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We study the problem of static, spherically symmetric, self-gravitatingelastic matter distributions in Newtonian gravity. To this purpose we firstintroduce a new definition of homogeneous, spherically symmetric (hyper)elasticbody in Euler coordinates, i.e., in terms of matter fields defined on thecurrent physical state of the body. We show that our definition is equivalentto the classical one existing in the literature and which is given inLagrangian coordinates, i.e., in terms of the deformation of the body from agiven reference state. After a number of well-known examples of constitutivefunctions of elastic bodies are re-defined in our new formulation, a detailedstudy of the Seth model is presented. For this type of material the existenceof single and multi-body solutions is established.

Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter