# Tarvos (S/2000 S 4)

Tarvos is ∼15 kilometers in size and thus one of the larger irregular moons of Saturn. It has been discovered in 2000 joint with eleven other outer moons. Tarvos’s mean distance to Saturn is ∼18 million kilometers, with one revolution around the planet on a prograde orbit requiring 2 years, 6 months and 2 weeks. The orbit eccentricity of 0.54 is among the largest of all known moons in the Saturn system. Tarvos is a member of the Gallic family.
From our Cassini measurements, the rotation period was determined to 10 h 41 min 28 sec ± 4 sec. By coincidence, this number is very close to the rotation period of Saturn itself (∼10 h 33 min).

Fig. (left): Short animation of Cassini images of Tarvos while moving through constellation Telescopium on 25 Apr 2013 (21 frames; time span: 2:24 h; exposure times: 100 sec; range: 8.9 million km; Cassini orbit: rev 187). In the first image, the object is marked by a black cross. The background stars move through the field of view because the camera of the fast moving Cassini spacecraft was tracking Tarvos, and they appear smeared because of the long exposure. The slight horizontal jitter of Tarvos is due to improper tracking at the arcseconds level. Flickering bright spots stem from cosmic-ray hits on the camera’s CCD detector, fixed bright or dark pixels are incorrectly calibrated hot or cold pixels on the CCD, respectively. The space background, in reality pitch black, is displayed in dark gray because this makes visibility of the object easier. Image IDs: N1745588734 to N1745597294.

Fig. (right): Lightcurves of Tarvos from Cassini imaging data obtained on 14 Aug 2014 (upper curve; 38° observation phase angle; Cassini orbit rev 207), 25-26 Apr 2013 (middle; 79° phase; rev 187), and 05 Sep 2013 (bottom; 101° phase; rev 197). The orange diamond signs indicate the very first measurement of an observation. The 79°-phase observation covered more than three rotational cycles. From Denk and Mottola (2019).

This page is intended to compile (much of) our knowledge of Tarvos in compact form. Its main focus will lie on the documentation of my Cassini-ISS work (observation planning and data analysis), but will also provide general information obtained from other work, like discovery circumstances and orbital and physical parameters. It will not include the raw data (images or spectra) taken by the Cassini spacecraft, these are available at NASA’s Planetary Data System (PDS). For further reading on Tarvos and on irregular moons of Saturn in general, see the reference list at my outer-Saturnian moons page.

This website is still in the early stages of development. As soon as papers will be reviewed or other information will be processed appropriately, more content will be added. I will remove this note when the page will be close to completion.

Last update: 27 Apr 2022 — page content is best displayed on a screen at least 1024 pixels wide

### (1) Astronomical and physical properties

 Moon name Saturn range Orbit period Orbit direction Size Rotation period Discovery year Tarvos million km years prograde ∼  km h  min 2000

Basic information about Tarvos is offered in tabular form:
(1A) Designations and discovery circumstances
(1B) Orbit parameters
(1C) Physical parameters (body properties)
← Tables (1A) to (1C) in text format

Most fundamental values are highlighted in red. The notes offer explanations, calculations, accuracies, references, etc. The data were obtained from spacecraft as well as from ground-based observations.

###### (1A) Designations and discovery circumstances
 Moon name(1) Tarvos IAU number(3) Saturn XXI First observation date(7) 23 Sep 2000 Moon abbrev. (TD)(2) Tar Provisional desig.(4) S/2000 S 4 Announcement date(7) 25 Oct 2000 SPICE ID(5) 621 IAU circ. announcement(7) no. 7513 Also-used label(6) S21 Discoverers(8) Kavelaars, Gladman, et al.

Notes for Table 1A:

(1) Tarvos’s name was announced on 08 Aug 2003 in IAU circ. 8177. It is named after Tarvos Trigaranus, a deity depicted as a bull god carrying three cranes alongside its back from Gaulish mythology. In the Gaulish language, “taruos” means “bull”.

(2) I use this 3-letter abbreviation in the diagrams of my publications simply for practicability reasons. These have no offcial character.

(3) Moon numbers are assigned by the International Astronomical Union (IAU)’s Committee for Planetary System Nomenclature. For satellites, roman numeral designations are used.

(4) Designation given to the object in the first announcement; the guidelines are explained here.

(5) SPICE is a commonly-used information system of NASA’s Navigation and Ancillary Information Facility (NAIF). It assists engineers in modeling, planning, and executing planetary-exploration missions, and supports observation interpretation for scientists. Each planet and moon obtained a unique SPICE number.

(6) ‘S’ for ‘Saturnian moon’ plus the roman numeral designation in arabic numbers are often-used labels for satellites. Not sure how official that is.

(7) The date of the photography wherein the object was spotted for the first time is given in the IAU circular released on the announcement date.

(8) The discoverer team included: Brett GladmanJJ Kavelaars, Jean-Marc Petit, Hans Scholl, Matthew Holman, Brian Marsden, Phil Nicholson, Joe Burns.

###### (1B) Orbit parameters
 Orbit direction(1) prograde Group member(2) Gallic Dynamical family(3) Gallic Periapsis range(4) 8.43 ⋅ 106 km Semi-major axis(5) 18.243 ⋅ 106 km Apoapsis range(6) 28.06 ⋅ 106 km Semi-major axis(7) 302 R♄ Semi-major axis(8) 0.122 au Semi-major axis(9) 0.279 RHill Orbit eccentricity(10) 0.538 Orbit inclination(11) 33.7° Inclination supplemental angle(12) 33.7° Orbital period(13) 929.9 d Orbital period(14) 2 y 6 m 2 w Mean orbit velocity(15) 1.44 km/s

Notes for Table 1B:

(1) Prograde (counterclockwise as seen from north) or retrograde (clockwise as seen from north)

(2) Norse, Inuit, or Gallic

(3) Classification based on the a,e,i space in Fig. 1 and Table 2 in Denk et al. (2018)

(4) $r_{Peri}=a\cdot(1-e)$

(5) Orbit semi-major axis a, from JPL’s Solar System Dynamics Planetary Satellite Mean Elements website

(6) $r_{Apo}=a\cdot(1+e)$

(7) Saturn radius R = 60330 km (100 mbar level)

(8) Astronomical Unit 1 au = 149 597 870.7 km

(9) Saturn’s Hill sphere radius $R_{Hill}=\sqrt[3]{m_♄/3m_☉}\cdot r_{♄↔☉}$= ∼65 ⋅ 106 km = ∼1085 R♄ = ∼3° as seen from Earth at opposition (with mass of Saturn m = 5.6836 ⋅ 1026 kg and perihel range Saturn↔Sun r♄↔ = 1.353 ⋅ 109 km)

(10) Orbit eccentricity e, from JPL’s Solar System Dynamics Planetary Satellite Mean Elements website

(11) Orbit inclination i, from JPL’s Solar System Dynamics Planetary Satellite Mean Elements website

(12) Orbit “tilt” or inclination supplemental angle i’ = i for prograde moons; i’ = 180°−i for retrograde moons

(13) From JPL’s Solar System Dynamics Planetary Satellite Mean Elements website

(14) Value from (13) in units of years, months, weeks

(15) $v=\sqrt{Gm_♄/a}$ (Gravitational constant G = 6.6741 ⋅ 10−20 kmkg−1 s−2 )

###### (1C) Physical parameters
 Mean size(1) 15 $^{+4}_{−3}$ km Min. equatorial axes ratio(4) 1.08 Mass(6) ∼ 8 ⋅ 1014 kg Mean radius(2) ∼ 7.3 km Axes radii (a × b × c)(5) unknown Mean density(7) 0.5 g/cm3 (?) Equatorial circumference(3) ∼ 50 km Surface escape velocity(8) ∼ 10 km/h Rotation period (sidereal)(9) 10.691 h +/- (9) 0.001 h Spin rate(9) 2.245 d−1 Spin direction(10) unknown Pole dir. (ecliptic longitude λ)(12) unknown Pole direction (geocentric, RA)(13) unknown Seasons(11) unknown Pole dir. (ecliptic latitude β)(12) unknown Pole direction (geocentric, Dec)(13) unknown Absolute visual magnitude(14) ∼ 12.9 mag Apparent vis. mag. from Earth(15) 22.1 mag Best apparent mag. for Cassini(16) 12.8 mag Spectral slope(17) ∼ +5.4 %/100nm B−R color index(17) ∼ 1.21 / ∼ 1.13 Albedo(18) 0.06 (?) Hill sphere radius(19) ∼ 650 km Hill sphere radius(20) ∼ 90 rTar

Notes for Table 1C:

(1) Determined from absolute visual magnitude H (see note (14)). The conversion from H to size (diameter of a reference sphere) was calculated through $D=1 \text{ au}\cdot \frac{2}{\sqrt{A}}\cdot 10^{−0.2·(H−M_☉)}$; with solar apparent V magnitude M = −26.71 ± 0.02 mag and Astronomical Unit 1 au = 149 597 870.7 km. For Tarvos’s albedo, see note (18). Due to the uncertain input values, a size determined this way may be uncertain to ∼ −15/+30% (for A ± 0.02 and H ± 0.1).

(2) Half the diameter value. While the diameter is the intuitive size number, the radius r is mainly used in formulas to calculate other quantities. Important: While the given number is the formal result from the equation of note (1), the true precision is much lower (also see note (1)).

(3) Estimated under assumption of a circular equatorial circumference.

(4) Determined from the range between minima and maxima of a lightcurve obtained at low phase angle (from Table 3 in Denk et al. (2018)).

(5) Here, a is the long equatorial, b the short equatorial, and c the polar axis dimension of the reference ellipsoid. Unknown because no shape model is available yet.

(6) The mass is a very rough guess, estimated through density ρ and volume $\frac{4\pi}{3}r^3$; see notes (7) and (2).

(7) The density of Tarvos is not known, the given number is speculative. There are indications from other Saturnian irregular moons that these objects have quite low densities (well below 1 g/cm3), similar to comets or some of the inner small moons of Saturn. However, a higher density, maybe up to 2.5 g/cm3, cannot be ruled out.

(8) $v_{esc}=\sqrt{\frac{2GM}{R}}$; very rough guess as well since it depends on Tarvos’s mass (note (6)) and radius (notes (1) and (2)) which are not well known. = 6.674 · 1011 mkg−1 s−2 (Gravitational constant).

(9) Rotation period P and error determined with Cassini data; from Table 3 in Denk and Mottola (2018). See the lightcurves section below for details. The spin rate is 24/P, measured in units of one per day.

(10) Valid entries: Prograde (counterclockwise as seen from north), retrograde (clockwise as seen from north), ‘lying on the side’ (pole direction almost perpenticular to ecliptic pole), or ‘unknown’.

(11) Valid entries: “None” (rotation axis points close to one of the ecliptic poles), “moderate” (rotation axis is moderately tilted), or “extreme” (rotation axis is highly tilted, points somewhere close to the ecliptic equator), or ‘unknown’.

(12) —

(13)

(14) From Table 2 in Denk et al. (2018); the number may be uncertain by several tenths of magnitude. The absolute visual magnitude HV is the magnitude (brightness) of an object (in the visible wavelength range) if located 1 au away from the sun and observed at 0° phase angle (i.e., in this definition, the observer virtually sits at the center of the sun). The magnitude scale is logarithmic, with an object of 6th mag being 100x darker than a 1st mag object.

(15) Apparent visual magnitude V; from Table 2 in Denk et al. (2018).

(16) From Table 2 in Denk and Mottola (2018). Given is the best apparent magnitude as seen from Cassini at a time when an observation took place.

(17) Color information: Mean spectral slope S’2 is from Table 3 in Grav and Bauer (2007). B−R color index: First value from Grav and Bauer (2007), second value from Graykowski and Jewitt (2018). The higher the value, the “redder” the color of the object. Mean wavelengths: 445 nm for B (“blue”), 658 nm for R (“red”) filters. BR of the Sun is 1.01 (Ramírez et al. 2012).

(18) Might vary by ±0.03; see discussions in Grav et al. (2015) and Denk et al. (2018).

(19) Hill radius at periapsis under the assumption of the given density (see note (7)). The number would be larger for a higher density, or lower for a lower density.

(20) Hill radius at periapsis in Tarvos-radius units. With $R_{Hill}=\sqrt[3]{4\pi\rho_{Tar}/9m_♄}\cdot r_{Tar↔♄}$, this number only depends on the object’s distance to the central body (Saturn; linear dependency) and on the object’s density (proportional to the cubic root; see also note (7)).

### (8) Cassini ISS observations: Planning

(8A) Table: Tarvos observations overview
(8B) Map: Tarvos in the sky of Cassini
(8C) Tarvos geometry and visibility graph (range, phase, and magnitude vs. time)

General overview on ISS planning
sheet (2B) [not yet available here, sorry]

High-level camera planning commands
(includes most IOI files plus post-downlink notes) [ not yet available ]

Fail notes (Cassini ISS)
– ISS_140OT_TARRES123 (15 Nov 2010): Completely lost due to spacecraft safing in sequence s64.
– ISS_217OT_TARPHA003 (16 Jun 2015): On thrusters from 09:03:40 to 09:30:22 UTC for reaction-wheel bias; this engineering activity was added late in the planning process and caused a strong shaking of the spacecraft, making 5 out of 34 images unusable ( example image).
– ISS_235OT_TARPOL109 (28 Apr 2016): A few frames (9 of 176) were lost due to rain in (!) Goldstone (telemetry outage and intermittant ‘glitching’ over ∼30 min).

###### (8A) Table: Tarvos observations overview

Observational circumstances and geometry information for three ISS observation requests of Tarvos. From Table 2 of Denk and Mottola (2019), plus additional data. Information for requests not used in this paper will follow at a later date.

Corresponding lightcurves → section (4) [ not yet posted here ]
← Table (8A) in text format

Notes:

a The naming scheme used for Cassini Solstice Mission observations (“requests”) gives information on the object (first three letters), the request’s primary goal (Rot=rotation period; Pol=pole-axis/shape), and the approximate observation phase angle (three digits). The three digits between the first and the second underline indicate Cassini’s orbit number. “OT” stands for “other target”.

b Rev. = revolution = Cassini orbit number. in = apoapsis segment inbound, out = apoapsis segment outbound, peri = periapsis segment. Note that (for some reasons) the true number of orbits since Saturn arrival in 2004 is off (ahead) by 1.5 compared to the official count which is noted here and used in all technical aspects.

c Time difference between shutter mid-time of first and of last image used for the lightcurve.

d A uniform Earth-to-object distance of 1.319·109 km (range at opposition in April 2013) is used here for the distance between the irregular moons and Earth.

e For full-resolution images. The values must be doubled when the NAC was operated in 2×2 summation mode.

f Calculated from the absolute magnitude H, the observation phase angle α, and the distances of Tarvos to the sun and to Cassini.

g Coordinates of the irregular moons (geocentric RA/Dec and ecliptic λ/β) as seen from Cassini during the observations, see also sheet 8B.

h Phase-angle bisector vector (longitude and latitude). For definition and use, see appendix in Harris et al. (1984).

###### (8B) Map: Tarvos in the sky of Cassini

Tarvos as visible to Cassini between 2010 and 2017. Orthographic projection of the sky; geocentric coordinate system (RA/Dec). As a prograde object, Tarvos moves from right to left.

Shown are Tarvos’s locations (colored, wiggled lines), the Tarvos locations during Cassini observations (light-yellow circles with annotations), the anti-directions of the Cassini observations (bluish diamonds), the location of the sun from 2004 to 2017 (smooth sinusoidal line from RA ∼ 290° to ∼ 85°; the sun moves from right to left), the location of the anti-sun (0° phase) from 2004 to 2017 (pale sinusoidal line from RA ∼ 110° to ∼ 265°), the Milky Way (yellow band) and the Magellanic clouds (yellow spots to the lower right), the ecliptic poles (gray diamonds), and Saturn’s poles (gray diamonds).

NP = north pole; SP = south pole.

###### (8C) Tarvos geometry and visibility graph

This graph has been used for Tarvos observation scheduling.

Notes: Left axis: Range of Tarvos to Cassini (red) and to Saturn (orange); right axes: phase angle (green) and apparent magnitude of Tarvos (blue) as seen from Cassini for the time range 01 Jan 2009 to 15 Sep 2017 (end-of-mission).

### (9) References for Tarvos

IAU circular, discovery: no. 7513
IAU circular, naming: no. 8177
Wikipedia:  Tarvos (moon) Tarvos (Mond)