Tidal evolution of close binary asteroid systems

Abstract

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than 5 times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent. This work has possible implications for the determination of the Roche limit and for spin-state alteration during close flybys.

Spin-up of rubble-pile asteroids: Disruption, satellite formation, and equilibrium shapes

“…Such a burst of mass into low orbit is what was simulated here as a consequence of our limited timescales, but its success in creating systems so similar to the observed population suggests that similar physics may be necessary even at the realistic timescales. Increasing the timescales in the computations is not a feasible method to attack this uncertainty in the model at the current time, so analytical approaches to understanding the many, and sometimes competing, effects of YORP, BYORP and tides will be needed (Ć uk and Burns, 2005;McMahon and Scheeres, 2010b;Ć uk and Nesvorný , 2010;Taylor and Margot, 2010;Goldreich and Sari, 2009). In fact, Jacobson and Scheeres (2011b) have suggested that a balance between the BYORP effect and solid body tides may play a stabilizing role for the observed satellites.…”

Physical modeling of triple near-Earth Asteroid (153591) 2001 SN263 from radar and optical light curve observations

“…However, the process acts very slowly at separations beyond a handful of primary radii for reasonable material properties (Taylor and Margot, 2010;Taylor and Margot, 2011) and is unlikely to evolve the separation sufficiently in the dynamical lifetime of a near-Earth asteroid of a few to tens of millions of years (Gladman et al, 1997;Bottke et al, 2002). Perhaps Beta was formed prior to the injection of 2001 SN263 from the main belt allowing a longer timescale for tidal evolution, but tides alone cannot account for the observed asynchronous rotation of Beta.…”

Tidal decay and orbital circularization in close-in two-planet systems

“…3 3 Note, however, that, for a more accurate description, a large number of harmonics in the expansion of the tidal potential should be considered when the star–planet distance is small enough (see Taylor & Margot 2010). …”

“…Note, however, that, for a more accurate description, a large number of harmonics in the expansion of the tidal potential should be considered when the star-planet distance is small enough (seeTaylor & Margot 2010). C 2011 The Authors, MNRAS 415, 2349-2358 Monthly Notices of the Royal Astronomical Society C 2011 RAS…”