# A Closed-Form Solution for a Linear Viscoelastic Self-gravitating Sphere

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## Abstract

Following up on the classical solutions by Love for a linear-elastic self-gravitating sphere, this paper presents the corresponding extension to a linear viscoelastic body of the Kelvin–Voigt type. The solution is expressed in closed form by making use of Laplace transforms. Applications to the genesis of terrestrial planets are sought and the evolution of the Love radius and possible extensions to large deformations are discussed. As a new result, it turns out that in the early days of planet formation there is no Love radius and that it takes time for the Love radius to develop.

## Keywords

Viscoelastic Model Terrestrial Planet Planet Formation Laplace Space Discrete Mechanic
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