On trouvera de même, pour le second satellites, les formules suivantes
Et l’on aura ensuite
Quant aux quantités marquées par Ξ {\displaystyle \Xi } et Φ , {\displaystyle \Phi ,} on aura
![{\displaystyle {\begin{aligned}x_{2}=&\varepsilon _{2}\cos(M_{2}t+\omega _{2})\\&-\chi _{1}\left[\Xi _{1}(a_{2},a_{1})\cos(\mu _{1}-\mu _{2})t+\Xi _{2}(a_{2},a_{1})\cos 2(\mu _{1}-\mu _{2})t+\ldots \right]\\&-\chi _{3}\left[\Xi _{1}(a_{2},a_{3})\cos(\mu _{3}-\mu _{2})t+\Xi _{2}(a_{2},a_{3})\cos 2(\mu _{3}-\mu _{2})t+\ldots \right]\\&-\chi _{4}\left[\Xi _{1}(a_{2},a_{4})\cos(\mu _{4}-\mu _{2})t+\Xi _{2}(a_{2},a_{4})\cos 2(\mu _{4}-\mu _{2})t+\ldots \right]\\&-\mathrm {K} _{2}\beta _{2}\cos 2(m-\mu _{2})t\,;\\\\y_{2}=&-{\frac {2\mu _{2}\varepsilon _{2}}{\mathrm {M} _{2}}}\sin(\mathrm {M} _{2}t+\omega _{2})\\&+\chi _{1}\left[\Phi _{1}(a_{2},a_{1})\sin(\mu _{1}-\mu _{2})t+\Phi _{2}(a_{2},a_{1})\sin 2(\mu _{1}-\mu _{2})t+\ldots \right]\\&+\chi _{3}\left[\Phi _{1}(a_{2},a_{3})\sin(\mu _{3}-\mu _{2})t+\Phi _{2}(a_{2},a_{3})\sin 2(\mu _{3}-\mu _{2})t+\ldots \right]\\&+\chi _{4}\left[\Phi _{1}(a_{2},a_{4})\sin(\mu _{4}-\mu _{2})t+\Phi _{2}(a_{2},a_{4})\sin 2(\mu _{4}-\mu _{2})t+\ldots \right]\\&+\mathrm {K} _{2}\gamma _{2}\sin 2(m-\mu _{2})t\,;\\\\z_{2}=&\lambda _{2}\sin(\mu _{2}t+\eta _{2}).\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/429d3d990896771c519034c55b15c5f796c72a80)
et 
on aura
![{\displaystyle {\begin{aligned}&\Xi _{1}(a_{2},a_{1})=\left[{\breve {\Gamma }}_{1}(a_{2},a_{1})+{\frac {2\mu _{2}}{\mu _{1}-\mu _{2}}}{\widehat {\Gamma }}_{1}(a_{2},a_{1})\right]{\frac {f_{2}}{(\mu _{1}-\mu _{2})^{2}-\mathrm {M} _{2}^{2}}},\\&\Xi _{2}(a_{2},a_{1})=\left[{\breve {\Gamma }}_{2}(a_{2},a_{1})+{\frac {2\mu _{2}}{2(\mu _{1}-\mu _{2})}}{\widehat {\Gamma }}_{2}(a_{2},a_{1})\right]{\frac {f_{2}}{4(\mu _{1}-\mu _{2})^{2}-\mathrm {M} _{2}^{2}}},\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \,;\\&\Phi _{1}(a_{2},a_{1})={\frac {2\mu _{2}}{\mu _{1}-\mu _{2}}}\Xi _{1}(a_{2},a_{1})+{\frac {f_{2}}{(\mu _{1}-\mu _{2})^{2}}}{\widehat {\Gamma }}_{1}(a_{2},a_{1}),\\&\Phi _{2}(a_{2},a_{1})={\frac {2\mu _{2}}{2(\mu _{1}-\mu _{2})}}\Xi _{2}(a_{2},a_{1})+{\frac {f_{2}}{4(\mu _{1}-\mu _{2})^{2}}}{\widehat {\Gamma }}_{2}(a_{2},a_{1}),\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d337afe57eae78310d9697525c7d90ea48a446e)
