Secular Variations in the Orbit and Spin of Asteroid (16) Psyche
Abstract
The obliquity, or angular separation between spin and orbit poles, of asteroid (16) Psyche is currently ~94 degrees. We are interested in knowing how much that angular separation varies, on time scales of 104 to 106 years. To answer that question, we have done several related analyses.
On short time scales, the orbital element variations of Psyche are dominated by perturbations from Jupiter. Jupiter's dominance has two basic causes: first is the large mass and relatively close position of Jupiter, and second is proximity to a 19:8 mean motion resonance. Jupiter completes 8 orbits in 94.9009 years, while Psyche takes 94.9107 years to complete 19 orbits. As a result of this, all of the orbital elements of Psyche exhibit significant periodic variations, with a 94.9 year period dominating. There are also significant variations at the synodic period, which is 8.628 years, or 1/11 of the resonant period. On longer time scales, the orbital elements of Psyche vary considerably, due to secular perturbations from the planets. Again, Jupiter is the main perturbing influence on Psyche. The eccentricity and inclination both oscillate, with dominant periods of 18.667 kyr. Using a recent shape model, and assumption of uniform density, to constrain relevant moments of inertia, we estimate the spin pole precession rate parameter to be 8.53 arcsec/year. The current spin pole is at ecliptic {lon, lat} = { 32, -7} deg, whereas the orbit pole is at {lon, lat} = {60.47, 86.91} deg. The current obliquity is thus 94.3 degree. Using nominal values of the input parameters, the recovered spin pole trajectory is such that, over a million year time span, centered on the present, the minimum and maximum values of obliquity are 92.36 and 98.56 deg. The obliquity oscillates with dominant periods of 18.45 and 48.40 kyr. There are thus 4 distinct sub-surface thermal waves. One is driven by the 4.195 hour diurnal cycle. The largest amplitude is driven by the 4.99 year annual cycle, and the large obliquity. Much longer periods are associated with obliquity oscillations. If the thermal properties are nearly constant with depth, the thermal skin depths of these waves will be in the ratio of the square roots of their periods, (1, 102, 6235, 10^4). If there are volatiles in the upper few kilometers of the Psyche sub-surface, they will respond to this thermal forcing.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.P51E3412B
- Keywords:
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- 6205 Asteroids;
- PLANETARY SCIENCES: SOLAR SYSTEM OBJECTS;
- 6207 Comparative planetology;
- PLANETARY SCIENCES: SOLAR SYSTEM OBJECTS;
- 6211 Centaurs;
- PLANETARY SCIENCES: SOLAR SYSTEM OBJECTS;
- 6224 Kuiper belt objects;
- PLANETARY SCIENCES: SOLAR SYSTEM OBJECTS