alone analyzed through magnetic field models, definitely confirms a longer period than the Voyager 2 one, with an accuracy improved by two orders of magnitude. This accuracy is mainly limited by the 11 year-long interval available. To achieve the most precise period possible, we repeated the χ 2 analysis by combining the Voyager 2 reference with the HST dataset. Namely, the longitude of the magnetic poles was fixed at Voyager 2 CA (see Figure S4) and propagated to the HST observing times by varying the period only. The combination of HST and Voyager 2 observations thus suppresses one free parameter, the longitude of the magnetic poles, from the analysis. We neglected any possible secular motion of the magnetic axis from 1986 to 2022, a reasonable assumption considering that the axial dipole component of Jupiter’s magnetic field remained unchanged over a 43 years-long interval 15 . Figure 2 displays the obtained results. Compared to Figure S3, both χ 2 curves display narrower local minima, as expected for a better-constrained analysis. They again minimize for nearby periods, within 5x10 -6 h. We retained the average period of 17.247864±0.000010h, more precise by another factor of 10. The corresponding longitude of the OTD northern (southern) magnetic pole lies at 357.1° (176.9°). We built up an associated IAU new SIII longitude model, which stands as a corrected version of the IAU 17.24h one. It can already be accessed by the community through the MIRIADE online ephemeris service of IMCCE (Institut de Mécanique Céleste et de Calcul des Ephémérides), with a query example provided in the Data Availability section. As a last step, we checked the validity of this updated period and IAU new longitude system over an extended set of auroral events captured by HST, as illustrated in Figure 3 with the Q 3 auroral model oval (see Figure S5 for the AH 5 one). For simplicity, an auroral event here refers to auroral emissions detected during a single HST orbit, so that two consecutive images of the same, rotating, emission region form a single auroral event. The predicted model auroral ovals match fairly well all the auroral events published previously 6,10-11 . The only exception concerns the HST tentative detection of faint auroral arcs on July 28 th , 1998 10 , morphologically different from the other cases, which did not match the predicted position of the auroral ovals, so that this candidate can be discarded. Figure 3 also displays new unpublished auroral events, either unreported (Figure 3a shows the first auroral detection obtained with HST/ACS), or considered previously as too faint (Figures 3b-c,e) or obtained recently (Figures 3m-t). The HST 2022 campaign provided the largest number of auroral detections to date, with elongated emissions in both hemispheres, most intense/localized in the south, rotating with the planet. The detailed analysis of these new auroral signatures, which probe a magnetospheric configuration intermediate between equinox and solstice, is beyond the purpose of this paper. Methods HST dataset The HST images displayed in Figure 1, 3, S1 and S5 (except for Figures 3a and S5a) correspond to STIS long exposures acquired either with the 25MAMA clear filter or the SrF2 one, using the time-tag mode and processed as described in past published studies 11 . The STIS images were calibrated through the Space Telescope Science Institute pipeline. A model planetary disc was adjusted to the solar reflected emission to retrieve accurate pixel coordinates in a physical frame (and fix any pointing error). They were corrected for any geocoronal contamination throughout the detector, by subtracting a uniform offset intensity derived on the sky, well beyond the disc. A background model of solar emissions reflected by the disc was then fitted to and subtracted from each individual image. We used two kinds of background model. When the number of images collected during a given HST campaign was large enough (as in 2011, 2012, 2020 and 2022), we used as an empirical model the median of the other images using the same filter, once rescaled at the same apparent size. This also accounts for atmospheric emissions extending beyond the limb. When the statistics of images was too low and/or intense extended auroral emissions could contaminate the median background (as in 2014 and 2017), we built up instead a numerical disc model from fitting the 2-D brightness distribution with a 1 st order Minnaert function 34 over 30° wide bands in latitude, complemented, outside the disc, by an exponentially decreasing brightness profile. In practice, an empirical model provides a more realistic but noisier estimate of the disc background. The background-subtracted images were then converted into kilo-Rayleighs of unabsorbed H 2 emission with standard conversion factors 35 and ultimately smoothed over a 5×5 pixels averaging filter to increase the signal-to-noise ratio (SNR), while preserving spatial resolution. Figures 3a and S5a show an HST image obtained with another FUV spectro-imager, the Advanced Camera for Surveys (ACS), which was used here with the F125LP filter comparable to the 25MAMA one. This image of the first reported auroral detection with ACS so far (this instrument has been regularly used in 2005, 2011 and 2012), has been processed in exactly the same way with an empirical model of disc background. It is worth mentioning here that, as for the weak auroral detection obtained with STIS in 2012, the northern auroral signal observed by ACS was seen to rotate with the planet in the sub-exposures of this observation. HST processed observations of Uranus are also directly accessible through the APIS service 36 . Model auroral ovals The model auroral ovals employed in this study correspond to the footprints at 1100 km above the 1 bar level (where the electrons are assumed to trigger the aurorae) of magnetic field lines with M-shells = 5 R U and20 R U . This altitude was transposed from the Saturn’s case whose atmospheric profile is comparable, under the assumption that Uranian auroral electrons are not more energetic 12 . The 5 R U and20 R U magnetic shells were chosen as, respectively, a typical low-latitude edge of the UV aurorae observed by UVS 9 , and a typical standoff distance of the magnetopause 3 . The associated magnetic shells thus encompass most of the magnetosphere. Northern and southern model auroral ovals were derived for both the AH 5 internal field model– as already done to fit the magnetic poles from the aurorae detected in 2012, 2014 12 and 2017 6 – and the Q 3 model for comparison purposes. We chose to limit ourselves to internal field models rather than magnetospheric ones 9,13 for simplicity. Deriving a more realistic magnetospheric model accounting for the compression of the magnetosphere by the solar wind would require to precisely know the solar wind parameters prevailing during the HST observations, which is beyond the current state of the art since the observations were scheduled on purpose during intervals encompassing strongly variable solar wind, whose parameters were additionally predicted with a ±2 days uncertainty 11 . More importantly, using a magnetospheric model would not significantly change the low latitude boundary of model ovals as the M-shell = 5 R U is located in the inner magnetosphere shielded from the solar wind 9 . This is particularly striking for the fit of images where northern and southern aurorae were observed simultaneously, as for the 2017 and 2022 images in Figure 1. While the auroral emissions were fitted with model auroral ovals defined from the multipolar Q 3 and AH 5 internal field models, the observable used in our analysis is the longitude of the magnetic poles defined for the Offset/Tilted Dipole (OTD) model. The link between model ovals and the longitude of the OTD magnetic poles is illustrated in Figure S4, which shows Uranus as seen from from Voyager 2 at CA. The AH 5 (left-hand side) and Q 3 (right-hand side) southern model ovals are displayed by pairs of solid lines. While they slightly differ from each other, they both correspond to the same OTD southern magnetic pole which lies at the intersection of the red dotted-dashed meridian (longitude) and the red dashed parallel (latitude). Auroral fitting and χ 2 analysis Table 1 provides the IAU 17.24h longitude of the OTD northern magnetic pole (which can be deduced from the southern one whenever not observed) for the six chosen reference HST images displayed in Figure 1. This longitude was obtained from the best-fit of the Q 3 and AH 5 model ovals and accompanied by an error bar (within parenthesis) obtained from the most extreme fits of the same ovals. Figure S2 illustrates this fitting procedure with the example of Q 3 model ovals applied to two representative images, one poorly constrained in 2011 and one strong constrained in 2022. Indeed, the former restricts to a single, localized, northern auroral spot, while the latter displayed elongated auroral emissions observed simultaneously in both hemispheres well beyond the limb. The uncertainty on the longitude of the best-fit ovals is +15°/-21° and ±12°, respectively Unlike a simple least-square fit, the calculation of the χ 2 data-model test described in the main text is weighted by the error on data points. Instead of the simple error bars (sometimes asymmetric) provided above, we used their quadratic sum as a typical, more realistic, uncertainty on the best-fit longitudes. Applied to the two examples of Figure S2, this corresponds to error bars of ±26° and ±17°, respectively, wider by a few degrees than the initial estimate but hence more robust. The modeled longitudes were obtained as detailed below. SIII longitudes As outlined in the introduction, in the ULS spin-aligned coordinate system used during the Voyager 2 epoch, the rotation axis points toward the north pole. Latitudes are counted positively toward the same direction, so that the northern and southern OTD magnetic poles lie at positive (+15.2°) and negative (-44.2°) latitude, respectively. The Uranus rotation is prograde and longitudes are counted positively westward, so that the CML of a fixed observer increases with time. This longitude system was arbitrarily referenced at CML = 302° at the Voyager 2 CA. The System III coordinate system referenced by IAU uses different conventions. The north pole is here defined as pointing northward to the ecliptic plane, so that IAU latitudes are opposite to ULS ones and the Uranus rotation is retrograde. IAU planetocentric longitudes are counted positively eastward, whatever the sense of planetary rotation, so that the CML of a fixed Uranus observer increases with time. IAU planetographic longitudes use another convention for historical reasons, and are defined as increasing with time whatever the sense of rotation. In the case of Uranus, both uranocentric and uranographic longitudes thus coincide. The IAU sub-observer planetocentric latitude δ and longitude ω are provided by the following set of equations 14 : sin δ = - sin δ 0 sin δ P - cos δ 0 cos δ P cos(α P - α 0 ) cos (W-ω) cos δ = - sin δ 0 sin δ P - cos δ 0 cos δ P sin(α P - α 0 ) sin (W-ω) cos δ = - cos δ 0 sin δ P + sin δ 0 cos δ P cos(α P - α 0 ) where (α P ,δ P ) are the equatorial apparent coordinates of Uranus center of mass, (α 0 ,δ 0 ) those of the north pole direction and W is the angle defining the position of the prime meridian in the Uranus equatorial plane according to the equation : W = W 0 + W 1 d where W 0 is the position of the prime meridian referenced to the intersection by the equatorial plane and the celestial equator at the J2000 epoch (JD 2451545.0 = 2000 January 1 12.0 h TDB), W1 is the SIII rotation period in degrees per day and d is the time interval between the observing time and the J2000 epoch. The numerical values of (α 0 ,δ 0 ), W 0 and W 1 were chosen from the latest report of the IAU working Group on cartographic coordinates and rotational elements 2 (see their Figure 1 for a visual representation of these angles) and those of (α P ,δ P ) were obtained at mid-exposure for each observation from the IMCCE/MIRIADE ephemeris service. Animation S6 illustrates that the proper motion of Uranus along its orbit is non negligible near solstice periods and/or for long enough intervals. It displays the position of the prime meridian and the planetary configuration as seen from Earth as a function of time for a non-rotating Uranus (W1 = 0). For our purpose, we first checked that we retrieved IAU longitudes from the above set of equations consistent with those provided by IMCCE/MIRIADE (planetocentric longitudes by default) and by the JPL Horizons ephemeris (planetographic longitudes by default). We then computed model SIII longitudes by varying W 1 , that is the rotation period. The IMCCE/MIRIADE online ephemeris service can already be used with the new 17.247864h rotation period obtained in this article to in turn provide IAU new corrected longitudes. The new CML at mid-exposure associated with the images displayed in Figure 3 are listed in Table 2. Discussion and implications The new rotation period of Uranus, 17.247864±0.000010h or 17h14m52.310s±0.036s, stands as the most precise determination of the inner rotation rate of a giant planet to date, comparable with the rotation period of Jupiter 2 determined from decades of ground-based observations of its decametric emissions and whose time variability has recently been questioned 16 . The developed method, based on the long-term tracking of the magnetic poles through imaging of the (ultraviolet) aurorae, can straightforwardly be re-applied to other giant planets whose auroral emissions have been imaged over a sufficiently long interval. The new period is 28s longer than the one derived in 1986 from Voyager 2 data alone. This difference is significant and the correct value can first of all be used to refine the existing models of internal magnetic field 7,9 . It also has strong implications to constrain the internal structure of Uranus, its evolution, dynamo theories and formation scenarios 17,18 . For instance, the shorter period of 16.58h (16h34m) derived in 2010 from the profile of atmospheric winds and proposed to probe the inner rotation rate 19 is largely inconsistent with the updated rotation period of the magnetic field. The IAU new longitude model is also much more precise. Reaching a ±10° uncertainty on longitudes now requires a century. Such a model therefore has immediate applications, both for re-analyzing past observations and for scheduling future ones. Past observations primarily include Voyager 2 in situ measurements in the magnetosphere together with Earth-based long-term observations tracking auroral emissions at optical, radio 20 or X-rays 21 wavelengths. In the UV range, this concerns the International Ultraviolet Explorer monitoring of variable H-Lyα emission over 1978-1993 and attributed to variable auroral activity 22 or HST observations other than those dealt with in this study, such as those involved in the study of the Uranus hydrogen corona 23 . In the IR domain, long-term observations of variable and inhomogeneous H 3 + emission have regularly been tentatively attributed to an auroral driver 24-25 , and a Keck/NIRSPEC observation on 5 th Sept. 2006 was recently presented as an unambiguous northern auroral detection 26 . In the latter case however, the IAU new longitude model predicts that the northern auroral region was not visible during the observation, so that this detection can also be discarded. The knowledge of the orientation of the magnetic axis is mandatory to unambiguously track any auroral footprint associated with the Uranian moons 27 and to perform realistic numerical modeling of the magnetosphere (magnetic reconnection conditions, global MHD models) to be compared to observational constraints 28-31 . Last and not least, this new SIII model will be an essential tool for the Uranus flagship mission currently in preparation, either for the definition of any orbital tour and/or for choosing an atmospheric entry site 32,33 . Declarations Acknowledgements We thank Claus Leitherer for HST director’s time allocated in 2020 and Alison Sherwin as our program coordinator. The French authors thank the CNES spatial agency and CNRS/INSU national programs of heliophysics (PNST, also funded by CEA) and planetology (PNP). Data availability This article is based on observations acquired with the Hubble Space Telescope, operated by NASA and ESA, through the observing programs GO #12601, 13012, 14036, 16313 and DDT #15380. The data can be accessed through the STSci MAST archive at https://archive.stsci.edu/missions-and-data/hst and the processed data through the CNRS/INSU APIS observation service operated by PADC/LESIA at https://apis.obspm.fr. The CNRS/INSU MIRIADE ephemeris service, operated by IMCCE/Obs. Paris, is accessible at https://ssp.imcce.fr/webservices/miriade/ The data can be queried through a web interface or url queries. An example of url query using the new rotation period to obtain IAU new SIII longitudes is provided below : https://ssp.imcce.fr/webservices/miriade/api/ephemph.php?-name=p:Uranus&-type=planet&-ep=2000-01-01T12:00:00&-nbd=2&-step=1h&-observer=@500&-so=3&-pop=P=-17.247864;model=newSIII&-mime=text&-output=--coord(eq2000) where the option -pop=P=-17.247864 defines the period in hours and the sign – the retrograde rotation of the planet. Author contributions LL led and processed the HST observations, conducted their analysis and wrote the manuscript. RP contributed to the data analysis, to the physical interpretation and to the writing of the manuscript. JB helped with the analytical determination of planetocentric ephemeris and developed a new module on the IMCCE/MIRIADE online service which enables the user to choose the planetary parameters. CT and TK performed MHD simulations of the solar wind which were used to schedule the observations and counter-checked the derived longitudes. 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J Geophys Res 117:A07316 Lamy L, Prangé R, Henry F, Le Sidaner P (2015) The Auroral Planetary Imaging and Spectroscopy (APIS) service. Astron Comput 11:138–145 Tables Table 1 : Characteristics of the HST/STIS images of the aurorae displayed in Fig. 1. Longitudes are derived at mid-exposure. Observing date (UT) Dataset (Filter) Exposure time (s) Visible aurorae IAU 17.24h CML (°) IAU 17.24h AH 5 N mag. lon. (°) IAU 17.24h Q3 N mag. pole lon. (°) 2011-11-29 02:09:24 obrx18hbq (25MAMA) 1000 North 319.5 276 (267-303) 282 (267-303) 2012-09-27 15:00:19 obz501dgq (25MAMA) 1250 South 162.6 336 (323-353) 336 (322-360) 2014-11-24 09:03:59 ocpl07cmq (F25SRF2) 900 South 31.9 148 (140-171) 147 (139-182) 2017-09-30 07:00:30 odq402yzq (25MAMA) 2518 North South 65.1 39 (31-61) 41 (34-62) 2020-10-09 22:29:47 oea005ghq (25MAMA) 2515 South 134.1 292 (270-304) 293 (270-315) 2022-10-10 11:05:35 oewy05coq (25MAMA) 2277 North South 127.0 100 (86-108) 98 (86-110) Table 2 : Characteristics of the HST STIS and ACS images of the aurorae displayed in Figures 3 and S5. The CML is computed at mid-exposure. Observing date (UT) Dataset Filter Exp. (s) Visible aurorae IAU new CML (°) 2005-08-10 00:32:04 j9eq01011 F115LP 1200 North 306.4 2011-11-13 07:41:13 obrx06j5q 25MAMA 1000 South 66.8 2011-11-14 12:25:52 obrx08dqq 25MAMA 1000 North 306.7 2011-11-16 15:32:10 obrx10p0q 25MAMA 1000 North 293.3 2011-11-19 05:49:24 obrx12ceq 25MAMA 1000 South 153.2 2011-11-29 02:09:24 obrx18hbq 25MAMA 1000 North 45.6 2012-09-27 15:00:19 obz501dgq 25MAMA 1250 South 179.3 2014-11-01 23:57:32 ocpl02nzq 25MAMA 1231 South 179.7 2014-11-24 09:03:59 ocpl07cmq F25SRF2 900 South 228.6 2017-09-29 15:06:52 odq401vwq 25MAMA 2518 North + South 52.2 2017-09-30 07:00:30 odq402yzq 25MAMA 2518 North + South 24.0 2017-10-21 00:28:58 odq403c4q 25MAMA 2533 North 327.4 2017-11-11 08:14:00 odq404m2q 25MAMA 2563 South 208.4 2020-10-09 22:29:47 oea005ghq 25MAMA 2515 South 200.4 2022-09-06 04:56:10 oewy01geq 25MAMA 2034 South 144.6 2022-10-08 17:50:36 oewy04icq 25MAMA 2218 South 245.2 2022-10-10 11:05:35 oewy05coq 25MAMA 2277 North + South 26.3 2022-10-16 11:34:09 oewy06i4q 25MAMA 2334 South 162.1 2022-10-24 08:26:01 oewy08c6q 25MAMA 1018 South 140.2 2022-12-18 00:45:28 oewy11ssq 25MAMA 1445 South 171.0 Additional Declarations There is NO Competing Interest. Supplementary Files AnimationS6.gif Animation S6: (Left) Position of the prime meridian and (right) planetary configuration with the prime meridian in red as a function of time over 1985-2069 (1 frame per month) for a terrestrial observer and a non-rotating Uranus (W1 = 0). This animation illustrates the effect of the proper motion of Uranus along its orbit onto the position of the prime meridian used to compute IAU longitudes. supplementoryFigures.docx Cite Share Download PDF Status: Published Journal Publication published 07 Apr, 2025 Read the published version in Nature Astronomy → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3876131","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":272405422,"identity":"c73f4a50-beb0-4fb2-a566-18c01083448b","order_by":0,"name":"Laurent Lamy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYBACPhTGB4YDDBAaD2CDUAZgBuMMiBYgTawWZh6itLCfMfvwcccfION0mrRNxR17c7EDjM0V+LTw5BjPnHkGaAtP7jbpnDPPEnfOTmBsPIPXYTnGzLxtIIcBteS2HU4wuJ3A/rABnxb+N8bMf0Fa+N9uk7ZsO2wP1MLYiFeLBNAWRpAWCaAtjG2HGTcQ1vKsmLG3zZiHTeLtZssesF8SG/Fq4edP3szws01Ojp8/d+ONH6AQk04+iFcLDPAAMYsEiGXAwEiMBghg/gDRMgpGwSgYBaMAFQAAaJlIOugaldUAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-8428-1369","institution":"LESIA, Observatoire de Paris-PSL","correspondingAuthor":true,"prefix":"","firstName":"Laurent","middleName":"","lastName":"Lamy","suffix":""},{"id":272405423,"identity":"976344ce-e1e1-4cbe-ac09-f2cfc65b1d26","order_by":1,"name":"Renee Prange","email":"","orcid":"https://orcid.org/0000-0001-8809-4563","institution":"Observatoire de Paris","correspondingAuthor":false,"prefix":"","firstName":"Renee","middleName":"","lastName":"Prange","suffix":""},{"id":272405424,"identity":"30b58fbd-e0d1-4e99-ae54-622caf33528e","order_by":2,"name":"Jerome Berthier","email":"","orcid":"https://orcid.org/0000-0003-1846-6485","institution":"IMCCE/Observatorie de Paris, Paris, France, 77, Avenue Denfert Rochereau, 75014, Paris, France","correspondingAuthor":false,"prefix":"","firstName":"Jerome","middleName":"","lastName":"Berthier","suffix":""},{"id":272405425,"identity":"dc5139a0-f564-4e07-9ff0-52a530ba24cf","order_by":3,"name":"Chihiro Tao","email":"","orcid":"https://orcid.org/0000-0001-8817-0589","institution":"National Institute of Information and Communications Technology (NICT)","correspondingAuthor":false,"prefix":"","firstName":"Chihiro","middleName":"","lastName":"Tao","suffix":""},{"id":272405426,"identity":"2fb7b6db-0ecd-4c39-893a-3a698074e61a","order_by":4,"name":"Tae Kim","email":"","orcid":"https://orcid.org/0000-0003-0764-9569","institution":"The University of Alabama in Huntsville","correspondingAuthor":false,"prefix":"","firstName":"Tae","middleName":"","lastName":"Kim","suffix":""},{"id":272405427,"identity":"dfba643f-7b80-4a6c-90de-5d94ae0f116d","order_by":5,"name":"Lorenz Roth","email":"","orcid":"https://orcid.org/0000-0003-0554-4691","institution":"KTH Royal Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Lorenz","middleName":"","lastName":"Roth","suffix":""},{"id":272405428,"identity":"13b36cc6-29bd-40cd-a267-0595663c67db","order_by":6,"name":"Mathieu Barthélémy","email":"","orcid":"","institution":"IPAG, Univ. Grenoble Alpes","correspondingAuthor":false,"prefix":"","firstName":"Mathieu","middleName":"","lastName":"Barthélémy","suffix":""},{"id":272405429,"identity":"565114e5-d4f8-47bb-b00b-65a4af97e605","order_by":7,"name":"Jean-Yves Chaufray","email":"","orcid":"","institution":"LATMOS","correspondingAuthor":false,"prefix":"","firstName":"Jean-Yves","middleName":"","lastName":"Chaufray","suffix":""},{"id":272405430,"identity":"d57d1a5f-9218-4dbd-bbe9-d1fd85e62cf9","order_by":8,"name":"Abigail Rymer","email":"","orcid":"","institution":"APL, JHUAPL","correspondingAuthor":false,"prefix":"","firstName":"Abigail","middleName":"","lastName":"Rymer","suffix":""},{"id":272405431,"identity":"eb1deb4b-d1fd-4971-b17d-8152f9994015","order_by":9,"name":"William Dunn","email":"","orcid":"https://orcid.org/0000-0002-0383-6917","institution":"University College London","correspondingAuthor":false,"prefix":"","firstName":"William","middleName":"","lastName":"Dunn","suffix":""},{"id":272405432,"identity":"1d49782b-1d3d-458e-b59a-c801418d5289","order_by":10,"name":"Affelia Wibisono","email":"","orcid":"","institution":"UCL, MSSL","correspondingAuthor":false,"prefix":"","firstName":"Affelia","middleName":"","lastName":"Wibisono","suffix":""},{"id":272405433,"identity":"274db49c-3c3b-460e-88a3-d85c2268f441","order_by":11,"name":"Henrik Melin","email":"","orcid":"https://orcid.org/0000-0001-5971-2633","institution":"University of Leicester","correspondingAuthor":false,"prefix":"","firstName":"Henrik","middleName":"","lastName":"Melin","suffix":""}],"badges":[],"createdAt":"2024-01-18 14:56:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3876131/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3876131/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41550-025-02492-z","type":"published","date":"2025-04-07T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54114652,"identity":"f5608f36-ad40-4643-820e-41e5609164ae","added_by":"auto","created_at":"2024-04-04 19:23:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":391637,"visible":true,"origin":"","legend":"\u003cp\u003eSelection of HST/STIS far-UV images of the Uranian aurorae from 2011 to 2022 used to derive the OTD magnetic pole longitudes listed in table 1. Planetocentric coordinates at 1100km above the 1-bar level are superimposed in white. The pairs of red (blue) lines map the best-fit southern (northern) model auroral ovals built with the (top) Q\u003csub\u003e3\u003c/sub\u003e and (bottom) AH\u003csub\u003e5\u003c/sub\u003e internal field models (see Methods section). The dashed colored lines map the corresponding meridians of the OTD magnetic poles. The solid red line indicates the IAU\u003csub\u003e17.24h\u003c/sub\u003e reference meridian.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3876131/v1/0f3b8659fa0db80569fee777.png"},{"id":54114655,"identity":"dc1337f8-6f8f-46bd-a27f-82a92ac21758","added_by":"auto","created_at":"2024-04-04 19:23:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":18398,"visible":true,"origin":"","legend":"\u003cp\u003eχ\u003csup\u003e2\u003c/sup\u003e data-model test between the longitudes of the magnetic poles (i) derived from the (black) AH\u003csub\u003e5\u003c/sub\u003e and (gray) Q\u003csub\u003e3\u003c/sub\u003e model auroral ovals fitted to the 6 HST images of Figure 1 and (ii) modeled for a variable rotation period and propagated from the Voyager 2 reference position of the magnetic poles at CA.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3876131/v1/e0adbf11d7552ef87820d73f.png"},{"id":54114653,"identity":"8465d1f4-b994-41c5-8fe4-742d8bb2af9b","added_by":"auto","created_at":"2024-04-04 19:23:36","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":893885,"visible":true,"origin":"","legend":"\u003cp\u003eExtended set of HST images of the Uranian aurorae from 2005 to 2022, in the same format as Figure 1. The superimposed Q\u003csub\u003e3\u003c/sub\u003e model auroral ovals are those predicted by the new IAU\u003csub\u003enew\u003c/sub\u003e longitude system. Images a-c, e and n-t are new auroral detections. The white arrows mark weak aurorae. This figure is replicated in Figure S4 with the AH\u003csub\u003e5\u003c/sub\u003e model ovals.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3876131/v1/66de61f9bf4e5a06f15bee58.png"},{"id":80119002,"identity":"10def1c6-7eb6-489b-b7c4-36f3bd091a0c","added_by":"auto","created_at":"2025-04-08 07:06:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2713252,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3876131/v1/4a67ebeb-91ad-4613-ba05-37ac56591b55.pdf"},{"id":54114657,"identity":"01ee5332-bda2-4de6-a760-ebcb9fea57fe","added_by":"auto","created_at":"2024-04-04 19:23:37","extension":"gif","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":22463607,"visible":true,"origin":"","legend":"\u003cp\u003eAnimation S6: (Left) Position of the prime meridian and (right) planetary configuration with the prime meridian in red as a function of time over 1985-2069 (1 frame per month) for a terrestrial observer and a non-rotating Uranus (W1 = 0). This animation illustrates the effect of the proper motion of Uranus along its orbit onto the position of the prime meridian used to compute IAU longitudes.\u003c/p\u003e","description":"","filename":"AnimationS6.gif","url":"https://assets-eu.researchsquare.com/files/rs-3876131/v1/83f5d1854e99018ca99c7763.gif"},{"id":54114654,"identity":"3b8bdaad-5eb5-4dc4-bd78-244588d5d781","added_by":"auto","created_at":"2024-04-04 19:23:36","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":11750293,"visible":true,"origin":"","legend":"","description":"","filename":"supplementoryFigures.docx","url":"https://assets-eu.researchsquare.com/files/rs-3876131/v1/e4c9351e69cfc443eefdd3cd.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A new rotation period and longitude system for Uranus","fulltext":[{"header":"Context ","content":"\u003cp\u003eUnlike the telluric planets, the\u0026nbsp;central part\u0026nbsp;of the giant planets is embedded within a large gaseous envelope subject to strong zonal winds, which prevent one from measuring directly its rotation period. This has been instead inferred by observing periodic phenomena tied to the magnetic field anchored in, and rigidly rotating with, the planetary core-mantle. Two main methods have been used so far for this purpose. The main one relies on long-term remote observations of auroral radio emissions produced near the magnetic poles. A second, complimentary, method consists of tracking \u003cem\u003ein situ\u003c/em\u003e the oscillations produced by the rotating magnetic field with spacecraft exploring the inner magnetosphere. The rotation rate of the giant planets’ interior stands as a fundamental planetary parameter referenced by the International Astronomical Union (IAU) and bases the definition of their System III (SIII) longitude system\u003csup\u003e2\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe Voyager 2 flyby of Uranus,\u0026nbsp;with a closest approach (CA) on January 24\u003csup\u003eth\u003c/sup\u003e, 1986, 18:00 during northern summer solstice, yielded the discovery of a highly tilted (59°) and offset (-0.3 Uranian radii, 1 R\u003csub\u003eU\u003c/sub\u003e = 25559 km) magnetic field\u003csup\u003e3\u003c/sup\u003e. The rotation axis is inclined by 98° from the celestial north, and it carves out a highly asymmetric magnetosphere whose auroral emissions were detected at radio and ultraviolet (UV) wavelengths\u003csup\u003e4-6\u003c/sup\u003e. A 17.24±0.01h rotation period of Uranus was determined by comparing remote radio and \u003cem\u003ein situ\u003c/em\u003e magnetic measurements. More precisely, monitoring the Uranian Kilometric Radiation (UKR) during a 1 month-long post-encounter interval (42 planetary rotations) revealed a radio period of 17.239±0.009h, while the independent analysis of magnetic oscillations measured during a 6h-long interval near the CA with a simple magnetic field model provided a coarser magnetic period of 17.29±0.2h. The 17.24h value retained as the rotation period\u0026nbsp;was used to define both the westward Uranian Longitude System (ULS) and the IAU SIII eastward longitude model (hereafter IAU\u003csub\u003e17.24h\u003c/sub\u003e), described in the Methods section. The northern and southern magnetic poles of an Offset/Tilted Dipole (OTD) simple model were located at (+15.2°,47.7°) and (-44.2°,227.5°) ULS latitude and longitude, respectively\u003csup\u003e3\u003c/sup\u003e. This period finally served to build up the Q\u003csub\u003e3\u003c/sub\u003e (3\u003csup\u003erd\u003c/sup\u003e order) Uranus internal magnetic field model from the spherical analysis of \u003cem\u003ein situ\u003c/em\u003e magnetic field measurements\u003csup\u003e7\u003c/sup\u003e. Overall, the ±0.01h period uncertainty transposes into a ±180° error on longitudes in only ~1.7 years, so that the orientation of the magnetic axis was completely lost only a few years after the Voyager 2 flyby.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn 2009, a third approach, based on the direct localization of the magnetic poles through the re-analysis of the UV aurorae mapped by the Voyager 2 Ultraviolet Spectrometer (UVS), was explored to further constrain the radio period. Despite the UVS limitations (partial and time variable slit coverage of the disc, lack of spatial resolution), the authors could reconstruct cylindrical maps of the UV aurorae observed over a few days before/after the flyby\u003csup\u003e8-9\u003c/sup\u003e. They achieved a UV period of\u0026nbsp;17.212+0.0/-0.04h, whose low degree of confidence results from the limited time period analyzed and UVS imaging capabilities. Assuming a north/south spatial magnetic conjugacy of the UV aurorae on average, the authors could further constrain the magnetic field data to build up the AH\u003csub\u003e5\u003c/sub\u003e (5\u003csup\u003eth\u003c/sup\u003e order) most recent magnetic field model\u003csup\u003e9\u003c/sup\u003e. In 2011, 25 years after the Voyager 2 flyby, the Hubble Space Telescope (HST) unambiguously redetected the Uranian UV aurorae from Earth\u003csup\u003e10\u0026nbsp;\u003c/sup\u003ewith the Space Telescope Imaging Spectrograph (STIS), providing the first reported auroral images and opening a new window to remotely study the Uranian magnetosphere on the long term. HST then subsequently observed the Uranian UV aurorae in 2012, 2014, 2017, 2020 and 2022. These observing campaigns, sampling various solar wind conditions while the magnetospheric configuration gradually shifted from equinox to southern summer solstice, revealed a diversity of auroral signatures gradually switching from scarce, transient, spot-like, signatures to more frequent, elongated, arc-like, emissions\u003csup\u003e10-12\u003c/sup\u003e. By fitting a model auroral oval to the average cylindrical map of the aurorae observed in 2014,\u0026nbsp;we retrieved the position the OTD southern magnetic pole in the ULS system, with a 104±26° longitude inconsistent with the Voyager 2 reference.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this study, we take advantage of HST/STIS high resolution images of Uranus’ UV aurorae collected between 2011 and 2022 to constrain the position of the magnetic poles and achieve a new, independent, rotation period. We then combine HST results and the Voyager 2 reference position of the magnetic poles to determine the most precise period possible. We use this new rotation period to provide a corrected SIII longitude system together with the longitude of the magnetic poles. We finally discuss the broader implications of these results.\u003c/p\u003e"},{"header":"Results ","content":"\u003cp\u003eUnlike the spot-like emissions observed across the disc from 2011 to 2014, the aurorae imaged late 2017 unexpectedly revealed an\u0026nbsp;elongated, well localized, northern auroral arc observed twice, 3 weeks apart\u003csup\u003e6\u003c/sup\u003e. By cross-correlating in longitude the cylindrical projections of the September 30\u003csup\u003eth\u003c/sup\u003e and October 21\u003csup\u003est\u003c/sup\u003e images (Figure S1), we determined a 304±12°\u0026nbsp;phase shift between the two auroral arcs, yielding pairs of solutions (rotation period, number of rotations). The only period matching the Voyager 2 estimate was 17.247±0.010h, with 28 rotations separating both images. This value, slightly longer than the Voyager 2 period, stands as the first\u0026nbsp;independent\u0026nbsp;measurement of the rotation period since 1986. It only assumes a similar emission region in the two images. The uncertainty, similar to that on the Voyager 2 estimate, demonstrates the value-added of Earth-based auroral observations for an independent period determination.\u003c/p\u003e\n\u003cp\u003eTo achieve a more precise period, we extended the temporal coverage and statistically analyzed the auroral images acquired from 2011 to 2022. To this end, we selected six reference images, one per HST observing campaign, displayed in Figure 1. The image processing is described in the Methods section. Whenever possible, we favoured observations where both the northern and southern auroral regions were simultaneously visible, which strongly constrain the orientation of the magnetic axis, as in 2017\u003csup\u003e12\u003c/sup\u003e and 2022. The aurorae were then individually fitted for each of the 6 references images with two families of model auroral ovals, defined by the footprints at 1100 km altitude of magnetic shells (M-shell)of 5 R\u003csub\u003eU\u0026nbsp;\u003c/sub\u003eand20 R\u003csub\u003eU\u003c/sub\u003e, using the Q\u003csub\u003e3\u003c/sub\u003e and AH\u003csub\u003e5\u003c/sub\u003e internal magnetic field models (see Methods and Figure S2 for details). Importantly, we chose to fit auroral emissions as observed in the HST field-of-view (rather than in cylindrical projections) in order not to exclude any high altitude emission from beyond the limb. The best-fit Q\u003csub\u003e3\u003c/sub\u003e (top) and AH\u003csub\u003e5\u003c/sub\u003e (bottom) northern (blue)\u0026nbsp;and southern (red) model auroral ovals are superimposed to the aurorae in Figure 1. Table 1 provides the IAU\u003csub\u003e17.24h\u003c/sub\u003e HST Central Meridian Longitude (CML) and the best-fit longitude (and uncertainty range) of the OTD northern magnetic pole at mid-exposure. The Q\u003csub\u003e3\u003c/sub\u003e ovals are more extended and less asymmetric than the AH\u003csub\u003e5\u003c/sub\u003e ones, so that the inferred longitude of the OTD magnetic poles is slightly less constrained. We then performed a χ\u003csup\u003e2\u003c/sup\u003e minimization analysis between (i) the observed best-fit longitude of the northern magnetic pole for each model oval and (ii) the longitude of the northern magnetic pole modeled for a set of rotation periods P\u003csub\u003ei\u003c/sub\u003e sampling the 17h-17.5h range. The computation of IAU longitudes for a given P\u003csub\u003ei\u003c/sub\u003e is described in the Methods section : for observations well separated in time, such as those dealt with here, it requires to account for the proper motion of Uranus along its orbit according to equations of celestial mechanics\u003csup\u003e2,14\u003c/sup\u003e. For each tested P\u003csub\u003ei\u003c/sub\u003e, we computed the χ\u003csup\u003e2\u0026nbsp;\u003c/sup\u003evalues for all possible longitudes of the northern magnetic pole (sampled with a 1° step) and retained the minimal value.\u0026nbsp;The final χ\u003csup\u003e2\u0026nbsp;\u003c/sup\u003ecurves displayed in Figure S3 minimize in both the AH\u003csub\u003e5\u003c/sub\u003e and Q\u003csub\u003e3\u003c/sub\u003e cases for very close\u0026nbsp;periods, only 5x10\u003csup\u003e-5\u003c/sup\u003eh apart. The inferred average period is 17.2478±0.0001h. This value, based on HST auroral observations alone analyzed through magnetic field models, definitely confirms a longer period than the Voyager 2 one, with an accuracy improved by two orders of magnitude.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis accuracy is mainly limited by the 11 year-long interval available. To achieve the most precise period possible, we repeated the\u0026nbsp;χ\u003csup\u003e2\u0026nbsp;\u003c/sup\u003eanalysis by combining the Voyager 2 reference with the HST dataset. Namely, the longitude of the magnetic poles was fixed at Voyager 2 CA (see Figure S4) and propagated to the HST observing times by varying the period only. The combination of HST and Voyager 2 observations thus suppresses one free parameter, the longitude of the magnetic poles, from the analysis. We neglected any possible secular motion of the magnetic axis from 1986 to 2022, a reasonable assumption considering that the axial dipole component of Jupiter’s magnetic field remained unchanged over a 43 years-long interval\u003csup\u003e15\u003c/sup\u003e. Figure 2\u0026nbsp;displays the obtained results. Compared to Figure S3, both χ\u003csup\u003e2\u0026nbsp;\u003c/sup\u003ecurves display narrower local minima, as expected for a better-constrained analysis. They again minimize\u0026nbsp;for nearby periods, within 5x10\u003csup\u003e-6\u003c/sup\u003eh. We retained the average period of 17.247864±0.000010h, more precise by another factor of 10. The corresponding longitude of the OTD northern (southern) magnetic pole lies at 357.1° (176.9°). We built up an associated IAU\u003csub\u003enew\u003c/sub\u003e SIII longitude model, which stands as a corrected version of the IAU\u003csub\u003e17.24h\u0026nbsp;\u003c/sub\u003eone. It can already be accessed by the community through the MIRIADE online ephemeris service of IMCCE (Institut de Mécanique Céleste et de Calcul des Ephémérides), with a query example provided in the Data Availability section.\u003c/p\u003e\n\u003cp\u003eAs a last step, we checked the validity of this updated period and IAU\u003csub\u003enew\u003c/sub\u003e longitude system over an extended set of auroral events captured by HST, as illustrated in Figure 3 with the Q\u003csub\u003e3\u003c/sub\u003e auroral model oval (see Figure S5 for the AH\u003csub\u003e5\u003c/sub\u003e one). For simplicity, an auroral event here refers to auroral emissions detected during a single HST orbit, so that two consecutive images of the same, rotating, emission region form a single auroral event. The predicted model auroral ovals match fairly well all the auroral events published previously\u003csup\u003e6,10-11\u003c/sup\u003e. The only exception concerns the HST tentative detection of faint auroral arcs on July 28\u003csup\u003eth\u003c/sup\u003e, 1998\u003csup\u003e10\u003c/sup\u003e, morphologically different from the other cases, which did not match the predicted position of the auroral ovals, so that this candidate can be discarded. Figure 3 also displays new unpublished auroral events, either unreported (Figure 3a shows the first auroral detection obtained with HST/ACS), or considered previously as too faint (Figures 3b-c,e) or obtained recently (Figures 3m-t). The HST 2022 campaign provided the largest number of auroral detections to date, with elongated emissions in both hemispheres, most intense/localized in the south, rotating with the planet. The detailed analysis of these new auroral signatures, which probe a magnetospheric configuration intermediate between equinox and solstice, is beyond the purpose of this paper.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eHST dataset\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe HST images displayed in Figure 1, 3, S1 and S5 (except for Figures 3a and S5a) correspond to STIS long exposures acquired either with the 25MAMA clear filter or the SrF2 one, using the time-tag mode and processed as described in past published studies\u003csup\u003e11\u003c/sup\u003e. The STIS images were calibrated through the Space Telescope Science Institute pipeline. A model planetary disc was adjusted to the solar reflected emission to retrieve accurate pixel coordinates in a physical frame (and fix any pointing error). They were corrected for any geocoronal contamination throughout the detector, by subtracting a uniform offset intensity derived on the sky, well beyond the disc. A background model of solar emissions reflected by the disc was then fitted to and subtracted from each individual image. We used two kinds of background model. When the number of images collected during a given HST campaign was large enough (as in 2011, 2012, 2020 and 2022), we used as an empirical model the median of the other images using the same filter, once rescaled at the same apparent size. This also accounts for atmospheric emissions extending beyond the limb. When the statistics of images was too low and/or intense extended auroral emissions could contaminate the median background (as in 2014 and 2017), we built up instead a numerical disc model from fitting the 2-D brightness distribution with a 1\u003csup\u003est\u003c/sup\u003e order Minnaert function\u003csup\u003e34\u003c/sup\u003e over 30\u0026deg; wide bands in latitude, complemented, outside the disc, by an exponentially decreasing brightness profile. In practice, an empirical model provides a more realistic but noisier estimate of the disc background. The background-subtracted images were then converted into kilo-Rayleighs of unabsorbed H\u003csub\u003e2\u003c/sub\u003e emission with standard conversion factors\u003csup\u003e35\u003c/sup\u003e and ultimately smoothed over a 5\u0026times;5 pixels averaging filter to increase the signal-to-noise ratio (SNR), while preserving spatial resolution. Figures 3a and S5a show an HST image obtained with another FUV spectro-imager, the Advanced Camera for Surveys (ACS), which was used here with the F125LP filter comparable to the 25MAMA one. This image of the first reported auroral detection with ACS so far (this instrument has been regularly used in 2005, 2011 and 2012), has been processed in exactly the same way with an empirical model of disc background. It is worth mentioning here that, as for the weak auroral detection obtained with STIS in 2012, the northern auroral signal observed by ACS was seen to rotate with the planet in the sub-exposures of this observation. HST processed observations of Uranus are also directly accessible through the APIS service\u003csup\u003e36\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eModel auroral ovals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe model auroral ovals employed in this study correspond to the footprints at 1100 km above the 1 bar level (where the electrons are assumed to trigger the aurorae) of magnetic field lines with M-shells = 5 R\u003csub\u003eU\u0026nbsp;\u003c/sub\u003eand20 R\u003csub\u003eU\u003c/sub\u003e. This altitude was transposed from the Saturn\u0026rsquo;s case whose atmospheric profile is comparable, under the assumption that Uranian auroral electrons are not more energetic\u003csup\u003e12\u003c/sup\u003e. The 5 R\u003csub\u003eU\u0026nbsp;\u003c/sub\u003eand20 R\u003csub\u003eU\u003c/sub\u003e magnetic shells were chosen as, respectively, a typical low-latitude edge of the UV aurorae observed by UVS\u003csup\u003e9\u003c/sup\u003e, and a typical standoff distance of the magnetopause\u003csup\u003e3\u003c/sup\u003e. The associated magnetic shells thus encompass most of the magnetosphere. Northern and southern model auroral ovals were derived for both the AH\u003csub\u003e5\u003c/sub\u003e internal field model\u0026ndash; as already done to fit the magnetic poles from the aurorae detected in 2012, 2014\u003csup\u003e12\u0026nbsp;\u003c/sup\u003eand 2017\u003csup\u003e6\u003c/sup\u003e \u0026ndash; and the Q\u003csub\u003e3\u003c/sub\u003e model for comparison purposes. We chose to limit ourselves to internal field models rather than magnetospheric ones\u003csup\u003e9,13\u003c/sup\u003e for simplicity. Deriving a more realistic magnetospheric model accounting for the compression of the magnetosphere by the solar wind would require to precisely know the solar wind parameters prevailing during the HST observations, which is beyond the current state of the art since the observations were scheduled on purpose during intervals encompassing strongly variable solar wind, whose parameters were additionally predicted with a \u0026plusmn;2 days uncertainty\u003csup\u003e11\u003c/sup\u003e. More importantly, using a magnetospheric model would not significantly change the low latitude boundary of model ovals as the M-shell = 5 R\u003csub\u003eU\u003c/sub\u003e is located in the inner magnetosphere shielded from the solar wind\u003csup\u003e9\u003c/sup\u003e. This is particularly striking for the fit of images where northern and southern aurorae were observed simultaneously, as for the 2017 and 2022 images in Figure 1.\u003c/p\u003e\n\u003cp\u003eWhile the auroral emissions were fitted with model auroral ovals defined from the multipolar Q\u003csub\u003e3\u003c/sub\u003e and AH\u003csub\u003e5\u003c/sub\u003e internal field models, the observable used in our analysis is the longitude of the magnetic poles defined for the Offset/Tilted Dipole (OTD) model. The link between model ovals and the longitude of the OTD magnetic poles is illustrated in Figure S4, which shows Uranus as seen from from Voyager 2 at CA. The AH\u003csub\u003e5\u003c/sub\u003e (left-hand side) and Q\u003csub\u003e3\u003c/sub\u003e (right-hand side) southern model ovals are displayed by pairs of solid lines. While they slightly differ from each other, they both correspond to the same OTD southern magnetic pole which lies at the intersection of the red dotted-dashed meridian (longitude) and the red dashed parallel (latitude).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuroral fitting and\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u0026chi;\u003csup\u003e2\u003c/sup\u003e analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTable 1 provides the IAU\u003csub\u003e17.24h\u003c/sub\u003e longitude of the OTD northern magnetic pole (which can be deduced from the southern one whenever not observed) for the six chosen reference HST images displayed in Figure 1. This longitude was obtained from the best-fit of the Q\u003csub\u003e3\u003c/sub\u003e and AH\u003csub\u003e5\u003c/sub\u003e model ovals and accompanied by an error bar (within parenthesis) obtained from the most extreme fits of the same ovals. Figure S2 illustrates this fitting procedure with the example of Q\u003csub\u003e3\u003c/sub\u003e model ovals applied to two representative images, one poorly constrained in 2011 and one strong constrained in 2022. Indeed, the former restricts to a single, localized, northern auroral spot, while the latter displayed elongated auroral emissions observed simultaneously in both hemispheres well beyond the limb. The uncertainty on the longitude of the best-fit ovals is +15\u0026deg;/-21\u0026deg; and \u0026plusmn;12\u0026deg;, respectively\u003c/p\u003e\n\u003cp\u003eUnlike a simple least-square fit, the calculation of the\u0026nbsp;\u0026chi;\u003csup\u003e2\u003c/sup\u003e data-model test described in the main text is weighted by the error on data points. Instead of the simple error bars (sometimes asymmetric) provided above, we used their quadratic sum as a typical, more realistic, uncertainty on the best-fit longitudes. Applied to the two examples of Figure S2, this corresponds to error bars of\u0026nbsp;\u0026plusmn;26\u0026deg; and\u0026nbsp;\u0026plusmn;17\u0026deg;, respectively, wider by a few degrees than the initial estimate but hence more robust. The modeled longitudes were obtained as detailed below.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSIII longitudes\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAs outlined in the introduction, in the ULS spin-aligned coordinate system used during the Voyager 2 epoch, the rotation axis points toward the north pole. Latitudes are counted positively toward the same direction, so that the\u0026nbsp;northern and southern OTD magnetic poles lie at positive (+15.2\u0026deg;) and negative (-44.2\u0026deg;) latitude, respectively. The Uranus rotation is prograde and longitudes are counted positively westward, so that the CML of a fixed observer increases with time. This longitude system was arbitrarily referenced at CML = 302\u0026deg; at the Voyager 2 CA.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe System III coordinate system referenced by IAU uses different conventions. The north pole is here defined as pointing northward to the ecliptic plane, so that IAU latitudes are opposite to ULS ones and the Uranus rotation is retrograde. IAU planetocentric longitudes are counted positively eastward, whatever the sense of planetary rotation, so that the CML of a fixed Uranus observer increases with time. IAU planetographic longitudes use another convention for historical reasons, and are defined as increasing with time whatever the sense of rotation. In the case of Uranus, both uranocentric and uranographic longitudes thus coincide.\u003c/p\u003e\n\u003cp\u003eThe IAU sub-observer planetocentric latitude \u0026delta; and longitude \u0026omega; are provided by the following set of equations\u003csup\u003e14\u003c/sup\u003e :\u003c/p\u003e\n\u003col style=\"list-style-type: lower-alpha;\"\u003e\n \u003cli\u003esin \u0026delta; = - sin \u0026delta;\u003csub\u003e0\u003c/sub\u003e sin \u0026delta;\u003csub\u003eP\u0026nbsp;\u003c/sub\u003e- cos \u0026delta;\u003csub\u003e0\u003c/sub\u003e cos \u0026delta;\u003csub\u003eP\u0026nbsp;\u003c/sub\u003ecos(\u0026alpha;\u003csub\u003eP\u003c/sub\u003e - \u0026alpha;\u003csub\u003e0\u003c/sub\u003e)\u003c/li\u003e\n \u003cli\u003ecos (W-\u0026omega;) cos \u0026delta; = - sin \u0026delta;\u003csub\u003e0\u003c/sub\u003e sin \u0026delta;\u003csub\u003eP\u0026nbsp;\u003c/sub\u003e- cos \u0026delta;\u003csub\u003e0\u003c/sub\u003e cos \u0026delta;\u003csub\u003eP\u0026nbsp;\u003c/sub\u003esin(\u0026alpha;\u003csub\u003eP\u003c/sub\u003e - \u0026alpha;\u003csub\u003e0\u003c/sub\u003e)\u003c/li\u003e\n \u003cli\u003esin (W-\u0026omega;) cos \u0026delta; = - cos \u0026delta;\u003csub\u003e0\u003c/sub\u003e sin \u0026delta;\u003csub\u003eP\u0026nbsp;\u003c/sub\u003e+ sin \u0026delta;\u003csub\u003e0\u003c/sub\u003e cos \u0026delta;\u003csub\u003eP\u0026nbsp;\u003c/sub\u003ecos(\u0026alpha;\u003csub\u003eP\u003c/sub\u003e - \u0026alpha;\u003csub\u003e0\u003c/sub\u003e)\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003ewhere (\u0026alpha;\u003csub\u003eP\u003c/sub\u003e,\u0026delta;\u003csub\u003eP\u003c/sub\u003e) are the equatorial apparent coordinates of Uranus center of mass, (\u0026alpha;\u003csub\u003e0\u003c/sub\u003e,\u0026delta;\u003csub\u003e0\u003c/sub\u003e) those of the north pole direction and W is the angle defining the position of the prime meridian in the Uranus equatorial plane according to the equation :\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;W = W\u003csub\u003e0\u003c/sub\u003e + W\u003csub\u003e1\u003c/sub\u003ed\u003c/p\u003e\n\u003cp\u003ewhere W\u003csub\u003e0\u0026nbsp;\u003c/sub\u003eis the position of the prime\u0026nbsp;meridian referenced to the intersection by the equatorial plane and the celestial equator at the J2000 epoch (JD 2451545.0 = 2000 January 1 12.0 h TDB), W1 is the SIII rotation period in degrees per day and d is the time interval between the observing time and the J2000 epoch. The numerical values of\u0026nbsp;(\u0026alpha;\u003csub\u003e0\u003c/sub\u003e,\u0026delta;\u003csub\u003e0\u003c/sub\u003e), W\u003csub\u003e0\u003c/sub\u003e and W\u003csub\u003e1\u003c/sub\u003e were chosen from the latest\u0026nbsp;\u003cem\u003ereport of the IAU working Group on cartographic coordinates and rotational elements\u003c/em\u003e\u003csup\u003e2\u0026nbsp;\u003c/sup\u003e(see their Figure 1 for a visual representation of these angles) and those of (\u0026alpha;\u003csub\u003eP\u003c/sub\u003e,\u0026delta;\u003csub\u003eP\u003c/sub\u003e) were obtained at mid-exposure for each observation from the\u0026nbsp;IMCCE/MIRIADE ephemeris service.\u003c/p\u003e\n\u003cp\u003eAnimation S6 illustrates that the proper motion of Uranus along its orbit is non negligible near solstice periods and/or for long enough intervals. It displays the position of the prime meridian and the planetary configuration as seen from Earth as a function of time for a non-rotating Uranus (W1 = 0).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFor our purpose, we first checked that we retrieved IAU longitudes from the above set of equations consistent with those provided by IMCCE/MIRIADE (planetocentric longitudes by default) and by the JPL Horizons ephemeris (planetographic longitudes by default). We then computed model SIII longitudes by varying W\u003csub\u003e1\u003c/sub\u003e, that is the rotation period.\u003c/p\u003e\n\u003cp\u003eThe IMCCE/MIRIADE online ephemeris service can already be used with the new\u0026nbsp;17.247864h\u0026nbsp;rotation period obtained in this article to in turn provide IAU\u003csub\u003enew\u003c/sub\u003e corrected longitudes. The new CML at mid-exposure associated with the images displayed in Figure 3 are listed in Table 2.\u0026nbsp;\u003c/p\u003e"},{"header":"Discussion and implications","content":"\u003cp\u003eThe new rotation period of Uranus, 17.247864\u0026plusmn;0.000010h or 17h14m52.310s\u0026plusmn;0.036s, stands as the most precise determination of the inner rotation rate of a giant planet to date, comparable with the\u0026nbsp;rotation\u0026nbsp;period of Jupiter\u003csup\u003e2\u003c/sup\u003e determined from decades of ground-based observations of its decametric emissions and whose time variability has recently been questioned\u003csup\u003e16\u003c/sup\u003e. The developed method, based on the long-term tracking of the magnetic poles through imaging of the (ultraviolet) aurorae, can straightforwardly be re-applied to other giant planets whose auroral emissions have been imaged over a sufficiently long interval.\u003c/p\u003e\n\u003cp\u003eThe new period is 28s longer than the one derived in 1986 from Voyager 2 data alone. This difference is significant and the correct value can first of all be used to refine the existing models of internal magnetic field\u003csup\u003e7,9\u003c/sup\u003e. It also has strong implications to constrain the internal structure of Uranus, its evolution, dynamo theories and formation scenarios\u003csup\u003e17,18\u003c/sup\u003e. For instance, the shorter period of\u0026nbsp;16.58h (16h34m) derived in 2010 from the profile of atmospheric winds and proposed to probe the inner rotation rate\u003csup\u003e19\u003c/sup\u003e is largely inconsistent with the updated rotation period of the magnetic field.\u003c/p\u003e\n\u003cp\u003eThe IAU\u003csub\u003enew\u003c/sub\u003e longitude model is also much more precise. Reaching a \u0026plusmn;10\u0026deg; uncertainty on longitudes now requires a century. Such a model therefore has immediate applications, both for re-analyzing past observations and for scheduling future ones.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePast observations primarily include Voyager 2 \u003cem\u003ein situ\u003c/em\u003e measurements in the magnetosphere together with Earth-based long-term observations tracking auroral emissions at optical, radio\u003csup\u003e20\u003c/sup\u003e or X-rays\u003csup\u003e21\u003c/sup\u003e wavelengths. In the UV range, this concerns the International Ultraviolet Explorer monitoring of variable H-Ly\u0026alpha; emission over 1978-1993 and attributed to variable auroral activity\u003csup\u003e22\u003c/sup\u003e or HST observations other than those dealt with in this study, such as those involved in the study of the Uranus hydrogen corona\u003csup\u003e23\u003c/sup\u003e. In the IR domain, long-term observations of variable and inhomogeneous H\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e+\u0026nbsp;\u003c/sup\u003eemission have regularly been tentatively attributed to an auroral driver\u003csup\u003e24-25\u003c/sup\u003e, and a Keck/NIRSPEC observation on 5\u003csup\u003eth\u003c/sup\u003e Sept. 2006 was recently presented as an unambiguous northern auroral detection\u003csup\u003e26\u003c/sup\u003e. In the latter case however, the\u0026nbsp;IAU\u003csub\u003enew\u003c/sub\u003e longitude model\u0026nbsp;predicts that the northern auroral region was not visible during the observation, so that this detection can also be discarded.\u003c/p\u003e\n\u003cp\u003eThe knowledge of the orientation of the magnetic axis is mandatory to unambiguously track any auroral footprint associated with the Uranian moons\u003csup\u003e27\u003c/sup\u003e and to perform realistic numerical modeling of the magnetosphere (magnetic reconnection conditions, global MHD models) to be compared to observational constraints\u003csup\u003e28-31\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eLast and not least, this new SIII model will be an essential tool for the Uranus flagship mission currently in preparation, either for the definition of any orbital tour and/or for choosing an atmospheric entry site\u003csup\u003e32,33\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank Claus Leitherer for HST director\u0026rsquo;s time allocated in 2020 and Alison Sherwin as our program coordinator. The French authors thank the CNES spatial agency and CNRS/INSU national programs of heliophysics (PNST, also funded by CEA) and planetology (PNP).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis article is based on observations acquired with the Hubble Space Telescope, operated by NASA and ESA, through the observing programs GO #12601, 13012, 14036, 16313 and DDT #15380. The data can be accessed through the STSci MAST archive at https://archive.stsci.edu/missions-and-data/hst and the processed data through the CNRS/INSU APIS observation service operated by PADC/LESIA at https://apis.obspm.fr.\u003c/p\u003e\n\u003cp\u003eThe CNRS/INSU MIRIADE ephemeris service, operated by IMCCE/Obs. Paris, is accessible at https://ssp.imcce.fr/webservices/miriade/ The data can be queried through a web interface or url queries. An example of url query using the new rotation period to obtain IAU\u003csub\u003enew\u003c/sub\u003e SIII longitudes is provided below :\u003c/p\u003e\n\u003cp\u003ehttps://ssp.imcce.fr/webservices/miriade/api/ephemph.php?-name=p:Uranus\u0026amp;-type=planet\u0026amp;-ep=2000-01-01T12:00:00\u0026amp;-nbd=2\u0026amp;-step=1h\u0026amp;-observer=@500\u0026amp;-so=3\u0026amp;-pop=P=-17.247864;model=newSIII\u0026amp;-mime=text\u0026amp;-output=--coord(eq2000)\u003c/p\u003e\n\u003cp\u003ewhere the option -pop=P=-17.247864 defines the period in hours and the sign \u0026ndash; the retrograde rotation of the planet.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLL led and processed the HST observations, conducted their analysis and wrote the manuscript. RP contributed to the data analysis, to the physical interpretation and to the writing of the manuscript. JB helped with the analytical determination of planetocentric ephemeris and developed a new module on the IMCCE/MIRIADE online service which enables the user to choose the planetary parameters. CT and TK performed MHD simulations of the solar wind which were used to schedule the observations and counter-checked the derived longitudes. All the authors read and commented the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interest.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDesch MD, Connerney JEP, Kaiser ML (1986) The rotation period of Uranus. Nature 322:42\u0026ndash;43\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArchinal BA et al (2018) Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015. Celest Mech Dyn Astr 130:22\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNess NF et al (1986) Magn fields Uranus Sci 233:85\u0026ndash;87\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWarwick JW et al (1986) Voyager 2 radio observations of Uranus. Science 233:74\u0026ndash;79\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBroadfoot AL et al (1986) Ultraviolet spectrometer observations of Uranus. Science 233:102\u0026ndash;106\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLamy L (2020) Auroral emissions from Uranus and Neptune. Phil Trans R Soc A 378:20190481\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eConnerney JEP, Acuna MH (1987) The magnetic field of Uranus. J Geophys Res 92:15329\u0026ndash;15336\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHerbert F, Sandel BR (1994) The Uranian aurora and its relationship to the magnetosphere. 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Phil Trans R Soc A 377:20180408\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThomas EM et al (2023) Detection of the infrared aurora at Uranus with Keck-NIRSPEC. Nat Astron. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41550-023-02096-5\u003c/span\u003e\u003cspan address=\"10.1038/s41550-023-02096-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLouis CK et al (2022) Predictions for Uranus-moons radio emissions and comparison with Voyager 2/PRA observations. Planet. Radio Em IX. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.25546/103106\u003c/span\u003e\u003cspan address=\"10.25546/103106\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMasters A (2014) Magnetic reconnection at Uranus\u0026rsquo; magnetopause. J Geophys Res : Sp Phys 115:5520\u0026ndash;5538\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCao X, Paty C (2017) Diurnal and seasonal variability of Uranus\u0026rsquo; magnetosphere. J Geophys Res : Sp Phys 122:6318\u0026ndash;6331\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGriton L, Pantellini F, Meliani Z (2018) Three-dimensional MHD simulations of the solar wind interaction with a hyperfact-rotating Uranus. J Geophys Res : Sp Phys 123:2018JA025331\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePantellini F (2020) A physical model for the magnetosphere of Uranus at solstice time. Astron Astrophys 643:A144\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArridge CS et al (2023) The science case for an orbital mission to Uranus: Exploring the origins and evolution of ice giant planets. Planet Sp Sci 104:122\u0026ndash;140\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOrigins (2023) Worlds, and Life, A Decadal Strategy for Planetary Science and Astrobiology 2023\u0026ndash;2032. NASA\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVincent MB et al (2000) Mapping Jupiter\u0026rsquo;s latitudinal bands and great red spot using HST/WFPC2 far-ultraviolet imaging. Icarus 143:189\u0026ndash;204\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGustin J, Bonfond B, Grodent D, G\u0026eacute;rard J-C (2012) Conversion from HST ACS and STIS auroral counts into brightness, precipitated power, and radiated power for H2 giant planets. J Geophys Res 117:A07316\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLamy L, Prang\u0026eacute; R, Henry F, Le Sidaner P (2015) The Auroral Planetary Imaging and Spectroscopy (APIS) service. Astron Comput 11:138\u0026ndash;145\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1 : Characteristics of the HST/STIS images of the aurorae displayed in Fig. 1. Longitudes are derived at mid-exposure.\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"595\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eObserving date (UT)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eDataset\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;(Filter)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eExposure time (s)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eVisible aurorae\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eIAU\u003csub\u003e17.24h\u003c/sub\u003e CML (\u0026deg;)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eIAU\u003csub\u003e17.24h\u003c/sub\u003e AH\u003csub\u003e5\u003c/sub\u003e N mag. lon. (\u0026deg;)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eIAU\u003csub\u003e17.24h\u003c/sub\u003e Q3 N mag. pole \u0026nbsp;lon. (\u0026deg;)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e2011-11-29 02:09:24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003eobrx18hbq\u003c/p\u003e\n \u003cp\u003e(25MAMA)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e319.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e276\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(267-303)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e282\u003c/p\u003e\n \u003cp\u003e(267-303)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e2012-09-27 15:00:19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003eobz501dgq\u003c/p\u003e\n \u003cp\u003e(25MAMA)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e1250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e162.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e336\u003c/p\u003e\n \u003cp\u003e(323-353)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e336\u003c/p\u003e\n \u003cp\u003e(322-360)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e2014-11-24 09:03:59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003eocpl07cmq\u003c/p\u003e\n \u003cp\u003e(F25SRF2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e31.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e148\u003c/p\u003e\n \u003cp\u003e(140-171)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e147\u003c/p\u003e\n \u003cp\u003e(139-182)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e2017-09-30 07:00:30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003eodq402yzq\u003c/p\u003e\n \u003cp\u003e(25MAMA)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e2518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e65.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003cp\u003e(31-61)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e41\u003c/p\u003e\n \u003cp\u003e(34-62)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e2020-10-09 22:29:47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003eoea005ghq\u003c/p\u003e\n \u003cp\u003e(25MAMA)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e2515\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e134.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e292\u003c/p\u003e\n \u003cp\u003e(270-304)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e293\u003c/p\u003e\n \u003cp\u003e(270-315)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.926174496644295%\" valign=\"top\"\u003e\n \u003cp\u003e2022-10-10 11:05:35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.422818791946309%\" valign=\"top\"\u003e\n \u003cp\u003eoewy05coq\u003c/p\u003e\n \u003cp\u003e(25MAMA)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.577181208053691%\" valign=\"top\"\u003e\n \u003cp\u003e2277\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.06711409395973%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.570469798657719%\" valign=\"top\"\u003e\n \u003cp\u003e127.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.798657718120804%\" valign=\"top\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003cp\u003e(86-108)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.63758389261745%\" valign=\"top\"\u003e\n \u003cp\u003e98\u003c/p\u003e\n \u003cp\u003e(86-110)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 2 : Characteristics of the HST STIS and ACS images of the aurorae displayed in Figures 3 and S5. The CML is computed at mid-exposure.\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"586\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eObserving date (UT)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eDataset\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eFilter\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eExp. (s)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eVisible aurorae\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eIAU\u003csub\u003enew\u003c/sub\u003e \u003csub\u003e\u0026nbsp;\u003c/sub\u003eCML\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e(\u0026deg;)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2005-08-10 00:32:04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003ej9eq01011\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003eF115LP\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e306.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2011-11-13 07:41:13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eobrx06j5q\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e66.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2011-11-14 12:25:52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eobrx08dqq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e306.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2011-11-16 15:32:10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eobrx10p0q\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e293.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2011-11-19 05:49:24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eobrx12ceq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e153.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2011-11-29 02:09:24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eobrx18hbq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e45.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2012-09-27 15:00:19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eobz501dgq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e179.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2014-11-01 23:57:32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eocpl02nzq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1231\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e179.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2014-11-24 09:03:59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eocpl07cmq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003eF25SRF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e228.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2017-09-29 15:06:52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eodq401vwq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth + South\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e52.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2017-09-30 07:00:30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eodq402yzq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth + South\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e24.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2017-10-21 00:28:58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eodq403c4q\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2533\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eNorth\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e327.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2017-11-11 08:14:00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eodq404m2q\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2563\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e208.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2020-10-09 22:29:47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eoea005ghq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2515\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e200.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2022-09-06 04:56:10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eoewy01geq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2034\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e144.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2022-10-08 17:50:36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eoewy04icq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e2218\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e245.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25.34246575342466%\" valign=\"top\"\u003e\n \u003cp\u003e2022-10-10 11:05:35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.726027397260275%\" valign=\"top\"\u003e\n \u003cp\u003eoewy05coq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n 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valign=\"top\"\u003e\n \u003cp\u003eoewy11ssq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.842465753424657%\" valign=\"top\"\u003e\n \u003cp\u003e25MAMA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.931506849315069%\" valign=\"top\"\u003e\n \u003cp\u003e1445\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.80821917808219%\" valign=\"top\"\u003e\n \u003cp\u003eSouth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.34931506849315%\" valign=\"top\"\u003e\n \u003cp\u003e171.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3876131/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3876131/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eIn the absence of any visible solid surface, the rotation period of the giant planets has been inferred from periodic phenomena tied to the magnetic field produced in their deep interior. The main method relied on remote radio auroral observations, sometimes complemented by \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ein situ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e magnetic measurements. For Uranus, such measurements acquired during the Voyager 2 flyby in 1986 yielded a rotation period of 17.24±0.01h\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e. This fundamental planetary parameter, referenced since then by the International Astronomical Union, is the basis of the Uranian longitude model\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e. Still, the period uncertainty limits its validity to a few years, after which the orientation of the magnetic axis was lost. Here, we use a novel approach, based on the long term (2011-2022) tracking of Uranus’ magnetic poles from Hubble Space Telescope images of its ultraviolet aurorae, to achieve a new rotation period of 17.247864±0.000010h. It is consistent with, although 28s longer than, the Voyager 2 period. This much more precise determination leads to a new longitude model now valid over decades, from before the Voyager 2 epoch up to the arrival of any future Uranus mission. It also has strong direct implications on formation scenarios, interior models, dynamo theories and studies of the magnetosphere. This novel approach stands as an alternate method to determine the rotation rate of any object hosting a magnetosphere and rotationally modulated aurorae, in our solar system and beyond.\u003c/strong\u003e\u003c/p\u003e","manuscriptTitle":"A new rotation period and longitude system for Uranus","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-04 19:23:31","doi":"10.21203/rs.3.rs-3876131/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-astronomy","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"natastron","sideBox":"Learn more about [Nature Astronomy](http://www.nature.com/natastron/)","snPcode":"","submissionUrl":"","title":"Nature Astronomy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Research","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"9ba0f230-2c44-4f72-9e9f-bf8cbae97d73","owner":[],"postedDate":"April 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":28709286,"name":"Physical sciences/Astronomy and planetary science/Planetary science/Giant planets"},{"id":28709287,"name":"Physical sciences/Astronomy and planetary science/Space physics/Aurora"},{"id":28709288,"name":"Physical sciences/Astronomy and planetary science/Space physics/Magnetospheric physics"},{"id":28709289,"name":"Physical sciences/Astronomy and planetary science/Space physics/Astronomical instrumentation"}],"tags":[],"updatedAt":"2025-04-08T07:06:40+00:00","versionOfRecord":{"articleIdentity":"rs-3876131","link":"https://doi.org/10.1038/s41550-025-02492-z","journal":{"identity":"nature-astronomy","isVorOnly":false,"title":"Nature Astronomy"},"publishedOn":"2025-04-07 04:00:00","publishedOnDateReadable":"April 7th, 2025"},"versionCreatedAt":"2024-04-04 19:23:31","video":"","vorDoi":"10.1038/s41550-025-02492-z","vorDoiUrl":"https://doi.org/10.1038/s41550-025-02492-z","workflowStages":[]},"version":"v1","identity":"rs-3876131","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3876131","identity":"rs-3876131","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}