Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 13.djvu/52

${\begin{aligned}&-84''{,}47\sin \left(2\varphi ^{\text{v}}-3\varphi ^{\text{vı}}+26^{\circ }{,}59\right)\\&+30''{,}43\sin \left(\ \ \varphi ^{\text{v}}-2\varphi ^{\text{vı}}+80^{\circ }{,}22\right)\\&+\ \ 4''{,}20\sin \left(\ \ \quad \qquad \varphi ^{\text{vı}}-46^{\circ }{,}26\right)\\&+\ \ 4''{,}70\sin(3\varphi ^{\text{v}}-2\varphi ^{\text{vı}}-97^{\circ }{,}95).\end{aligned}}$

Le rayon vecteur $r^{\text{v}}$ de Saturne est

${\begin{aligned}r^{\text{v}}=&\quad 9{,}5578331+t.0{,}00000167\\&-(0{,}536467-t.0{,}00002963)\cos \ \ \left(\varphi ^{\text{v}}-\omega ^{\text{v}}\right)\\&-(0{,}016090-t.0{,}00000167)\cos 2\left(\varphi ^{\text{v}}-\omega ^{\text{v}}\right)\\&-(0{,}000639-t.0{,}00000011)\cos 3\left(\varphi ^{\text{v}}-\omega ^{\text{v}}\right)\\&-\ 0{,}000032\cos 4\left(\varphi ^{\text{v}}-\omega ^{\text{v}}\right)\\&-\ 0{,}000340\cos 4\left(\varphi ^{\text{v}}-11^{\circ }{,}50\right)\end{aligned}}$

$+\left\{{\begin{aligned}&0{,}00811\cos \left(\ \ \varphi ^{\text{ıv}}-\ \ \varphi ^{\text{v}}+4^{\circ }{,}40\right)\\+&0{,}00138\cos \left(2\varphi ^{\text{ıv}}-2\varphi ^{\text{v}}\right)\\+&0{,}00032\cos \left(3\varphi ^{\text{ıv}}-3\varphi ^{\text{v}}\right)\\+&0{,}00010\cos \left(4\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}\right)\\+&0{,}00004\cos \left(5\varphi ^{\text{ıv}}-5\varphi ^{\text{v}}\right)\\+&0{,}00001\cos \left(6\varphi ^{\text{ıv}}-6\varphi ^{\text{v}}\right)\\\end{aligned}}\right.$

${\begin{aligned}&+(0{,}00535+t.0{,}00000027)\cos \left(\ \ \varphi ^{\text{ıv}}-2\varphi ^{\text{v}}-13^{\circ }{,}2952+t.45''{,}5\right)\\&+(0{,}01520-t.0{,}00000034)\cos \left(2\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}+62^{\circ }{,}2324+t.151''{,}4\right)\\&+0{,}00117\cos \left(3\varphi ^{\text{v}}-\ \ \varphi ^{\text{ıv}}-100^{\circ }{,}2330\right)\\&-0{,}00138\cos \left(2\varphi ^{\text{ıv}}-3\varphi ^{\text{v}}-\ \ 25^{\circ }{,}9130\right)\\&-0{,}00022\cos \left(3\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}-\ \ 68^{\circ }{,}1717\right)\\&+0{,}00352\cos \left(5\varphi ^{\text{v}}-2\varphi ^{\text{ıv}}+14^{\circ }{,}4782\right)\end{aligned}}$

$+\left\{{\begin{aligned}&0{,}00015\cos \ \ \left(\ \ \varphi ^{\text{v}}-\ \ \varphi ^{\text{vı}}\right)\\-&0{,}00040\cos 2\left(\ \ \varphi ^{\text{v}}-\ \ \varphi ^{\text{vı}}\right)\\-&0{,}00005\cos 3\left(2\varphi ^{\text{v}}-3\varphi ^{\text{vı}}\right)\\\end{aligned}}\right.$

$-\qquad 0{,}00061\cos \left(2\varphi ^{\text{v}}-3\varphi ^{\text{vı}}+26^{\circ }{,}37\right)$

Enfin la latitude de Saturne au-dessus de l’écliptique vraie est

${\begin{aligned}(27748''{,}2&-t.0''{,}478816)\sin \left(\mathrm {V} ^{\text{v}}-\theta ^{\text{v}}\right)\\&-\ \qquad 2''{,}19\sin 3\left(\mathrm {V} ^{\text{v}}-\theta ^{\text{v}}\right)\\&+\ \ 5''{,}52\sin \left(\ \ \varphi ^{\text{ıv}}+60^{\circ }{,}29\right)\\&-\ \ 9''{,}70\sin \left(\ \ \varphi ^{\text{ıv}}-2\varphi ^{\text{v}}-60^{\circ }{,}29\right)\\&-28''{,}28\sin \left(2\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}+66^{\circ }{,}12\right).\end{aligned}}$