Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/694

51. Faisant donc toutes ces substitutions dans les formules générales (49), on trouvera les expressions suivantes

Pour la Terre.

${\begin{aligned}s_{2}=\quad \ 0{,}028127&+0{,}002685\cos(25''{,}337t)+0{,}001910\sin(25''{,}337t)\\&+0{,}001484\cos \left(\ \ 5''{,}980t\right)-0{,}015857\sin \left(\ \ 5''{,}980t\right)\\&-0{,}032068\cos(19''{,}798t)+0{,}007063\sin(19''{,}798t)\\&-0{,}000229\cos(18''{,}308t)-0{,}000296\sin(18''{,}308t),\\\\u_{2}=-0{,}007180&-0{,}001910\cos(25''{,}337t)+0{,}002685\sin(25''{,}337t)\\&+0{,}015857\cos \left(\ \ 5''{,}980t\right)+0{,}001484\sin \left(\ \ 5''{,}980t\right)\\&-0{,}007063\cos(19''{,}798t)-0{,}032068\sin(19''{,}798t)\\&+0{,}000296\cos(18''{,}308t)-0{,}000229\sin(18''{,}308t)\,;\end{aligned}}$

Pour Vénus.

${\begin{aligned}s_{3}=\quad \ 0{,}028127&-0{,}000228\cos(25''{,}337t)-0{,}000162\sin(2\%{,}3374,\\&+0{,}001839\cos \left(\ \ 5''{,}980t\right)-0{,}019653\sin \left(\ \ 5''{,}980t\right)\\&+0{,}025447\cos(19''{,}798t)-0{,}005604\sin(19''{,}798t)\\&+0{,}001884\cos(18''{,}308t)+0{,}002438\sin(18''{,}308t),\\\\u_{3}=-0{,}007180&+0{,}000162\cos(25''{,}337t)-0{,}000228\sin(25''{,}337t)\\&+0{,}019653\cos \left(\ \ 5''{,}980t\right)+0{,}001839\sin \left(\ \ 5''{,}980t\right)\\&+0{,}005604\cos(19''{,}708t)+0{,}025447\sin(19''{,}798t)\\&-0{,}002438\cos(18''{,}308t)+0{,}001884\sin(18''{,}308t)\,;\end{aligned}}$

Pour Mars.

${\begin{aligned}s_{4}=-0{,}028127&+0{,}008754\cos(25''{,}337t)+0{,}006227\sin(25''{,}337t)\\&+0{,}000472\cos \left(\ \ 5''{,}980t\right)-0{,}005043\sin \left(\ \ 5''{,}980t\right)\\&+0{,}008380\cos(19''{,}798t)-0{,}001846\sin(19''{,}798t)\\&-0{,}021836\cos(18''{,}308t)-0{,}028249\sin(18''{,}308t),\\\\u_{4}=-0{,}007180&-0{,}006227\cos(25''{,}337t)+0{,}008754\sin(25''{,}337t)\\&+0{,}005043\cos \left(\ \ 5''{,}980t\right)+0{,}000472\sin \left(\ \ 5''{,}980t\right)\\&+0{,}001846\cos(19''{,}798t)+0{,}008380\sin(19''{,}798t)\\&+0{,}028249\cos(18''{,}308t)-0{,}021836\sin(18''{,}308t).\end{aligned}}$