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

When 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, ; Rapp, 1989, ). 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. Plain Language Summary We used the available models of shape and gravity field of the solar system bodies. We study how the amplitude of the mountains and valleys in gravity and topography depends on their size. Mountains on Mars are greater than on the Earth and yet larger on asteroid Vesta compared relative to the body's size. The same is true for gravity: Relative variations in gravity are larger on smaller bodies. We quantify this dependence and develop a method to predict the variations in gravity and topography depending on the body's size and density.