Fenrir (S/2004 S 16) – Tilmann Denk

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Fenrir is ∼4 kilometers in size and thus one of the small Irregular moons of Saturn. It has been discovered in 2004 joint with eleven other outer moons. Fenrir’s mean distance to Saturn is ∼22½ million kilometers, with one revolution around the planet on a retrograde orbit requiring 3 years, 5 months and 2 weeks.
Fenrir was never bright enough to be observable with Cassini to do photometry. Its ephemeris (position in the sky) was also not known accurately. Therefore, we never made an attempt to look for it with Cassini.

(1) Astronomical and physical properties

This page is intended to compile (much of) our knowledge of Fenrir in compact form, including general information like discovery circumstances and orbital and physical parameters. For further reading on Irregular moons of Saturn in general, see the reference list at my outer-Saturnian moons page.

This website is still under development and will get additional content in the near future. I will remove this note when the page will be close to completion.

Last update: 20 May 2023 — page content is best displayed on a screen at least 1024 pixels wide

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(1) Astronomical and physical properties

Moon name	Saturn range	Orbit period	Orbit direction	Size	Rotation period	Discovery year
Fenrir	million km	years	retrograde	∼ km	unknown	2004

Basic information about Fenrir 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.

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(1A) Designations and discovery circumstances

Moon name⁽¹⁾	Fenrir	IAU number⁽³⁾	Saturn XLI	First observation date⁽⁷⁾	13 Dec 2004
Moon abbrev. (TD)⁽²⁾	Fen	Provisional desig.⁽⁴⁾	S/2004 S 16	Announcement date⁽⁷⁾	04 May 2005
		SPICE ID⁽⁵⁾	641	IAU circ. announcement⁽⁷⁾	no. 8523
		Also-used label⁽⁶⁾	S41	Discoverers⁽⁸⁾	D. Jewitt et al.

Notes for Table 1A:

⁽¹⁾ Fenrir’s name was announced on 05 Apr 2007 in IAU circ. 8826. It was named after Fenrisúlfr, a monstrous wolf from Norse mythology, son of Loki and father of the wolves Hati Hróðvitnisson and Sköll, foretold to kill the god Odin during the events of Ragnarök.

⁽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: David Jewitt, Scott Sheppard, and Jan Kleyna.

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(1B) Orbit parameters

Orbit direction⁽¹⁾	retrograde	Group member⁽²⁾	Norse	Dynamical family⁽³⁾	Ymir
Periapsis range⁽⁴⁾	19.42 ⋅ 10⁶ km	Semi-major axis⁽⁵⁾	22.454 ⋅ 10⁶ km	Apoapsis range⁽⁶⁾	25.49 ⋅ 10⁶ km
Semi-major axis⁽⁷⁾	372 R_♄	Semi-major axis⁽⁸⁾	0.150 au	Semi-major axis⁽⁹⁾	0.343 R_Hill
Orbit eccentricity⁽¹⁰⁾	0.135	Orbit inclination⁽¹¹⁾	165.0°	Inclination supplemental angle⁽¹²⁾	15.0°
Orbital period⁽¹³⁾	1263.0 d	Orbital period⁽¹⁴⁾	3 y 5 m 2 w	Mean orbit velocity⁽¹⁵⁾	1.30 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 km³kg⁻¹s⁻²)

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(1C) Physical parameters

Mean size⁽¹⁾	4 $^{+1}_{−½}$ km	Min. equatorial axes ratio⁽⁴⁾	unknown	Mass⁽⁶⁾	∼ 1 ⋅ 10¹³ kg
Mean radius⁽²⁾	∼ 1.8 km	Axes radii (a × b × c)⁽⁵⁾	unknown	Mean density⁽⁷⁾	0.5 g/cm³ (?)
Equatorial circumference⁽³⁾	∼ 12 km			Surface escape velocity⁽⁸⁾	∼ 2 km/h

Rotation period⁽⁹⁾	unknown	+/- ⁽⁹⁾	—	Spin rate⁽⁹⁾	unknown
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⁾	∼ 15.9 mag	Apparent vis. mag. from Earth⁽¹⁵⁾	25.0 mag	Best apparent mag. for Cassini⁽¹⁶⁾	17.0 mag
		Color⁽¹⁷⁾	unknown	Albedo⁽¹⁸⁾	0.06 (?)

Hill sphere radius⁽¹⁹⁾	∼ 380 km	Hill sphere radius⁽²⁰⁾	∼ 205 r_Fen

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 Fenrir’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⁾ Ratio between long equatorial reference axis a and short equatorial reference axis b; unknown because no lightcurve is available.

⁽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.

⁽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 Fenrir 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 Fenrir’s mass (note (6)) and radius (notes (1) and (2)) which are not well known. G = 6.674 · 10¹¹m³kg⁻¹s⁻² (Gravitational constant).

⁽⁹⁾ Unknown because Cassini could not observe the object.

⁽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 H_V 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 et al. (2018) (but no observations were performed).

⁽¹⁷⁾ —

⁽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 Fornjot-radius units. With $R_{Hill}=\sqrt[3]{4\pi\rho_{Fen}/9m_♄}\cdot r_{Fen↔♄}$, 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)).

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Table of contents

(1) Astronomical and physical properties

(1A) Designations and discovery circumstances

(1B) Orbit parameters

(1C) Physical parameters