Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 13.djvu/50

Le rayon vecteur $r^{\text{ıv}}$ de Jupiter est donné par la formule

${\begin{aligned}r^{\text{ıv}}=&\quad 5{,}3087333+t.0{,}0000003737\\&-(0{,}249971+t.0.000007932\ \ )\cos \ \ \left(\varphi ^{\text{ıv}}-\omega ^{\text{ıv}}\right)\\&-(0{,}006004+t.0{,}0000003726)\cos 2\left(\varphi ^{\text{ıv}}-\omega ^{\text{ıv}}\right)\\&-(0{,}000217+t.0{,}0000000207)\cos 3\left(\varphi ^{\text{ıv}}-\omega ^{\text{ıv}}\right)\\&-\ \ \qquad \qquad \qquad \qquad 0{,}000010\cos 4\left(\varphi ^{\text{ıv}}-wo^{\text{ıv}}\right)\end{aligned}}$

$+\left\{{\begin{aligned}&0{,}000655\cos \left(\ \ \varphi ^{\text{ıv}}-\ \ \varphi ^{\text{v}}-1^{\circ }{,}4963\right)\\-&0{,}002797\cos \left(2\varphi ^{\text{ıv}}-2\varphi ^{\text{v}}-1^{\circ }{,}1506\right)\\-&0{,}000289\cos \left(3\varphi ^{\text{ıv}}-3\varphi ^{\text{v}}\right)\\-&0{,}000074\cos \left(4\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}\right)\\-&0{,}000026\cos \left(5\varphi ^{\text{ıv}}-5\varphi ^{\text{v}}\right)\\-&0{,}000010\cos \left(6\varphi ^{\text{ıv}}-6\varphi ^{\text{v}}\right)\end{aligned}}\right.$

$+\left\{{\begin{aligned}&-0{,}000265\cos \left(\ \ \varphi ^{\text{ıv}}-2\varphi ^{\text{v}}-24^{\circ }{,}8842+t.58''{,}0\right)\\&-0{,}000096\cos \left(2\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}+56''{,}7419\right)\end{aligned}}\right.$

${\begin{aligned}&-0{,}000883\cos \left(2\varphi ^{\text{ıv}}-3\varphi ^{\text{v}}-69^{\circ }{,}8254+t.81''{,}0\right)\\&-(0{,}002018-t.0{,}0000000505)\cos \left(3\varphi ^{\text{ıv}}-5\varphi ^{\text{v}}+61^{\circ }{,}7749+t.155''{,}6\right)\\&+0{,}000237\cos \left(3\varphi ^{\text{ıv}}-4\varphi ^{\text{v}}-69^{\circ }{,}0565\right)\\&-0{,}000127\cos \left(3\varphi ^{\text{ıv}}-2\varphi ^{\text{v}}-\ \ 8^{\circ }{,}4166\right)\\\end{aligned}}$

$+\left\{{\begin{aligned}&-0{,}000068\cos \left(\ \ \varphi ^{\text{v}}+32^{\circ }{,}4691\right)\\&+0{,}000077\cos \left(2\varphi ^{\text{v}}+12^{\circ }{,}1277\right)\end{aligned}}\right.$

${\begin{aligned}&+0{,}000095\cos \left(4\varphi -5\varphi -15^{\circ }{,}9873\right)\\&-0{,}000265\cos \left(5\varphi -2\varphi -13^{\circ }{,}4950\right).\end{aligned}}$

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

${\begin{aligned}(14638''{,}3&-t.0''{,}69412)\sin \left(\mathrm {V} ^{\text{ıv}}-\theta ^{\text{ıv}}\right)\\&-\ \ 1''{,}66\sin \left(\ \ \quad \qquad \varphi ^{\text{v}}+60^{\circ }{,}4440\right)\\&+\ \ 1''{,}96\sin \left(\ \ \varphi ^{\text{ıv}}-2\varphi ^{\text{v}}-60^{\circ }{,}4440\right)\\&+\ \ 3''{,}30\sin \left(2\varphi ^{\text{ıv}}-3\varphi ^{\text{v}}-60^{\mathrm {m} }{,}4440\right)\\&+11''{,}61\sin \left(3\varphi ^{\text{ıv}}-5\varphi ^{\text{v}}+66^{\circ }{,}1219\right).\end{aligned}}$