Surface potential of a rotating duplex consisting of two conjoined spheres

Abstract

Many small Solar System bodies have bilobate shapes which may be approximated as “duplexes” consisting of two spheres. Duplexes may be “detached”, “tangent”, “cohering”, or “enveloping”, depending on whether the two spheres are separate, just touching, overlapping, or one inside the other, respectively. Thus cohering and enveloping duplexes are inherently inhomogeneous. This paper treats all four types of duplex, but mainly concerns cohering duplexes, where the two spheres overlap in a lens-shaped imbricated “crush zone”.This paper analytically derives the effective potential on the surface of a rotating duplex, and uses it to locate its equilibria, and to classify them as maxima, minima, or saddle points. The results reveal that duplexes have surprisingly complicated patterns of surface equilibria. Depending on the rotation rate, up to 14 surface equilibria may exist; those in the neck are particularly interesting. As a case study, this analysis is applied to Kuiper Belt Object (486958) Arrokoth (also known as 2014 MU69).For comparison with the main text, Appendix A discusses homogeneous cohering duplexes. All cohering duplexes possess concavities with reduced exposure to impacts and insolation; Appendix B derives and plots some relevant properties of these concavities, and demonstrates how some concavities may actually be warmer than the rest of the body because of radiative heat trapping. Finally, Appendix C derives the surface gravity, potential, and equilibria of a “biplex”: a special case of an enveloping duplex when the smaller sphere represents a void or density deficit inside the larger sphere.