Paaliaq (S/2000 S 2)

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Paaliaq is ~25 kilometers in size and thus one of the largest irregular moons of Saturn. Joint with Ymir, its discovery in 2000 was the first detection of an irregular moon of Saturn after the Phoebe discovery a century ago. Paaliaq’s mean distance to Saturn is ~15 million kilometers; this is among the smallest of all known Saturnian irregular moons, with one revolution around the planet on a prograde orbit requiring 1 year, 10 months and 2½ weeks. Paaliaq is a member of the Inuit family.
From our Cassini measurements, the rotational period was determined to 18 h and 47½ min ± 6 min. One lightcurve shows 4 maxima and 4 minima, which is very unusual for minor bodies in the solar system. It infers an unusual shape, and it may even be possible that Paaliaq is a contact-binary “double” moon.

Table of contents

(1) Astronomical and physical properties

Fig. (middle): Cassini observation of Paaliaq from 27 Jan 2017 10:24 UTC (cropped to 200×200 pixels and 2× zoomed).
Fig. (right): The lightcurve obtained from 31 Jul to 01 Aug 2013 at 102° phase shows 4 maxima and 4 minima before the pattern repeats. The observation duration was 37 h and 15 min.

This page is intended to compile (much of) our knowledge of Paaliaq 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 Paaliaq 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: 31 Oct 2018 — 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
 million km

Basic information about Paaliaq 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.

(1A) Designations and discovery circumstances
Moon name(1) Paaliaq IAU number(3) Saturn XX First observation date(7) 07 Aug 2000
Moon abbrev. (TD)(2) Paa Provisional desig.(4) S/2000 S 2 Announcement date(7) 25 Oct 2000
SPICE ID(5) 620 IAU circ. announcement(7) no. 7512
Also-used label(6) S20 Discoverers(8) B. Gladman et al.

Notes for Table 1A:

(1) Paaliaq’s name was announced on 08 Aug 2003 in IAU circ. 8177. It is named after a fictional shaman in the book The Curse of the Shaman by Michael Kusugak (Kusugak 2006).

(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) Inuit Dynamical family(3)
Periapsis range(4) 10.14 ⋅ 106 km Semi-major axis(5) 15.20 ⋅ 106 km Apoapsis range(6) 20.26 ⋅ 106 km
Semi-major axis(7) 252 R Semi-major axis(8) 0.102 au Semi-major axis(9) 0.23 RHill
Orbit eccentricity(10) 0.33 Orbit inclination(11) 46.2° Inclination supplemental angle(12) 46.2°
Orbital period(13) 688 d Orbital period(14) 1 y 10 m 2½ w Mean orbit velocity(15) 1.58 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 Table 2 in Denk et al. (2018)

(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 Table 2 in Denk et al. (2018)

(11) Orbit inclination i, from Table 2 in Denk et al. (2018)

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

(13) From the Planetary Satellite Mean Orbital Parameters page of JPL’s solar system dynamics 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) 25 $^{+7}_{−4}$ km Min. equatorial axes ratio(4) 1.05 Mass(6) ∼ 4.3 ⋅ 1015 kg
Mean radius(2) ∼ 12.7 km Axes radii (a × b × c)(5) unknown Mean density(7) 0.5 g/cm3 (?)
 Equatorial circumference(3)  ∼ 80 km Surface escape velocity(8) ∼ 17 km/h
Rotation period(9) 18.79 h +/- (9) 0.09 h Spin rate(9) 1.28 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) ∼ 11.7 mag Apparent vis. mag. from Earth(15) 21.3 mag Best apparent mag. for Cassini(16) 11.2 mag
Spectral slope(17) ∼ +10.0 %/100nm BR color index(17) ∼ 1.26 Albedo(18) 0.06 (?)
Hill sphere radius(19) ∼ 1300 km Hill sphere radius(20) ∼ 105 rPaa

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 Paaliaq’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 Paaliaq 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 Paaliaq’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) —


(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), the BR color index is from the same paper. 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 Paaliaq-radius units. With $R_{Hill}=\sqrt[3]{4\pi\rho_{Paa}/9m_♄}\cdot r_{Paa↔♄}$, 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)).

© Tilmann Denk (2018)