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The five largest satellites of Uranus: astrometric observations spread
over 29 years at the Pico dos Dias Observatory
Camargo, J.I.B.1,2, Veiga, C.H.1, Vieira-Martins, R.1,2, Fienga, A.3,4, Assafin, M.5,2
1Observat´
orio Nacional/MCTI, R. General Jos´
e Cristino 77, CEP 20921-400 Rio de Janeiro, RJ, Brazil
2Laborat´
orio Interinstitucional de e-Astronomia - LIneA, Rua Gal. Jos ´
e Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil
3G´
eoazur-CNRS 7329, Observatoire de la Cˆ
ote d’Azur, Valbonne, France
4IMCCE-CNRS 8028, Observatoire de Paris, Paris, France
5Observat´
orio do Valongo/UFRJ, Ladeira do Pedro Antˆ
onio 43, CEP 20080-090 Rio de Janeiro, RJ, Brazil
Received:; Accepted:
Abstract
We present the astrometry of the five largest satellites of Uranus from observations spread over almost three decades
with photographic plates and CCDs (mainly), taken at the Pico dos Dias Observatory - Brazil. All positions presented here
are obtained from the reanalysis of measurements and images used in previous publications. Reference stars are those
from the Gaia Early Data Release 3 (Gaia EDR3) allowing, in addition to a higher accuracy, a larger number of positions of
the largest satellites as compared to our previous works. From 1982 to 1987, positions were obtained from photographic
plates. From 1989 to 2011, CCDs were used. On average, we obtained ∆αcosδ=−11 (±52) milli-arcseconds and
∆δ=−14 (±43) milli-arcseconds for the differences in the sense observation minus ephemerides (DE435+ura111).
Comparisons with different ephemerides (DE440, INPOP21a, INPOP19a and NOE-7-2013-MAIN) and results from
stellar occultations indicate a possible offset in the (Solar System) barycentric position of the Uranian system barycenter.
Overall, our results are useful to improve dynamical models of the Uranian largest satellites as well as the orbit of Uranus.
Keywords— Astrometry – Catalogs – Ephemerides
1 Introduction
Seventh planet from the Sun, the ice giant Uranus was discovered by accident by Sir William Herschel (1738-1822) in 1781 (Irwin
2009). Few years later, in 1787, Herschel himself discovered Uranus’ two largest moons: Titania and Oberon. Ariel and Umbriel
were discovered later, in 1851, by William Lassell. Miranda, completing the five largest satellites of Uranus, was discovered almost a
century later, in 1948, by Gerard Kuiper (Hall 2016). Table 1 presents relevant information about the main satellites and a review of
the dynamics of the Uranian system, as well as its observations, can be seen in Emelyanov & Nikonchuk (2013) and Jacobson (2014).
Astrometry of these satellites are relevant mainly to improve their dynamical models (see, for instance, Laskar & Jacobson 1987;
Lainey 2016) as well as the orbit of Uranus itself (Fienga et al. 2013, 2021, - INPOP10e and INPOP21a respectively). It should be
arXiv:2112.02167v1 [astro-ph.EP] 3 Dec 2021
clarified here, in addition, the context of the works by Emelyanov & Nikonchuk (2013) and Laskar & Jacobson (1987). The first
presents an example of ephemeris built on the basis of observations spread over a time interval of 220 years and reaching dates close to
those of the discovery of the satellites. The latter was based on a general analytical theory (GUST - General Uranus Satellite Theory,
Laskar 1986), fitted to Earth-based observations acquired from 1911 to 1986 and to optical navigation and radio data from Voyager.
Positions of these satellites may also be improved from mutual events (e.g. Hidas et al. 2008; Assafin et al. 2009; Arlot et al. 2013)
and stellar occultations (e.g. Widemann et al. 2009). In addition, with this latter technique, sizes/shapes can be determined and the
presence of rings, atmospheres and even topographic features can be detected and studied (see, for instance, Sicardy et al. 2011; Ortiz
et al. 2012; Braga-Ribas et al. 2013, 2014; Gomes-J´
unior et al. 2015; Dias-Oliveira et al. 2015; Sicardy et al. 2016; Dias-Oliveira et al.
2017; Ortiz et al. 2017, for some examples involving different objects). Whatever the case, accurate astrometry of Solar System objects
is needed.
This paper presents an homogeneous analysis to translate plate/CCD coordinates into celestial equatorial coordinates from an
observational data set explored by Veiga et al. (2003) and Camargo et al. (2015) (C15 hereafter). This data set (plate/CCD measurements
and images, see details later in the text) represents the observational history of our team from 1982 to 2011 associated to the astrometry
of the main satellites of Uranus (exception made to the observations of mutual phenomena). The main improvements over our previous
publications are: a larger number of positions of the main Uranian satellites; use of Gaia EDR3 as reference for astrometry (therefore,
a larger number of reference stars and virtually no systematics due to the reference catalogue); same procedures to translate plate/CCD
coordinates into celestial equatorial coordinates in the ICRF (International Celestial Reference Frame, Ma et al. 1998). In brief, more
than two decades of observations of the Uranus’ main satellites treated in a homogeneous way, providing accurate astrometry along
with a better and more complete use of our observational data set thanks to Gaia EDR3. The coronographed images used in C15 were
completely remeasured.
In Sect. 2, we briefly present the data and the instruments from which they were obtained. Methods and a brief discussion on lower
accuracy limits to the determination of centroids are presented in Sect. 3 and the data analysis, in Sect. 4. Conclusions and comments
are then provided in Sect. 5.
2 Observations and data
All observations used in this paper were made at the Pico dos Dias Observatory (IAU code: 874, run by the Laborat´
orio Nacional de
Astrof´
ısica/MCTI1), using photographic plates (MAY/1982 to JUL/1987) and CCDs (SEP/1989 to OCT/2011) and involving telescopes
of apertures 1.6m (Perkin-Elmer - photographic plates, CCDs) and 0.6m (Boller&Chivens or Zeiss - CCDs only). A brief description
of the photographic plates (Table 2) as well as the distribution of observations per night (Fig. 1) are given below. Further details about
the instruments can be found in Veiga et al. (1987), Veiga et al. (2003) and C15.
3 Methods and precision limits
As previously indicated, this paper brings no observations other than those belonging to the observational history of Veiga et al. (2003)
and C15. Data from the first paper were made available to this work from tables with (x,y) plate/CCD coordinates, mid-time of the
observation, astrometric ICRF equatorial coordinates associated to the (x,y) coordinates as well as an identification of the type of object
in each of them (field star, Ariel, Miranda, Oberon, Titania, Umbriel and Uranus). Those equatorial coordinates are a first step to the
determination of plate or CCD constants. Data from the second paper were obtained directly from images that were submitted to a
1https://www.gov.br/mcti/pt-br/rede- mcti/lna
Table 1: Columns: satellite ID; orbital inclination; semi-major axis; satellite size; sidereal orbit period; calculated magni-
tude. a,iand Twere obtained from the JPL HORIZONS Web-Interface, using as reference epoch J2000 TDB, the Uranus
equator and node of date as reference plane, and Uranus as the central body. Magnitudes were also obtained from the
JPL HORIZONS Web-Interface. Mean radii were obtained from the JPL’s Planetary Satellite Physical Parameters. The
reference mentioned therein for them is Archinal et al. (2018). Ephemeris source: ura111.
Satellite i a Mean radius TMag.
(deg.) (km) (km) (days) (V)
Miranda 175.6 129 871.8 235.8 1.414 16.7
Ariel 180.0 190 941.3 578.9 2.521 14.5
Umbriel 180.0 266 012.3 584.7 4.145 15.2
Titania 179.9 436 294.5 788.9 8.706 14.1
Oberon 179.8 583 551.9 761.4 13.468 14.3
Table 2: Characteristics of the photographic plates as provided by Veiga et al. (1987).
Manufacturer Emulsion Size
(cm)
Kodak IIIaJ 12 ×10
Kodak IIaO 12 ×10
Kodak IIaD 12 ×10
Kodak 103aO 12 ×10
Figure 1: Number of observations per night. This figure takes into consideration all runs, irrespective of the quality of the
data and its presence in the final catalogue.
0
200
400
600
800
1000
1200
1400
1600
1800
1980 1985 1990 1995 2000 2005 2010
Number of Observations per Year
Year
process of digital coronagraphy (see Assafin et al. 2008, C15). Those coronagraphed images were completely re-reduced with the
PRAIA astrometric package (Assafin et al. 2011).
In all cases, positions from the Gaia EDR3 (Gaia Early Data Release 3, Lindegren et al. 2021) were used as reference for astrometry.
The relationship between CCD and gnomonic coordinates were obtained through a first degree polynomial and no Gaia EDR3 star
fainter than G=16.5 was used. With this, we avoided using low SNR stars as astrometric references.
CCD observations from Veiga et al. (2003) and C15 have an overlap. Whenever it happened, only the results obtained from the
image re-reduction were kept. Table 3 shows the time intervals in which each set of data was taken.
Subroutines from the SPICE toolkit (Acton 1996; Acton et al. 2018), Standards of Fundamental Astronomy2(SOFA) and Naval
Observatory Vector Astrometry Software3(NOVAS) were used to determine topocentric positions of the satellites and/or to determine
geocentric positions, proper motion corrected, reference (Gaia EDR3) stars.
3.1 Position filtering
This paper adopts a simpler filtering method as compared to the procedure presented by C15: an iterative 3σfilter was applied to
each satellite in each night it was observed; then, a second iterative 3σfilter was applied to all observations of each satellite. This
was done separately to plate and CCD observations, given the larger standard deviation in the measurements of the former. One of
the consequences from this simpler filtering method, thanks to the use of Gaia EDR3 as astrometric reference, was a more efficient
exploration of our observational data set and the determination of a larger and more accurate number of CCD positions as compared to
Veiga et al. (2003) and C15.
One relevant point is the angular distance, projected on to plane of the sky, between Uranus and each satellite. We performed no
selection based on it and a discussion is presented later in the text. Our catalogue with positions of the satellites also contains those
angular distances along the RA and DEC axes. However, we eliminated by hand from our catalogues 3 positions of Miranda and 1
position of Ariel that were obtained from spurious detections.
3.2 Position precision
One interesting verification here is an estimation of the best positional precision we can obtain from the observational data. For this,
we will accept the existence of a function (Φ), in the sense of equations (8, 17, 21) in King (1983), as a good representation of the
flux distribution of the object over the CCD. This is reasonable since the Point Spread Function (PSF) is mostly dominated by the
atmosphere and pixel scale is a fraction (10%-25%) of the seeing.
Now, two extreme cases are considered: (i) precision derived from signal dominated signal-to-noise ratios (σbright ) and (ii) precision
derived from sky dominated signal-to-noise ratios. (σfaint).
Expressions for these two cases, when a circular Gaussian is chosen to describe the PSF (model used in this work), can be given by
equations Eqs. 1 and 2 (Mighell (2005), see also King (1983))
σbright =σPSF
√c(1)
and
σfaint =2√2π·B·σ2
PSF
c(2)
, where σPSF is the standard deviation of the gaussian distribution, cis the number of electrons due to the source and Bis the number of
2http://www.iausofa.org
3http://aa.usno.navy.mil/software/novas/novas_info.php
Figure 2: The main satellites of Uranus in an image that went through a digital coronography procedure (see Assafin et al.
2008). North is up, east is left. Image obtained on the night 18-19/JUL/1992 at the Pico dos Dias Observatory with its
1.6m telescope.
electrons due to the sky. It should be emphasized that Eqs. 1 and 2 provide, therefore, the best precision for the object’s centroid along
the CCD’s x-axis (and, by symmetry, along the y-axis) in the context of cases (i) and (ii), respectively.
We adopt, from Mighell (2005), the following expression to determine the lower limit of the centroid uncertainty from a PSF fitting:
σx,y=qσ2
bright +σ2
faint (3)
We used images of Ariel and Oberon taken with the 1.6m telescope on 19/JUL/1992 and determined lower limits for their precisions,
from Eqs. 1 to 3, of 5 mas (most frequent value) for Oberon and of 9 mas (most frequent value) for Ariel (see Fig. 2). From the
differences with the ephemerides, we have (σαcosδ,σδ)=(13 mas,10 mas) for Oberon and (σαcosδ,σδ)=(16 mas,11 mas) for Ariel.
The determination of Bin Eq. 2 was obtained from the standard deviation of the background (σbg). More specifically, to estimate the
background noise overall contribution, we adopted the simple relationship given by
B=nσ2
bg (4)
, where nis the number of background pixels over which the object is sampled. We opted for this way to estimate the background
because the digital coronography procedure subtracts it in the process of attenuation of the scattered light from Uranus. Equation 4
takes into consideration noise sources other than those from the sky only (the scattered light from Uranus is a relevant such other
source). For considerations on the analysis of sky-subtracted CCD data, see Newberry (1991).
These lower limits for the precision in the centroid of the Ariel and Oberon are not much smaller than those obtained for their
respective right ascension and declination. It is also interesting to mention that, to the images considered in these calculations, the
standard deviations from the observed minus calculated values for the reference stars are 22 mas in RA and 14 mas in DEC.
There is an obvious loss of precision when we go from CCD to celestial equatorial coordinates. Possible origins are remaining
distortion patterns of the CCD and a PSF that may differ from a circular one. Other issues, mentioned in C15 and that justifies larger
standard deviations in RA as compared to those in DEC, are known mechanical problems in the telescope tracking system and incorrect
Figure 3: Differences in right ascension (upper panels) and declination (bottom panels) in the sense observations minus
ephemerides (DE435+ura111) for Miranda, as a function of time (left panels), true anomaly (middle panels) and the angle
Sun-Observer-Target (right panels). The ”*” means multiplication by the cosine of the declination.
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆α* (mas)
Date (year)
Miranda
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆α* (mas)
True anomaly (deg)
Miranda
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆α* (mas)
Angle Sun−Observer−Miranda (deg)
Miranda
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆δ (mas)
Date (year)
Miranda
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆δ (mas)
True anomaly (deg)
Miranda
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆δ (mas)
Angle Sun−Observer−Miranda (deg)
Miranda
Table 3: Time intervals that encompass the observations. CCD (1): data from Veiga et al. (2003). CCD (2): data from
C15. Note: photographic plates were used until 1988 but there were no observations of the main satellites of Uranus made
in that year.
Data set Time interval
Photographic plates 28MAY1982 to 19JUL1987
CCD (1) 18SEP1989 to 23AUG2004
CCD (2) 09JUN1992 to 25OCT2011
timing inserted in the image header (known to have happened before 2000). Also, as mentioned in that paper, mechanical and timing
issues may slightly increase or decrease our right ascensions so that no general systematic effects on the positions of the satellites are
expected from them.
4 Comparison with stellar occultation results and different ephemerides
Here, we compare our observed positions with those given by stellar occultations and different ephemerides: the planetary ephemerides
DE4354(JPL) and INPOP19a5(Fienga et al. 2019) (Paris Observatory), and ura1116and NOE-7-2013-MAIN7(ephemerides for the
motions of the main satellites around the Uranian barycenter). NOE-7-2013-MAIN is a more recent adjustment of the motions of
the satellites as compared to that given by (Lainey 2008) and ura111 is the latest JPL ephemeris for the Uranian satellites. IN-
POP21a (Fienga et al. 2021) is also used for comparisons. This new planetary ephemeris is an update of INPOP19a including additional
Juno and Mars orbiters observations, but also including the observations presented in this paper in its construction. In the same way,
the recent JPL planetary and lunar ephemerides DE4408(Park et al. 2021) is used in the comparisons.
4https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/, see also ftp://ssd.jpl.nasa.gov/pub/eph/planets/
ioms/
5https://www.imcce.fr/recherche/equipes/asd/inpop/download19a
6https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/
7ftp.imcce.fr/pub/ephem/satel/NOE/URANUS/SPICE/
8https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/
Figure 4: Same as Fig. 3 for Ariel.
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆α* (mas)
Date (year)
Ariel
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆α* (mas)
True anomaly (deg)
Ariel
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆α* (mas)
Angle Sun−Observer−Ariel (deg)
Ariel
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆δ (mas)
Date (year)
Ariel
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆δ (mas)
True anomaly (deg)
Ariel
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆δ (mas)
Angle Sun−Observer−Ariel (deg)
Ariel
Figure 5: Same as Fig. 3 for Umbriel.
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆α* (mas)
Date (year)
Umbriel
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆α* (mas)
True anomaly (deg)
Umbriel
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆α* (mas)
Angle Sun−Observer−Umbriel (deg)
Umbriel
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆δ (mas)
Date (year)
Umbriel
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆δ (mas)
True anomaly (deg)
Umbriel
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆δ (mas)
Angle Sun−Observer−Umbriel (deg)
Umbriel
Table 4: olumns: satellite name; offsets (observed minus ephemerides - DE435+ura111 and DE435+NOE-7-2013-MAIN)
in right ascension and declination for plate and CCD measurements. Standard deviations are given between parenthesis.
Last column shows the total number of plate and CCD filtered measurements, respectively, for each satellite. The notation
”<>” indicates mean value. The ”*” means multiplication by the cosine of the declination. Standard deviations are those
of the measurements, not of the mean
.
ura111 NOE-7-2013-MAIN Number of
Satellite <∆α∗> < ∆δ > < ∆α∗> < ∆δ > objects
(mas) (mas)
Miranda −9(±96) −20(±73) −9(±95) −22(±76) 1680
Ariel −9(±48) −10(±39) −8(±48) −10(±39) 3485
Umbriel −12(±49) −15(±42) −12(±49) −15(±42) 3666
Titania −11(±41) −16(±37) −10(±42) −16(±36) 4442
Oberon −14(±40) −13(±37) −13(±40) −13(±37) 4456
Figure 6: Same as Fig. 3 for Titania.
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆α* (mas)
Date (year)
Titania
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆α* (mas)
True anomaly (deg)
Titania
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆α* (mas)
Angle Sun−Observer−Titania (deg)
Titania
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆δ (mas)
Date (year)
Titania
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆δ (mas)
True anomaly (deg)
Titania
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆δ (mas)
Angle Sun−Observer−Titania (deg)
Titania
Figure 7: Same as Fig. 3 for Oberon.
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆α* (mas)
Date (year)
Oberon
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆α* (mas)
True anomaly (deg)
Oberon
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆α* (mas)
Angle Sun−Observer−Oberon (deg)
Oberon
−600
−400
−200
0
200
400
600
1980 1985 1990 1995 2000 2005 2010 2015
∆δ (mas)
Date (year)
Oberon
−600
−400
−200
0
200
400
600
0 50 100 150 200 250 300 350
∆δ (mas)
True anomaly (deg)
Oberon
−600
−400
−200
0
200
400
600
60 80 100 120 140 160 180
∆δ (mas)
Angle Sun−Observer−Oberon (deg)
Oberon
Table 5: Columns: satellite name; differences in right ascension and declination between the offsets of a satellite (except
Oberon) and those of Oberon in the sense Satellite minus Oberon as a function of the separation between the satellite
and Uranus. This distance is given by d. No differences were formed when the distance between Oberon and Uranus
was smaller than 2500. Standard deviations are given between parenthesis. The notation ”<>” indicates mean value. The
distance range 000 ≤d≤500 presented 0 measurement to Miranda, Ariel and Umbriel and 3 to Titania
. The symbol ”∆∆” indicates differences between offsets. The ”*” means multiplication by the cosine of the declination. Standard deviations are those of the measurements, not of the mean.
Sat. <∆∆α∗> < ∆∆δ > < ∆∆α∗> < ∆∆δ > < ∆∆α∗> < ∆∆δ > < ∆∆α∗> < ∆∆δ > < ∆∆α∗> < ∆∆δ > < ∆∆α∗> < ∆∆δ >
(mas) (mas) (mas) (mas) (mas) (mas)
(500 ≤d≤1000) (1000 ≤d≤1500 ) (1500 ≤d≤2000) (2000 ≤d≤2500 ) (2500 ≤d≤3000) (3000 ≤d≤3500)
Miranda −2(±84) −5(±69) −−−−−−−−−−
Ariel +14(±40) +8(±39) +3(±37) −1(±31) −−−−−−−−
Umbriel +18(±39) +9(±45) −4(±24) 0(±33) +3(±37) −2(±33) −8(±73) +2(±57) −−−−
Titania +31(±40) +8(±42) +11(±30) −13(±31) +5(±37) +7(±30) −1(±27) +1(±29) +3(±23) −5(±29) +2(±35) −4(±35)
Figure 8: Differences in right ascension (left panel) and declination (middle panel) in the sense observations minus
ephemerides (DE435+ura111) for Miranda, as a function of the angular distance from Uranus. Right panel: Angular
distance of Miranda from Uranus as a function of time. The ”*” means multiplication by the cosine of the declination.
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆α* (mas)
Distance from Uranus (arcsec)
Miranda
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆δ (mas)
Distance from Uranus (arcsec)
Miranda
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
1980 1985 1990 1995 2000 2005 2010 2015
Distance from Uranus (arcsec)
Date (year)
Miranda
Figure 9: Same as Fig. 8 for Ariel.
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆α* (mas)
Distance from Uranus (arcsec)
Ariel
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆δ (mas)
Distance from Uranus (arcsec)
Ariel
5
6
7
8
9
10
11
12
13
14
15
1980 1985 1990 1995 2000 2005 2010 2015
Distance from Uranus (arcsec)
Date (year)
Ariel
Figure 10: Same as Fig. 8 for Umbriel.
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆α* (mas)
Distance from Uranus (arcsec)
Umbriel
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆δ (mas)
Distance from Uranus (arcsec)
Umbriel
6
8
10
12
14
16
18
20
22
1980 1985 1990 1995 2000 2005 2010 2015
Distance from Uranus (arcsec)
Date (year)
Umbriel
Figure 11: Same as Fig. 8 for Titania.
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆α* (mas)
Distance from Uranus (arcsec)
Titania
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆δ (mas)
Distance from Uranus (arcsec)
Titania
0
5
10
15
20
25
30
35
1980 1985 1990 1995 2000 2005 2010 2015
Distance from Uranus (arcsec)
Date (year)
Titania
Figure 12: Same as Fig. 8 for Oberon.
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆α* (mas)
Distance from Uranus (arcsec)
Oberon
−600
−400
−200
0
200
400
600
0 5 10 15 20 25 30 35 40 45
∆δ (mas)
Distance from Uranus (arcsec)
Oberon
5
10
15
20
25
30
35
40
45
1980 1985 1990 1995 2000 2005 2010 2015
Distance from Uranus (arcsec)
Date (year)
Oberon
Figure 13: Average number of reference stars per year. These data were determined from the set of observations of Oberon
.
5
10
15
20
25
30
35
1980 1985 1990 1995 2000 2005 2010 2015
Number of stars
Date (year)
Table 6: Satellite mean offsets with respect to Oberon. The ”*” means multiplication by the cosine of the declination.
The notation ”<>” indicates mean value. The symbol ”∆∆” indicates differences between offsets. Standard deviations are
those of the measurements, not of the mean. No restriction to the distance Oberon-Uranus was made
.
Satellite <∆∆α∗> < ∆∆δ > Number of
(mas) objects
Miranda −2(±84) −5(±69) 1567
Ariel +4(±38) +1(±33) 3192
Umbriel 0(±37) −1(±35) 3332
Titania +3(±31) −3(±33) 4028
4.1 Comparisons with results from stellar occultations
Widemann et al. (2009) determined an accurate position of Titania from a stellar occultation on 2001-SEP-08. The difference between
that position and DE4059+ura02710 (based on the GUST86 theory), in the sense observed minus ephemeris, is
∆αcosδ=−108 ±13 mas
∆δ=−62 ±7 mas
(5)
We do not have observations in September 2001, but we do have data taken in August and October of that year. In this way,
differences were calculated with respect to DE405+ura027 and mean offsets in right ascension and declination were determined from
70 measurements. They are
∆αcosδ=−95 ±32 mas
∆δ=−123 ±35 mas
(6)
A significant disagreement can be seen in declination. It is interesting to note, however, that Widemann et al. (2009) mention in
their paper a survey made with the Bordeaux meridian transit circle where it is shown that Uranus’ offset, averaged over several months
around September 2001 amounts to ∆αcosδ=−98 ±10 mas and ∆δ=−122 ±10 mas (see also Arlot, J. E. et al. 2008). Note that these
offsets are consistent to those given by Eq. 6. This is an indication that most of the offsets we find may be attributed to the motion of
the barycenter of the Uranian system around that of the Solar System.
A second occultation event by Titania, in 2003-AUG-01 is also reported by Widemann et al. (2009), whose offsets are
∆αcosδ=−127 ±20 mas
∆δ=−97 ±13 mas
(7)
Our 36 observations of Titania, taken in August 2003 and compared to DE405+ura027 give:
∆αcosδ=−122 ±47 mas
∆δ=−129 ±43 mas
(8)
Both results are consistent within their respective 1σuncertainties. These comparisons - at least to the positions of Titania used in
this section - indicate the consistency of our positions with respect to independent accurate astrometry of the Uranian system as well as
the reliability of our standard deviations.
4.2 Comparisons with different ephemerides
Here, we present comparisons with the dynamical model for the motion of the five main satellites of Uranus NOE-7-2013-MAIN and
ura111, and the planetary ephemerides INPOP19a, INPOP21a, DE435 and DE440.
4.2.1 DE435+ura111 and DE435+NOE-7-2013-MAIN
Figures 3 to 7 show, for right ascension and declination, the behaviour of the offsets (those that survived to the filtering) in the sense
observation minus ephemerides as a function of time, true anomaly, and the angle Sun-Observer-Satellite. Those figures also show
9ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/de405.iom.pdf and https://naif.jpl.nasa.gov/pub/naif/generic kernels/spk/planets/a old versions/
10https://naif.jpl.nasa.gov/pub/naif/generic kernels/spk/satellites/a old versions/
that the values presented in Table 4 are a suitable global representation of the offsets along the x-axes (time, true anomaly, satellite
elongation).
It should be noted that, as compared to C15, this work presents smaller offsets (absolute values), indicating a better agreement
between observations and DE435+ura111. Given that DE432 (used in C15) and DE435 do not differ significantly (few mas level) for
Uranus within the time span of our observations, this better agreement comes from the use of Gaia EDR3 (see Table 4).
As expected from C15, also given by Table 4, NOE-7-2013-MAIN and ura111 yielded very similar results. This reinforces the
indication that most of the offsets we find in the position of the satellites come from the motion of the Uranian barycenter around the
barycenter of the Solar System as given by the planetary ephemerides.
Another important feature also comes from the use of Gaia EDR3. Although two images of the Uranian system, taken at sufficiently
distant instants, will not have the same reference stars, we expect that those two sets of stars locally materialize accurately the same
coordinate axes, namely, the ICRF. In this context, we understand that our observed positions have a better coherence with respect to
those from C15 and that this is reflected in the overall offsets and standard deviations as given by Table 4.
Table 5 complements the information given by Tables 4 and 6 by providing some numerical details about remaining effects of
the distance Uranus-satellite on our positions. Figures 8 to 12 illustrate the details of Table 5, whereas Fig. 13 estimates the average
number of reference stars per year. Overall, they show the effectiveness of the digital coronography procedure to attenuate the effects
of the scattered light from Uranus as well as the quality of Gaia EDR3 to materialize the celestial frame even when few reference stars
are available.
It should be noted in Table 5 that the difference between offsets ∆∆α∗for Titania within the distance interval from Uranus 500 ≤
d≤1000,+31(±40) mas, is larger than that for the other satellites. Most of the data in this bin of distances come from 81 observations
of Titania made in 2011 (the remaining 16 measurements within this same bin of distances from Uranus show values ∆∆α∗and ∆∆δof
few mas only), where an asymmetric light distribution made it difficult to free Titania from the scattered light from Uranus. Given our
successful efforts to attenuate that scattered light, and knowing that our positions will mostly serve to improve the orbits of Uranus and
its main satellites, we believe it is useful to keep in our final data set all measurements and to also provide in our catalogue of positions,
as mentioned earlier, the distances between the satellites and Uranus.
Table 6 compares the offsets in right ascension and declination of a given satellite to those of Oberon. The standard deviations
derived from these differences between offsets provide a more trustworthy evaluation of angle measurements among point-like objects.
These results are similar to those presented in C15 as zero-point errors are cancelled out when differences between offsets are formed.
If we consider only measurements from CCD data, then the standard deviations shown in Table 6 become slightly smaller to Miranda.
4.2.2 INPOP19a, DE440 and INPOP21a
In these comparisons, the ephemeris of the five main Uranian moons is still ura111 but the motion of the Uranian barycenter around
the barycenter of the Solar System is given by the IMCCE planetary ephemerides INPOP19a and INPOP21a, and the JPL planetary
ephemeris DE440 - see Table 7 and compare it to Table 4. In order to estimate the impact of the Gaia EDR3 reduction on the Uranian
barycentric orbits, an update of the INPOP planetary ephemerides has been made by introducing into the INPOP adjustment the Uranian
satellite positions presented in this work. In Table 7 one can see the clear reduction of the offset in declination of about 30 mas thanks
to the use of Gaia EDR3 reduced satellite positions. This result enhances the importance of such determination for the link between
planetary planes and the Gaia reference frame.
The planetary and lunar ephemerides DE440 has recently replaced11 DE430 and includes seven years of new data in its computation,
in addition to using improved models and data calibration (Park et al. 2021). Although the main objective of this paper is to present
11https://ssd.jpl.nasa.gov/?horizons_news
Table 7: Columns: satellite name; offsets (observed minus ephemeris) in right ascension and declination for plate and
CCD measurements. Standard deviations are given between parenthesis. Last column shows the total number of plate
and CCD filtered measurements, respectively, for each satellite. The notation ”<>” indicates mean value. The ”*” means
multiplication by the cosine of the declination. Standard deviations are those of the measurements, not of the mean
.
INPOP19a INPOP21a DE440 Number of
Satellite <∆α∗> < ∆δ > < ∆α∗> < ∆δ > < ∆α∗> < ∆δ > objects
(mas) (mas) (mas)
Miranda −14(±94) −46(±73) −11(±101) −16(±74) −15(±96) −19(±74) 1680
Ariel −3(±48) −32(±42) −3(±50) −4(±39) −19(±49) −9(±39) 3485
Umbriel −6(±48) −37(±44) −7(±50) −9(±42) −22(±51) −14(±42) 3666
Titania −2(±41) −38(±39) −3(±42) −9(±37) −21(±43) −16(±37) 4442
Oberon −5(±40) −34(±39) −6(±41) −5(±38) −24(±42) −12(±37) 4456
Table 8: A
ngular measurements have the same meaning as those provided by the the JPL’s HORIZONS system (ephemeris
service). Columns: astrometric right ascension and declination, with origin at the observing site (IAU code 874) and
referred to the ICRF; Year, Month, Day and Fraction of a day (YMDF) along with JD of the observation mid-time;
satellite apparent position, in the plane of the sky, with respect to the central body in the sense satellite minus central
body. The difference in right ascension is multiplied by the cosine of the declination.
RA DEC YMDF JD DX DY
(ICRF) (UTC) (arcsec)
15 56 10.5902 −20 15 08.385 19820711.94166667 2445162.44166667 −35.875 −22.175
15 56 10.5410 −20 15 08.224 19820711.94930556 2445162.44930556 −35.953 −22.039
15 56 10.4777 −20 15 07.841 19820711.95902778 2445162.45902778 −36.052 −21.865
15 56 10.4221 −20 15 07.626 19820711.96562500 2445162.46562500 −36.118 −21.747
15 56 10.3844 −20 15 07.397 19820711.97326389 2445162.47326389 −36.195 −21.610
15 56 10.3377 −20 15 07.192 19820711.97916667 2445162.47916667 −36.254 −21.504
15 56 10.2973 −20 15 06.912 19820711.98541667 2445162.48541667 −36.316 −21.392
.
.
.
the astrometry of the main Uranus’ satellites and its quality, accomplished with the ephemerides used so far, it is interesting to have a
comparison between our positions and those from DE440. This is also given by Table 7.
The results presented in Table 4 for ura111 differ from those in Table 7 only by the use of the planetary ephemerides (DE435
in the first table and INPOP19a, INPOP21a and DE440 in the latter). Both tables lead to the same conclusion: with respect to our
observations, a systematic effect in the motion of the Uranian barycenter around the Solar System barycenter can be seen.
4.3 The catalogue
The positions of the Uranian main satellites determined here are provided in the form of catalogues and are available at CDS via
anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5). An extract with the first lines of the catalogue for Oberon is shown by Table 8.
All right ascensions and declinations in the catalogue are astrometric ones, with origin at the observing site (IAU code: 874) and
referred to the ICRF. We also emphasize that this work does not provide positions of Uranus and does not make any direct measurement
of them. All positions in the catalogue are obtained from images containing the Uranian satellites and stars for which astrometry can
be extracted from Gaia EDR3 (reference stars). Calculated positions of the satellites were obtained from a planetary ephemeris plus an
ephemeris that describes the motion of the satellites around the Uranian barycenter.
Table 9: Columns: satellite name; standard deviations, in right ascension and declination, that can be used as weights for
each measurement in position; total number of observations involved in each determination of standard deviations. The
”*” means multiplication by the cosine of the declination
.
Satellite σα*σδNumber of
(mas) objects
Miranda 96 73 1680
Ariel/Umbriel/Titania/Oberon 44 39 16049
5 Conclusions and Comments
We provide a set of accurate positions of Uranus’ main satellites spread over almost 3 decades of observations with photographic plates
and CCDs.
On average, we obtained offsets ∆αcosδ=−11 (±52) milli-arcseconds and ∆δ=−14 (±43) milli-arcseconds for the differences in
the sense observation minus ephemerides (DE435+ura111). When the offsets ∆αcosδand ∆δof Miranda, Ariel, Umbriel and Titania
are compared, for the same dates, to those of Oberon, we obtain overall differences of +2 (±45) milli-arcseconds in right ascension and
−2 (±40) milli-arcseconds in declination. Comparisons of the observations with various ephemerides, along with results from stellar
occultations, indicate a possible offset in the (Solar System) barycentric position of the Uranian system barycenter. These results are
an improvement with respect to our previous works, individually, not only because of the longer time span of the observations but
mainly due to the use of Gaia EDR3 as reference for astrometry, which decreased the systematic effects in the observed positions of the
satellites.
The data presented here will mostly serve as a source to improve the orbits of the satellites and that of Uranus. In this context,
a number that could describe the accuracies of the satellites’ positions, in a general way, is useful. The standard deviations in right
ascension and declination, from the full set of observations, is a simple way to provide conservative figures and are shown in Table 9. We
recognize, however, that the observations of Miranda are not as accurate as those of the other satellites so we provide them separately.
Acknowledgements
The following authors acknowledge the respective CNPq grants: J.I.B.C. 308150/2016-3 and 305917/2019-6; RV-M 304544/2017-
5, 401903/2016-8; M.A 427700/2018-3, 310683/2017-3 and 473002/2013-2. The results were based on observations taken at Pico
dos Dias Observatory of the National Laboratory of Astrophysics (LNA/Brazil). Software Routines from the IAU SOFA Collection
were used. Copyright ©International Astronomical Union Standards of Fundamental Astronomy (http://www.iausofa.org). The
authors acknowledge the numerous and dedicated colleagues that contributed to the observing runs over many years.
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