Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 11.djvu/414

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THÉORIE DES SATELLITES DE JUPITER.

${\begin{alignedat}{2}{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}=&0{,}475958,\qquad \qquad &{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}=&1{,}2008140,\\{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}=&0{,}681198,&{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}=&0{,}329654.\end{alignedat}}$

Premier et quatrième satellites.

$\alpha =0{,}2239857\,;$

${\begin{alignedat}{2}b_{-{\frac {1}{2}}}^{(0)}=&1{,}02516446,\qquad \qquad &b_{-{\frac {1}{2}}}^{(1)}=&-0{,}2225721,\\b_{\frac {1}{2}}^{(0)}\ =&2{,}025818,&b_{\frac {1}{2}}^{(1)}\ =&\quad \ 0{,}228337,\\b_{\frac {1}{2}}^{(2)}\ =&0{,}038441,&b_{\frac {1}{2}}^{(3)}\ =&\quad \ 0{,}007184,\\b_{\frac {1}{2}}^{(4)}\ =&0{,}001413\,;\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}=&0{,}237823,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}=&1{,}059549,\\{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}=&0{,}350753,&{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}=&0{,}097666.\end{alignedat}}$

Deuxième et troisième satellites.

$\alpha =0{,}6268933\,;$

${\begin{alignedat}{2}b_{-{\frac {1}{2}}}^{(0)}=&2{,}20188916,\qquad \qquad &b_{-{\frac {1}{2}}}^{(1)}=&-0{,}5943582,\\b_{\frac {1}{2}}^{(0)}\ =&2{,}257063,&b_{\frac {1}{2}}^{(1)}\ =&\quad \ 0{,}751475,\\b_{\frac {1}{2}}^{(2)}\ =&0{,}360861,&b_{\frac {1}{2}}^{(3)}\ =&\quad \ 0{,}190599,\\b_{\frac {1}{2}}^{(4)}\ =&0{,}105262\,;\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}=&1{,}093010,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}=&1{,}743536,\\{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}=&1{,}444696,&{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}=&1{,}076185.\end{alignedat}}$