et il n’y aura qu’à mettre, dans les expressions de
de l’Article X,
au lieu de
au lieu de
au lieu de
au lieu de
et supposer
De cette manière on aura, en vertu de l’action du Soleil,
![{\displaystyle {\begin{aligned}\mathrm {R} _{1}=&\circledast \left[{\frac {r_{1}-\rho _{1}\cos(\psi -\varphi _{1})}{\delta _{1}^{3}}}+{\frac {\cos(\psi -\varphi _{1})}{\rho _{1}^{2}}}\right],\\\mathrm {Q} _{1}=&\circledast \left[{\frac {\rho _{1}\sin(\psi -\varphi _{1})}{\delta _{1}^{3}}}-{\frac {\sin(\psi -\varphi _{1})}{\rho _{1}^{2}}}\right],\\\mathrm {P} _{1}=&\circledast {\frac {r_{1}p_{1}}{\delta _{1}^{3}}}.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/725ec90e11cf1f31204eadc855e4f66c58854aef)
XII.
Donc, en joignant ensemble les forces qui proviennent de l’action des trois satellites
et du Soleil sur le satellite
on aura les valeurs complètes de
exprimées de la manière suivante
![{\displaystyle {\begin{aligned}\mathrm {R} _{1}&={\mathfrak {S}}_{2}\left[{\frac {r_{1}-r_{2}\cos(\varphi _{2}-\varphi _{1})}{\Delta (r_{1},r_{2})^{3}}}+{\frac {\cos(\varphi _{2}-\varphi _{1})}{r_{2}^{2}\left(1+p_{2}^{2}\right)^{\frac {3}{2}}}}\right]\\&+{\mathfrak {S}}_{3}\left[{\frac {r_{1}-r_{3}\cos(\varphi _{3}-\varphi _{1})}{\Delta (r_{1},r_{3})^{3}}}+{\frac {\cos(\varphi _{3}-\varphi _{1})}{r_{3}^{2}\left(1+p_{3}^{2}\right)^{\frac {3}{2}}}}\right]\\&+{\mathfrak {S}}_{4}\left[{\frac {r_{1}-r_{4}\cos(\varphi _{4}-\varphi _{1})}{\Delta (r_{1},r_{4})^{3}}}+{\frac {\cos(\varphi _{4}-\varphi _{1})}{r_{4}^{2}\left(1+p_{4}^{2}\right)^{\frac {3}{2}}}}\right]\\&+\circledast \ \ \left[{\frac {r_{1}-\rho _{1}\cos(\psi \ -\varphi _{1})}{\delta _{1}^{3}}}+{\frac {\cos(\ \psi \ -\varphi _{1})}{\rho _{1}^{2}}}\right],\\\\\mathrm {Q} _{1}&={\mathfrak {S}}_{2}\left[{\frac {r_{2}\sin(\varphi _{2}-\varphi _{1})}{\Delta (r_{1},r_{2})^{3}}}-{\frac {\sin(\varphi _{2}-\varphi _{1})}{r_{2}^{2}\left(1+p_{2}^{2}\right)^{\frac {3}{2}}}}\right]\\&+{\mathfrak {S}}_{3}\left[{\frac {r_{3}\sin(\varphi _{3}-\varphi _{1})}{\Delta (r_{1},r_{3})^{3}}}-{\frac {\sin(\varphi _{3}-\varphi _{1})}{r_{3}^{2}\left(1+p_{3}^{2}\right)^{\frac {3}{2}}}}\right]\\&+{\mathfrak {S}}_{4}\left[{\frac {r_{4}\sin(\varphi _{4}-\varphi _{1})}{\Delta (r_{1},r_{4})^{3}}}-{\frac {\sin(\varphi _{4}-\varphi _{1})}{r_{4}^{2}\left(1+p_{4}^{2}\right)^{\frac {3}{2}}}}\right]\\&+\circledast \ \ \left[{\frac {r_{4}\sin(\psi \ -\varphi _{1})}{\delta _{1}^{3}}}-{\frac {\sin(\ \psi \ -\varphi _{1})}{\rho _{1}^{2}}}\right],\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ceeea161559c59cd68af543763b33a020c5d58cc)