Elsevier

Icarus

Volume 229, February 2014, Pages 418-422
Icarus

Note
Tidal end states of binary asteroid systems with a nonspherical component

https://doi.org/10.1016/j.icarus.2013.11.008Get rights and content

Highlights

  • Tidal end states are derived for binary asteroids with a nonspherical component.

  • Certain conditions result in collapse to a contact binary.

  • We illustrate our analytical results with asteroids 1996 HW1, 1999 KW4, and Hermes.

Abstract

We derive the locations of the fully synchronous end states of tidal evolution for binary asteroid systems having one spherical component and one oblate- or prolate-spheroid component. Departures from a spherical shape, at levels observed among binary asteroids, can result in the lack of a stable tidal end state for particular combinations of the system mass fraction and angular momentum, in which case the binary must collapse to contact. We illustrate our analytical results with near-Earth Asteroids (8567) 1996 HW1, (66391) 1999 KW4, and 69230 Hermes.

Introduction

Recent studies have examined energy, stability, and orbital relative equilibria in the planar two-body problem for a non-rotating sphere and an arbitrary, rotating ellipsoid (Scheeres, 2007, Bellerose and Scheeres, 2008) and approximately for two arbitrary, rotating ellipsoids (Scheeres, 2009). Here, we examine the special case of a rotating sphere interacting with a rotating oblate or prolate spheroid and provide exact, tractable analytical results for the locations of the fully synchronous end states of tidal evolution. The terms fully synchronous tidal end state and orbital relative equilibrium can be used interchangeably to describe a zero-eccentricity binary system that has ceased tidally evolving because the spin rates of both components have synchronized to the mean motion of the components about the center of mass of the system.

This note is organized as follows. In Section 2, we review fully synchronous tidal end states of a binary system consisting of two spheres. Section 3 extends the discussion to a sphere interacting with an ellipsoid and explores the specific cases of oblate and prolate spheroids with applications to real asteroid systems. Comparisons to previous work in Sections 3 Fully synchronous orbits with a nonspherical component, 4 Discussion place this work in context and possible avenues for contact-binary formation are suggested.

Section snippets

Fully synchronous orbits with spherical components

The locations of the fully synchronous end states of tidal evolution for binary asteroids with spherical components were discussed by Taylor and Margot (2011) and are summarized here. For components of equal, uniform density ρ with radii R1 and R2 and mass ratio q=M2/M1=(R2/R1)3 separated by a distance a in their circular mutual orbit, the sum of the orbital and spin angular momentum J upon full synchronization, scaled by J=G(M1+M2)3Reff, where Reff is the effective radius of a sphere with the

Fully synchronous orbits with a nonspherical component

Let component 1 of the binary system be a uniform-density ellipsoid with principal semi-axes a0a1a2 such that the equivalent radius of the ellipsoid is R1=(a0a1a2)1/3. For rotation about the shortest principal axis, the ratio of the moment of inertia of the ellipsoid to that of its equivalent-volume sphere with radius R1 is the nonsphericity parameter (Descamps and Marchis, 2008):λ=1+β22(αβ)2/3,where α=a2/a0,β=a1/a0, and αβ1. The nonsphericity parameter is always larger than unity because

Discussion

We have presented analytical formulae for contours of constant angular momentum for ensembles of binary systems consisting of an oblate/prolate component and a spherical component that, in turn, determine the fully synchronous tidal end states for specific binary systems according to their mass fractions. In retaining the spin angular momentum of the sphere, we extend the results of Bellerose and Scheeres (2008). In general, the presence of a nonspherical component breaks the symmetry about v=

Acknowledgement

This material is based upon work supported by the National Aeronautics and Space Administration under Grant No. NNX12AF24G issued through the Near-Earth Object Observations Program.

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