Evection

Abstract: A common origin for the Moon and Earth is required by their identical isotopic composition. However, simulations of the current giant impact hypothesis for Moon formation find that most lunar material originated from the impactor, which should have had a different isotopic signature. Previous Moon-formation studies assumed that the angular momentum after the impact was similar to that of the present day; however, Earth-mass planets are expected to have higher spin rates at the end of accretion. Here, we show that typical last giant impacts onto a fast-spinning proto-Earth can produce a Moon-forming disk derived primarily from Earth’s mantle. Furthermore, we find that a faster-spinning early Earth-Moon system can lose angular momentum and reach the present state through an orbital resonance between the Sun and Moon.

Abstract: Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because in secular theories the disturbing function is generally averaged over the Sun's orbital motion, whereas instead one should take into account some periodic terms, most notably the so-called evection, which can be large for distant, slow-moving satellites. This problem is identical to that initially encountered by Newton and other historical researchers when studying the Moon's motion. Here we demonstrate that the evection and other terms from lunar theory can be incorporated into the more modern Kozai formalism and that our synthetic approach produces much better agreement with results from symplectic integrations. Using this method, we plot the locations of secular resonances in the orbital-element space inhabited by the irregular satellites. Our model is found to predict correctly those satellites that are resonant or near-resonant. We also analyze the octupole term in the disturbing function to determine the strengths of resonant locking for satellites whose longitudes of pericenter are librating. By independently integrating these satellites' nominal orbits using a symplectic integrator, we show that the strength of this resonance can be successfully obtained from simple analytical arguments. We note that the distribution of irregular satellite clusters in the space of proper orbital elements appears to be nonrandom. We find that the large majority of irregular-satellite groups cluster close to the secular resonances, with several objects (Pasiphae, Sinope, Siarnaq, formerly S/2000 S3, and Stephano, formerly S/1999 U2) having practically stationary pericenters. After proposing the name main sequence to describe this grouping, we point out that none of the largest satellites (those with radii R > 100 km) belong to this class. Finally, we argue that this dichotomy implies that the smaller near-resonant satellites might have been captured differently than the largest irregulars.

Abstract: Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moon's orbital evolution through evection. We find that exit from formal evection occurs early and that subsequently, the Moon enters a quasi-resonance regime, in which evection still regulates the lunar eccentricity even though the resonance angle is no longer librating. Although not in resonance proper, during quasi-resonance angular momentum is continuously removed from the Earth-Moon system and transferred to Earth's heliocentric orbit. The final angular momentum, set by the timing of quasi-resonance escape, is a function of the ratio of tidal strength in the Moon and Earth and the absolute rate of tidal dissipation in the Earth. We consider a physically-motivated model for tidal dissipation in the Earth as the mantle cools from a molten to a partially molten state. We find that as the mantle solidifies, increased terrestrial dissipation drives the Moon out of quasi-resonance. For post-impact systems that contain >2 L_EM, final angular momentum values after quasi-resonance escape remain significantly higher than the current Earth-Moon value.