MG14 - Talk detail

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Abstract

We review the derivation of the standard geodesic deviation equation in spherically symmetric situations. We reconsider geodesic deviation in Newtonian gravity first to uncover in a second step the relativistic effects within the full theory of general relativity. The standard Jacobi equation, linearized in the deviation and the relative velocity between two neighboring geodesics, can be used to model various satellite constellations or the behavior of test masses within only one satellite. We give the full solution for a spherically symmetric and static background but focus mainly on the situation in Schwarzschild spacetime. We comment on initial conditions and free integration parameters that appear in the solution and show their impact on the deviating orbit. We further uncover effects that are due to the linearization to explore the range of validity of the Jacobi equation.

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