Power Laws of Topography and Gravity Spectra of the Solar System Bodies

Abstract

AbstractWhen a spacecraft visits a new planetary body, it is useful to know the properties of its shape and gravity field. This knowledge helps predict the magnitude of the perturbations in the motion of the spacecraft due to nonsphericity of a body's gravity field as well as planning for an observational campaign. It has been known for the terrestrial planets that the power spectrum of the gravity field follows a power law, also known as the Kaula rule (Kaula, 1963, https://doi.org/10.1029/RG001i004p00507; Rapp, 1989, https://doi.org/10.1111/j.1365-246X.1989.tb02031.x). A similar rule was derived for topography (Vening Meinesz, 1951). The goal of this study is to generalize the power law dependence of the gravity and topography spectra for solid surface solar system bodies across a wide range of body sizes. Traditionally, it is assumed that the gravity and topography power spectra of planets scale as g−2, where g is the surface gravity. This gravity scaling also works for the minor bodies to first order. However, we find that a better fit can be achieved using a more general scaling based on the body's radius and mean density. We outline a procedure on how to use this general scaling for topography to provide an a priori estimate for the gravity power spectrum. We show that for irregularly shaped bodies the gravity power spectrum is no longer a power law even if their topography spectrum is a power law. Such a generalization would be useful for observation planning in the future space missions to the minor bodies for which little is known.