# Ymir (S/2000 S 1)

Ymir is ∼19 kilometers in size and thus one of the large irregular moons of Saturn. Joint with Paaliaq, its discovery in 2000 was the first detection of an irregular moon of Saturn after the Phoebe discovery a century earlier. Ymir’s mean distance to Saturn is ∼23 million kilometers; this is among the largest of all known Saturnian moons, with one revolution around the planet on a retrograde orbit requiring 3 years, 7 months and 1.5 week.
From our Cassini measurements, the rotation period was determined to 11 h 55 min 20 sec. Like the orbit direction, the spin direction is also retrograde. Since the north pole of Ymir’s rotation axis points close to the ecliptic south pole, there are no seasonal variations on the surface of this moon. The convex-shape model shows a triangularly-shaped equatorial cross-section, and it might be possible that Ymir is a contact-binary “double” object. Most measured lightcurves show a very large brightness variation.

### Table of contents

Fig. (left): Short animation of Cassini images of Ymir while moving through constellation Leo on 01 May 2012 (21 frames; time span: 3:49 h; exposure times: 82 sec; range: 15.1 million km; Cassini orbit: rev 165). 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 Ymir, and they appear slightly smeared because of the long exposure. The slight horizontal jitter of Ymir is due to improper tracking at the arcseconds level. Flickering bright spots or streaks 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: N1714571998 to N1714585678.

Fig. (right): Photograph of a 3D print of the shape model of Ymir with a Cassini image used for the background.

This page is intended to compile (much of) our knowledge of Ymir in compact form. Its main focus lies on the documentation of my Cassini-ISS work (observation planning and data analysis). In the 1st section, it also provides general information obtained from other work, like discovery circumstances and orbital and physical parameters. It does 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 Ymir and on irregular moons of Saturn in general, see the reference list at the end of this page.

This website is still under development. As soon as more papers will be published, additional 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 Ymir million km years retrograde ∼  km h  min 2000

Sheet (1) offers basic information about Ymir 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) Ymir IAU number(3) Saturn XIX First observation date(7) 07 Aug 2000 Moon abbrev. (TD)(2) Ymi Provisional desig.(4) S/2000 S 1 Announcement date(7) 25 Oct 2000 SPICE ID(5) 619 IAU circ. announcement(7) no. 7512 Also-used label(6) S19 Discoverers(8) B. Gladman et al.

Notes for Table 1A:

(1) Ymir’s name was announced on 08 Aug 2003 in IAU circ. 8177. It is taken from the Norse mythology where Ymir is the ancestor of all the jötnar or frost giants.

(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) retrograde Group member(2) Norse Dynamical family(3) Ymir Periapsis range(4) 15.40 ⋅ 106 km Semi-major axis(5) 23.128 ⋅ 106 km Apoapsis range(6) 30.85 ⋅ 106 km Semi-major axis(7) 383 R♄ Semi-major axis(8) 0.155 au Semi-major axis(9) 0.353 RHill Orbit eccentricity(10) 0.334 Orbit inclination(11) 173.5° Inclination supplemental angle(12) 6.5° Orbital period(13) 1319.9 d Orbital period(14) 3 y 7 m 1 w Mean orbit velocity(15) 1.28 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 km3 kg−1 s−2 )

###### (1C) Physical parameters
 Mean size(1) 19 $^{+5}_{−3}$ km Min. equatorial axes ratio(4) 1.37 Mass(6) ∼ 2 ⋅ 1015 kg Mean radius(2) ∼ 9.6 km Axes radii (a × b × c)(5) ∼ 12 × 11 × 8 km Mean density(7) 0.5 g/cm3 (?) Equatorial circumference(3) ∼ 65 km Side lengths (equat. cross-sect.)(5) ∼ 25 × 24 × 20 km Surface escape velocity(8) ∼ 13 km/h Rotation period (sidereal)(9) 11.92220 h +/- (9) 0.00002 h Spin rate(9) 2.01305 d−1 Spin direction(10) retrograde Pole dir. (ecliptic longitude λ)(12) 230°±20° Pole direction (geocentric, RA)(13) 100°±20° Seasons(11) none Pole dir. (ecliptic latitude β)(12) −85°±10° Pole direction (geocentric, Dec)(13) −70°±10° Absolute visual magnitude(14) ∼ 12.3 mag Apparent vis. mag. from Earth(15) 21.7 mag Best apparent mag. for Cassini(16) 13.2 mag Spectral slope(17) ∼ +8.1 %/100nm B−R color index(17) ∼ 1.22 Albedo(18) 0.06 (?) Hill sphere radius(19) ∼ 1500 km Hill sphere radius(20) ∼ 160 rYmi

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 Ymir’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 from the equatorial side lengths, see note (5).

(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. Since Ymir has a rather triangular cross-section, three equatorial side lengths are also given. These numbers were determined from the shape model.

(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 Ymir 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 gcm3), 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 Ymir’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 et al. (2018). See the lightcurves section below for details. 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) From Cassini data (Denk and Mottola 2013). See the pole-direction sheet below for details.

(13) As (12), but in geocentric coordinates (Right Ascension and Declination).

(14) From Table 2 in Denk et al. (2018); the number may be uncertain by several tenths of magnitude. The absolute visual magnitude H 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 3 in Denk et al. (2018). Given is the best apparent magnitude as seen from Cassini at a time when an observation took place.

(17) Color information: Spectral slope S’2  and BR color index; from Table 3 in Grav and Bauer (2007). 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 discussion in 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 Ymir-radius units. With $R_{Hill}=\sqrt[3]{4\pi\rho_{moon}/9m_♄}\cdot r_{moon↔Saturn}$, 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)).

### (2) Cassini observations: Overview

Table of contents:
(2A) Availability of Cassini observations and results
(2B) Imaging observations (ISS)
(2C) UVIS and VIMS

Note: ISS is the abbreviation for the Cassini cameras (Imaging Science Subsystem) and has nothing to do with the International Space Station which was named ISS many years later. A high-level instrument’s description is given in Porco et al. (2004).

###### (2A) Availability of Cassini observations and results

General overview on product and data availability. For imaging (ISS) high-level planning details → section (8).

 Cassini observations yes (disk-integrated) Rotation period yes sidereal to ± 0.1 sec Object size not yet (only from ground-based research) Pole direction yes to ± 10° Shape model yes (convex shape) Phase curve not yet (from 2° to 102° phase) Color (ISS, visible) yes in 5 color filters (Uv3, Bl1, Grn, Ir1, Ir2) Spectra (UV; vis., IR) maybe (UVIS and VIMS took data, but no spectra extracted yet)
###### (2B) Imaging observations (ISS)

General data-acquisition overview for Ymir:

 No. of observation requests (“visits”) — 13 No. of successful requests of duration >6 h — 8 Observation dates — 11/2007 – 07/2015 Apparent visual magnitudes — 13.2 – 15.1 mag Distances to Cassini — 15.1 – 21.9 ⋅ 106 km Phase angles — 2° – 105° Approx. number of images — ∼ 1750

Detailed ISS planning → section (8)

###### (2C) Ultraviolet spectrograph (UVIS) and Infrared spectrometer (VIMS) observations

UVIS and VIMS were occasionally taking data (outside my responsibility) while Cassini pointed toward Ymir, but (to the best of my knowledge) nobody analyzed them so far. Since the irregular moons were quite dark for Cassini, it is unclear if the object was bright enough to leave a measurable signal on the UVIS sensor. For VIMS, this appears even more doubtful. Another potential problem is that the pixel field-of-views of UVIS and VIMS are quite large, increasing the chance of light pollution through closeby background stars.

### (3) Images, artwork, movies

General:
– Available
– Raw images from the Cassini mission are provided at NASA’s Planetary Data System (PDS)

File resources:

 File type Link Description .png Images: Calibrated example image (annotated) ISS_165OT_YMIROTA065 N1714563106 2012-May-01 10:39:22 SCET/UTC .gif Images: Short animated gif (loop) from clear filter images ISS_159OT_YMIPHA002 N1704509212 – 10252 2012-Jan-06 .jpg Artwork: 3D print of an Ymir model (with rotation axis) in front of a Cassini image .zip [ #.# MB ] Movie: mp3 example [ not yet available ] .zip [ ### MB ] Movie: All 8 Ymir observations; in .mov format (→ lists in section (4) and sheet (8A) for observation-request names and details) [ not yet available ]

Note: SCET/UTC…Spacecraft Event Time/ Coordinated Universal Time

### (4) Lightcurves

General:
– Available
References: Denk and Mottola (2019); Denk et al. (2018); Denk and Mottola (2014)

Major scientific results:
– Rotation period (sidereal): 11.92220 ± 0.00002 h  =  11 h 55 m 19.9 s ± 0.1 s
– Mean diameter [ not yet determined from Cassini data ]
– Large lightcurve amplitudes due to irregular shape
– Absolute magnitudes [ not yet determined from Cassini data ]
– Mostly 3-max/3-min lightcurve extrema pattern → “triangular” cross-section of object
– Ymir might be a contact-binary object (but this is speculative, not proven)

Lightcurve plots:
– Table of high-level observation details → sheet (8A)
– Data files are provided in text format

 Request-ID Obs. date Phase Lightcurve Data Notes and references ISS_064OT_YMIR099 08 Apr 2008 55° ISS_218OT_YMICOL029 ISS_165OT_YMIROTA065 ISS_165OT_YMIROTB065 ISS_168OT_YMIROT095 11 Jul 2015 01 May 2012 03 May 2012 22 Jun 2012 29° 65° 63° 95° Denk and Mottola (2019) Symbol assignments: Orange diamonds: First observation measurement points; the start times are given in the legend boxes. 95° curve: covers 3.1 rotation cycles; each cycle has another symbol. ISS_159OT_YMIPHA002 ISS_167OT_YMIROT077 ISS_169OT_YMIPHA102 06 Jan 2012 29 May 2012 11 Jul 2012 2° 77° 102° [ ] [ not yet available ]

### (5) Pole direction and shape

General:
– Available (convex-shape model) (preliminary version)
– References: Denk et al. (2018); Denk and Mottola (2014); Denk and Mottola (2013)

Major scientific results:
– Shape: Roughly triangular equatorial cross-section
– North-pole direction: → Table (1C) ‘Physical parameters’, notes (12) and (13)
– Spin direction: Retrograde (rotation axis points near southern ecliptic pole)
– No noticeable seasonal variations over one Saturn year

Shape-model plots and file resources:

 File type Link Notes and references .png Denk and Mottola (2014) (presented at AGU meeting) .jpg Photograph of 3D print of convex-shape model .gif [ ] rotation movie (animated gif) [ not yet available ] .obj object file [ not yet available ]

### (6) Phase curve

General:
– Not yet available

### (7) Surface-color variations

General:
– Available (search for regional surface variegations) (preliminary results)
– References: no major publication yet; minor notes in Denk et al. (2018); Denk and Mottola (2018 EPSC)
– Observation request: ISS_218OT_YMICOL029_PRIME (11 Jul 2015)
– Used ISS color filters (effective wavelengths [nm]): Uv3 (340), Bl1 (445), Grn (563), Ir1 (758), Ir2 (868)
– Observation phase angle: 29°
– Predicted apparent magnitude: 14.1 mag

Major scientific result:
– Cassini: 5-color observation shows no longitudinal color variation on the surface
– Non-Cassini (Grav and Bauer 2007): Reddish color (positive spectral slope); from ground-based 4-color observations (BVRI) [→ Table (1C) ‘Physical parameters’, note (17)].

### (8) Cassini ISS observations: Planning

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

General overview on ISS planning:
sheet (2B)

High-level camera planning commands:
(includes most IOI files plus post-downlink notes)

Fail notes (Cassini ISS):
– ISS_218OT_YMICOL029 (11 Jul 2015): Last five images lost due to “data policing” (not enough bits allocated on the recorders)

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

Observational circumstances and geometry information for five ISS observation requests of Ymir. 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)
← 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; Col=color; Sup=”supporting”; Pha=phase coverage; Res=resolution), 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 Ymir 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: Ymir in the sky of Cassini

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

Shown are Ymir’s locations (colored, wiggled lines), the Ymir 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. The pole-axis directions of Ymir are marked by black diamonds.

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

This graph was used for Ymir observation scheduling.

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

### (9) References for Ymir

IAU circular, discovery: no. 7512
IAU circular, naming: no. 8177
Wikipedia:  Ymir (moon) Ymir (Mond)
My ‘Outer Moons of Saturn’ website: Sheet ‘links and references’

References (that include my work)

 Denk, T., Mottola, S. (2019): Studies of Irregular Satellites: I. Lightcurves and Rotation Periods of 25 Saturnian Moons from Cassini Observations. Icarus 322, 80-103. doi:10.1016/j.icarus.2018.12.040 Denk, T., Mottola, S., Tosi, F., Bottke, W.F., Hamilton, D.P. (2018): The Irregular Satellites of Saturn. In: Enceladus and the Icy Moons of Saturn (Schenk, P.M., Clark, R.N., Howett, C.J.A., Verbiscer, A.J., Waite, J.H., editors), Space Science Series, The University of Arizona Press, pp. 409-434. Denk, T., Mottola, S. (2018 EPSC): Cassini Observations of Saturn’s Irregular Moons. European Planetary Science Congress, EPSC2018−103, Berlin, 16−21 Sep 2018. Denk, T., Mottola, S. (2014 AGU): Irregular-Moons Science Today and in Cassini’s Final Three Years. 47th AGU annual fall meeting, Paper #20845, poster P13A-3795, San Francisco, 15−19 Dec 2014. ◊ Denk, T., Mottola, S. (2013 DPG): Saturns äußerer Mond Ymir. DPG/AEF-Tagung, abstract EP 7.2, Jena, 28 Februar 2013.

References (work from colleagues)

 Bauer, J.M., Grav, T., Buratti, B.J., Hicks, M.D. (2006): The phase curve survey of the irregular saturnian satellites: A possible method of physical classification. Icarus 184, 181-197. Buratti, B.J., Hicks, M.D., Davies, A. (2005): Spectrophotometry of the small satellites of Saturn and their relationship to Iapetus, Phoebe, and Hyperion. Icarus 175, 490-495. [ Word of caution: Nomenclature is erroneously mixed in this paper. S/2000 S3 is (S29) Siarnaq, not (S21) Tarvos. S/2000 S11 is (S26) Albiorix, not (S29) Siarnaq. The four irregulars observed for this work were Ymir, Paaliaq, Siarnaq, and Albiorix — but not Tarvos. ] Grav, T., Bauer, J. (2007): A deeper look at the colors of the saturnian irregular satellites. Icarus 191, 267−285. Porco, C.C. West, R.A., Squyres, S.W., McEwen, A.S., Thomas, P.C., Murray, C.D., Del Genio, A., Ingersoll, A.P., Johnson, T.V., Neukum, G., Veverka, J., Dones, L., Brahic, A., Burns, J.A., Haemmerle, V., Knowles, B., Dawson, D., Roatsch, Th., Beurle, K., Owen, W. (2004): Cassini imaging science: Instrument characteristics and capabilities and anticipated scientific investigations at Saturn. Space Sci. Rev. 115, 363-497.

© Tilmann Denk (2022)