Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 11.djvu/420

406

THÉORIE DES SATELLITES DE JUPITER.

Enfin, on aura

${\begin{alignedat}{3}{\begin{array}{|c|}\hline 0,\ 1\\\hline \end{array}}=&9554''{,}90m',&{\begin{array}{|c|}\hline 0,\ 2\\\hline \end{array}}=&\ \ 812''{,}96m'',&{\begin{array}{|c|}\hline 0,\ 3\\\hline \end{array}}=&\quad 69''{,}10m''',\\{\begin{array}{|c|}\hline 1,\ 0\\\hline \end{array}}=&7574''{,}52m,\quad &{\begin{array}{|c|}\hline 1,\ 2\\\hline \end{array}}=&4686''{,}58m'',\quad &{\begin{array}{|c|}\hline 1,\ 3\\\hline \end{array}}=&\ \ 256''{,}06m''',\\{\begin{array}{|c|}\hline 2,\ 0\\\hline \end{array}}=&\ \ 510''{,}26m,&{\begin{array}{|c|}\hline 2,\ 1\\\hline \end{array}}=&3710''{,}67m',&{\begin{array}{|c|}\hline 2,\ 3\\\hline \end{array}}=&1294''{,}22m''',\\{\begin{array}{|c|}\hline 3,\ 0\\\hline \end{array}}=&\quad 32''{,}70m,&{\begin{array}{|c|}\hline 3,\ 1\\\hline \end{array}}=&\ \ 152''{,}87m',&{\begin{array}{|c|}\hline 3,\ 2\\\hline \end{array}}=&\ \ 975''{,}87m''.\end{alignedat}}$

Les équations (I) de l’article XV deviendront ainsi

(Q)

$\left\{{\begin{aligned}0&=h(f-259072''{,}62\mu -33''{,}46-12893''{,}96m'-1685''{,}25m''\\&-248''{,}38m'')+9554''{,}90m'h'+812''{,}96m''h''\\&+69''{,}10m'''h'''-m'h{\frac {263465''m+166781''m'}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}}\\\\&+m'h'{\frac {95537''m+60478''m'-81843''m''}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}}+{\frac {29915''m'm''h''}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}},\\0&=h'(f-50971''{,}27\mu -67''{,}16-10221''{,}52m-6337''{,}75m''\\&-584''{,}40m'')+7574''{,}52mh+4686''{,}58m''h''+256''{,}06m'''h'''\\&+mh{\frac {75736''m+47943''m'-64880''m''}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}}\\&-h'{\frac {\begin{aligned}27463''m^{2}&+17385''mm'-47054''mm''\\&+31682''m'm''+20154''m''^{2}\end{aligned}}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}}\\&+m''h''{\frac {-8599''{,}3m+11580''m'+7366{,}7m''}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}},\\\\0&=h''(f-9942''{,}67\mu -135''{,}31-1057''{,}77m-5018''{,}01m'\\&-1907''14m'')+510''{,}26mh+3710''{,}67m'h'+1294''{,}22m'''h'''\\&+{\frac {18777''mm'h}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}}-m'h'{\frac {6808''{,}6m-9168''{,}9m'-5832''{,}7m''}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}}\\&-m'h''{\frac {3351''{,}4m'+2131''{,}9m''}{\left(1+{\cfrac {f}{973254''}}\right)^{2}}},\\\\0&=h'''(f-1377''{,}82\mu -315''{,}64-117''{,}55m-348''{,}89m'\\&-1438''{,}02m'')+32''{,}70mh+152''{,}87m'h'+975''{,}87m''h''.\end{aligned}}\right.$