Bergelmir (S/2004 S 15)

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Bergelmir is ∼5 kilometers in size and thus one of the “mid-sized” Irregular moons of Saturn. It has been discovered in 2004 joint with eleven other outer moons. Bergelmir’s mean distance to Saturn is ∼19½ million kilometers, with one revolution around the planet on a retrograde orbit requiring 2 years and 9 months.

From our Cassini measurements, the rotation period was determined to 8 h and 7½ min ± 5½ min. The Bergelmir lightcurves are quite flat, indicative for a rather circular equatorial cross-section of this moon.

(1) Astronomical and physical properties

Fig. (left): Short animation of Cassini images of Bergelmir while moving through constellation Libra on 13 Sep 2015 (23 frames; time span: 1:46 h; exposure times: 220 sec; range: 20.1 million km; Cassini orbit: rev 221). In the first image, the object is marked by a black cross. During the observation, 3.3-mag star σ Librae (SigLib) crossed the field-of-view of the Cassini Narrow Angle Camera. Because of the long exposure times, this star is hopelessly overexposed. Bergelmir itself was an ∼16 mag object for Cassini during the observation and thus more than 100,000x darker than σ Lib. The faint circular structures to the left of the star as well as the prominent flare at the end of the movie are caused by reflections within the camera. The background stars move through the field of view because the camera of the fast moving Cassini spacecraft was tracking Bergelmir, and they appear smeared because of the long exposure. The slight horizontal jitter of Bergelmir 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: N1820831250 to N1820837410.

Fig. (right): Lightcurve of Bergelmir from Cassini imaging data obtained on 13 to 14 Sep 2015 (16° observation phase angle; Cassini orbit rev 221). The orange diamond sign indicates the very first measurement of the observation. During the 37-hours long observation, Bergelmir made 4½ rotations. Adapted from Denk and Mottola (2019).

This page is intended to compile (much of) our knowledge of Bergelmir 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 Bergelmir and on Irregular moons of Saturn in general, see the reference list at my outer-Saturnian moons page.

This website is still under 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: 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
Bergelmir	million km	years	retrograde	∼ km	h min	2004

Basic information about Bergelmir is offered in tabular form:
(1A) Designations and discovery circumstances
(1B) Orbit parameters
(1C) Physical parameters (body properties)
← Tables (1A) to (1C) in ASCII 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⁾	Bergelmir	IAU number⁽³⁾	Saturn XXXVIII	First observation date⁽⁷⁾	12 Dec 2004
Moon abbrev. (TD)⁽²⁾	Ber	Provisional desig.⁽⁴⁾	S/2004 S 15	Announcement date⁽⁷⁾	04 May 2005
		SPICE ID⁽⁵⁾	638	IAU circ. announcement⁽⁷⁾	no. 8523
		Also-used label⁽⁶⁾	S38	Discoverers⁽⁸⁾	D. Jewitt et al.

Notes for Table 1A:

⁽¹⁾ Bergelmir’s name was announced on 05 Apr 2007 in IAU circ. 8826. It was named after Bergelmir, a frost giant from Norse mythology, grandson of Ymir, and progenitor of a new race of giants at the dawn of time.

⁽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⁾	Bergelmir
Periapsis range⁽⁴⁾	16.59 ⋅ 10⁶ km	Semi-major axis⁽⁵⁾	19.336 ⋅ 10⁶ km	Apoapsis range⁽⁶⁾	22.08 ⋅ 10⁶ km
Semi-major axis⁽⁷⁾	321 R_♄	Semi-major axis⁽⁸⁾	0.129 au	Semi-major axis⁽⁹⁾	0.295 R_Hill
Orbit eccentricity⁽¹⁰⁾	0.142	Orbit inclination⁽¹¹⁾	158.6°	Inclination supplemental angle⁽¹²⁾	21.4°
Orbital period⁽¹³⁾	1006.9 d	Orbital period⁽¹⁴⁾	2 y 9 m ¼ w	Mean orbit velocity⁽¹⁵⁾	1.40 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⁾	5 $^{+1½}_{−1}$ km	Min. equatorial axes ratio⁽⁴⁾	1.13	Mass⁽⁶⁾	∼ 3 ⋅ 10¹³ kg
Mean radius⁽²⁾	∼ 2.5 km	Axes radii (a × b × c)⁽⁵⁾	unknown	Mean density⁽⁷⁾	0.5 g/cm³ (?)
Equatorial circumference⁽³⁾	∼ 15 km			Surface escape velocity⁽⁸⁾	∼ 3 km/h

Rotation period⁽⁹⁾	8.13 h	+/- ⁽⁹⁾	0.09 h	Spin rate⁽⁹⁾	2.95 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⁾	∼ 15.2 mag	Apparent vis. mag. from Earth⁽¹⁵⁾	24.2 mag	Best apparent mag. for Cassini⁽¹⁶⁾	15.9 mag
		B−R color index⁽¹⁷⁾	∼ 1.10	Albedo⁽¹⁸⁾	0.06 (?)

Hill sphere radius⁽¹⁹⁾	∼ 450 km	Hill sphere radius⁽²⁰⁾	∼ 175 r_Ber

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 Bergelmir’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 spherical 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 Bergelmir 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 Bergelmir’s mass (note (6)) and radius (notes (1) and (2)) which are not well known. G = 6.674 · 10¹¹m³kg⁻¹s⁻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 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 and Mottola (2018). Given is the best apparent magnitude as seen from Cassini at a time when an observation took place.

⁽¹⁷⁾ Color information: B−R color index is 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. B−R 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 Fornjot-radius units. With $R_{Hill}=\sqrt[3]{4\pi\rho_{Ber}/9m_♄}\cdot r_{Ber↔♄}$, 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