## 4.7 Equations of Relative Motion under the Influence of $J2$

The equations of motion of a satellite under the influence of gravitational and thrust perturbations can be written in frame $ℐ$ as (see our discussion of orbital perturbations in Section 2.5)

$\stackrel{̈}{r}=-{\nabla }_{r}\mathcal{V}+u$

(4.89)

where $r$ is the position vector, $V=U−R$ is the total gravitational potential (the nominal ...

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