Page:Joseph Louis de Lagrange - Œuvres, Tome 7.djvu/528

Pour la Terre.

${\begin{alignedat}{2}(s)=&0,&\left({\frac {ds}{dt}}\right)=&-0''{,}0286+0''{,}1050m+0''{,}0116n,\\(u)=&0,\qquad &\left({\frac {du}{dt}}\right)=&-0''{,}1702-0''{,}3793m-0''{,}0127n.\end{alignedat}}$

Pour Vénus.

${\begin{alignedat}{2}(s)=&11772'',&\left({\frac {ds}{dt}}\right)=&-0''{,}1910+0''{,}0031n,\\(u)=&3259'',\qquad &\left({\frac {du}{dt}}\right)=&0''{,}5264+0''{,}0171n.\end{alignedat}}$

Pour Mars.

${\begin{alignedat}{2}(s)=&4929'',&\left({\frac {ds}{dt}}\right)=&-0''{,}4160-0''{,}0101m,\\(u)=&4482'',\qquad &\left({\frac {du}{dt}}\right)=&0''{,}0471-0''{,}0564m.\end{alignedat}}$

Et de là j’ai trouvé pour la Terre

${\begin{aligned}\left({\frac {d^{2}s}{dt^{2}}}\right)=&0''{,}000001951\\&+0''{,}000035701m+0''{,}000001021n+0''{,}000012221m^{2}\\&+0''{,}000001791mn+0''{,}000000031n^{2},\\\\\left({\frac {d^{2}u}{dt^{2}}}\right)=&0''{,}000001851\\&+0''{,}000008901m+0''{,}000001401n+0''{,}000003381m^{2}\\&+0''{,}000000571mn+0''{,}000000031n^{2}.\end{aligned}}$

Ainsi l’on aura les valeurs suivantes approchées de $\sigma$ et $\upsilon ,$ savoir :

${\begin{aligned}\sigma =&\left(-0''{,}0284+0''{,}1050m+0''{,}0116n\right)t\\&+\left[{\begin{aligned}&0''{,}000000971+0''{,}000017851m+0''{,}0000n0501n\\+&0''{,}000006111m^{2}+0''{,}000000891mn+0''{,}000000021n^{2}\end{aligned}}\right]t^{2},\\\\\upsilon =&\left(-0''{,}1702-0''{,}3593m-0''{,}0127n\right)t\\&+\left[{\begin{aligned}&0''{,}000000921+0''{,}000004451m+0''{,}000000701n\\&0''{,}000001691m^{2}+0''{,}00000028mn+0''{,}000000021n^{2}\end{aligned}}\right]t^{2},\end{aligned}}$