Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/263

$+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[{\rm {B}}_{2}^{(2)}-2+(1-m)(3-2m-g){\rm {B}}_{1}^{(0)}\right]$

$\times e\gamma \sin(gv+cv-\theta -\varpi )$

$+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[{\rm {B}}_{2}^{(3)}-2-2{\rm {A}}_{1}^{(1)}+(1+m)(3-2m-g){\rm {B}}_{1}^{(0)}\right]$

$\times e\gamma \sin(gv-cv-\theta +\varpi )$

$+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[(1+g)(1-m)-2{\rm {B_{1}^{(0)}+B_{2}^{(1)}}}\right]$

$\times e\gamma \sin(2v-2mv-gv+cv+\theta -\varpi )$

$+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[(g-1)(1+m)+{\rm {B_{2}^{(5)}-2A_{1}^{(1)}}}\right]$

$\times e\gamma \sin(2v-2mv+gv-cv+\theta +\varpi )$

$+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[(1+g)(1+m)+{\rm {B_{2}^{(6)}+2A_{1}^{(1)}-2B_{1}^{(0)}}}\right]$

$\times e\gamma \sin(2v-2mv-gv-cv+\theta +\varpi )$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[3+2{\rm {B}}_{1}^{(7)}+{\frac {1}{2}}(3-2m-g){\rm {B}}_{1}^{(0)}-(3-3m-g){\rm {B}}_{1}^{(10)}\right]$

$\times e'\gamma \sin(gv+c'mv-\theta -\varpi ')$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[3+2{\rm {B}}_{1}^{(8)}+{\frac {7}{2}}(3-2m-g){\rm {B}}_{1}^{(0)}-(3-m-g){\rm {B}}_{1}^{(9)}\right]$

$\times e'\gamma \sin(gv-c'mv-\theta +\varpi ')$

$+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[{\frac {1+g}{2}}+2{\rm {B}}_{1}^{(9)}+3{\rm {B}}_{1}^{(0)}-(1+g-m){\rm {B}}_{1}^{(8)}\right]$

$\times e'\gamma \sin(2v-2mv-gv+c'mv+\theta -\varpi ')$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left[2{\rm {B}}_{1}^{(10)}-{\frac {7}{2}}(1+g)+3{\rm {B}}_{1}^{(0)}-(1+g-m){\rm {B}}_{1}^{(7)}\right]$

$\times e'\gamma \sin \left({\begin{aligned}&2v-2mv-gv\\&\ -c'mv+\theta +\varpi '\end{aligned}}\right)$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left\{{\begin{aligned}&2{\rm {B}}_{1}^{(11)}-5-10{\rm {A}}_{1}^{(1)}+4{\rm {A}}_{1}^{(11)}-(3-2m-2c+g){\rm {B}}_{1}^{(12)}\\&\ +\left[{\frac {3-2m-g}{4}}+{\frac {(2-2m-g)^{2}-1}{2(2c+2m-2)}}\right]\\&\qquad \qquad \times \left(10+19m+8m^{2}\right){\rm {B}}_{1}^{(0)}\end{aligned}}\right\}$

$\times e^{2}\gamma \sin(2cv-gv-2\varpi +\theta )$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left\{{\begin{aligned}&2{\rm {B}}_{1}^{(12)}+(1-g){\frac {10+19m+8m^{2}}{4}}\\&\ +10{\rm {A}}_{1}^{(1)}-4{\rm {A}}_{1}^{(11)}-2{\rm {B}}_{0}^{(11)}\end{aligned}}\right\}$

$\times e^{2}\gamma \sin(2v-2mv-2cv+gv+2\varpi -\theta )$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {10+19m+8m^{2}}{2}}+2{\rm {B_{1}^{(13)}}}\\&\ +10{\rm {A_{1}^{(1)}-4A_{1}^{(11)}-5B_{1}^{(0)}}}\end{aligned}}\right\}$

$\times e^{2}\gamma \sin(2cv+gv-2v+2mv-2\varpi -\theta )$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left(3+2{\rm {B}}_{2}^{(14)}\right){\frac {a}{a'}}\gamma \sin(gv-v+mv-\theta )$

$+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}\left({\frac {5}{2}}+2{\rm {B}}_{2}^{(15)}\right){\frac {a}{a'}}\gamma \sin(gv+v-mv-\theta ).$

14. On doit faire, sur l’intégration de l’équation différentielle précédente, des remarques analogues à celles du n^o 11. On considérera donc $\gamma$ et $\theta$ comme variables en vertu de la variation de l’excentricité de l’orbe terrestre ; en substituant ensuite, pour $s,$ la fonc-