Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 11.djvu/416

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THÉORIE DES SATELLITES DE JUPITER.

Premier satellite.

${\begin{aligned}\delta r=&\quad \ 0{,}000466995m'\cos \ \ (nt-n't+\varepsilon -\varepsilon ')\\&-0{,}09968077\ \ m'\cos 2(nt-n't+\varepsilon -\varepsilon ')\\&-0{,}000408870m'\cos 3(nt-n't+\varepsilon -\varepsilon '),\\\\\delta v=&-\quad 60''{,}687\quad m'\sin \ \ (nt-n't+\varepsilon -\varepsilon ')\\&+7185''{,}05\quad \ \ m'\sin 2(nt-n't+\varepsilon -\varepsilon ')\\&+\quad 22''{,}9407\ \ m'\sin 3(nt-n't+\varepsilon -\varepsilon ').\end{aligned}}$

Deuxième satellite.

${\begin{aligned}\delta r'=&\quad \ 0{,}05128288\quad m\ \ \cos \ \ (nt\ -n't\ +\varepsilon \ -\varepsilon ')\\&+0{,}0005917397m\ \ \cos 2(nt\ -n't\ +\varepsilon \ -\varepsilon ')\\&+0{,}0001399405m\ \ \cos 3(nt\ -n't\ +\varepsilon \ -\varepsilon ')\\&+0{,}0007321374m''\cos \ \ (n't-n''t+\varepsilon '-\varepsilon '')\\&-0{,}0879380\quad \ \ m''\cos 2(n't-n''t+\varepsilon '-\varepsilon '')\\&-0{,}0006339091m''\cos 3(n't-n''t+\varepsilon '-\varepsilon ''),\\\\\delta v'=&-2279''{,}40\qquad m\ \ \sin \ \ (nt\ -n't\ +\varepsilon \ -\varepsilon ')\\&-\quad 17''{,}0497\quad m\ \ \sin 2(nt\ -n't\ +\varepsilon \ -\varepsilon ')\\&-\quad \ \ 3''{,}4090\quad m\ \ \sin 3(nt\ -n't\ +\varepsilon \ -\varepsilon ')\\&-\quad 59''{,}766\quad \ \ m''\sin \ \ (n't-n''t+\varepsilon '-\varepsilon '')\\&+3979''{,}83\qquad m''\sin 2(n't-n''t+\varepsilon '-\varepsilon '')\\&+\quad 22''{,}321\quad \ \ m''\sin 3(n't-n''t+\varepsilon '-\varepsilon '').\end{aligned}}$

Troisième satellite.

${\begin{aligned}\delta r''=&\quad \ 0{,}0414925\quad \ \ m'\ \ \cos \ \ (n't\,-n''t+\varepsilon '\ -\varepsilon '')\\&+0{,}000917144\ \ m'\ \ \cos 2(n't\,-n''t+\varepsilon '\ -\varepsilon '')\\&+0{,}000217082\ \ m'\ \ \cos 3(n't\,-n''t+\varepsilon '\ -\varepsilon '')\\&+0{,}0007621007m'''\cos \ \ (n''t-n'''t+\varepsilon ''-\varepsilon ''')\\&-0{,}00449712\quad m'''\cos 2(n''t-n'''t+\varepsilon ''-\varepsilon ''')\\&-0{,}00039794\quad m'''\cos 3(n''t-n'''t+\varepsilon ''-\varepsilon '''),\\\\\delta v''=&-1130''{,}33\qquad m'\ \ \sin \ \ (n't\,-n''t\ +\varepsilon '-\varepsilon '')\\&-\quad 16''{,}5039\quad m'\ \ \sin 2(n't\,-n''t\ +\varepsilon '-\varepsilon '')\\&-\quad \ \ 3''{,}3067\quad m'\ \ \sin 3(n't\,-n''t\ +\varepsilon '-\varepsilon '')\\&-\quad 34''{,}4108\quad m'''\sin \ \ (n''t-n'''t+\varepsilon ''-\varepsilon ''')\\&+\ \ 117''{,}360\quad \ \ m'''\sin 2(n''t-n'''t+\varepsilon ''-\varepsilon ''')\\&+\quad \ \ 8''{,}24894\ \ m'''\sin 3(n''t-n'''t+\varepsilon ''-\varepsilon ''')\\\end{aligned}}$