English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The hydrostatic equilibrium of multi-layer bodies lacks a satisfactorytheoretical treatment despite its wide range of applicability. Here we showthat by using the exact analytical potential of homogeneous ellipsoids we canobtain recursive analytical solutions and an exact numerical method for thehydrostatic equilibrium shape problem of multi-layer planets and synchronousmoons. The recursive solutions rely on the series expansion of the potential interms of the polar and equatorial shape eccentricities, while the numericalmethod uses the exact potential expression. These solutions can be used toinfer the interior structure of planets and synchronous moons from the observedshape, rotation, and gravity. When applied to dwarf planet Ceres, we show thatit is most likely a differentiated body with an icy crust of equatorialthickness 30-90 km and a rocky core of density 2.4-3.1 g/cm$^3$. Forsynchronous moons, we show that the $J_2/C_{22} \simeq 10/3$ and the$(b-c)/(a-c) \simeq 1/4$ ratios have significant corrections of order$\Omega^2/(\pi G \rho)$, with important implications on how their gravitationalcoefficients are determined from flyby radio science data and on how we assesstheir hydrostatic equilibrium state.

Multi-Layer Hydrostatic Equilibrium of Planets and Synchronous Moons: Theory and Application to Ceres and to Solar System Moons