Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/265

Variations annuelles des inclinaisons sur l’écliptique vraie.

${\begin{aligned}{\frac {d\vartheta \ \ \ }{dt}}=&0''{,}0589m'-0''{,}0125m''-0''{,}2665m^{\scriptscriptstyle {\text{IV}}}-0''{,}0110m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\vartheta '\ \ }{dt}}=&-0''{,}0751m-0''{,}0106m''-0''{,}1767m^{\scriptscriptstyle {\text{IV}}}-0''{,}0095m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\vartheta ''\ }{dt}}=&-0''{,}0125m-0''{,}1320m'+0''{,}1795m^{\scriptscriptstyle {\text{IV}}}-0/''{,}0005m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\vartheta ^{\scriptscriptstyle {\text{IV}}}}{dt}}=&0''{,}0035m+0''{,}0260m'-0''{,}0042m''+0''{,}0194m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\vartheta ^{\scriptscriptstyle {\text{V}}}\ }{dt}}=&0''{,}0104m+0''{,}0987m'+0''{,}0006m''+0''0946m^{\scriptscriptstyle {\text{IV}}}.\end{aligned}}$

Mouvements annuels des nœuds sur l’écliptique fixe de 1700.

${\begin{aligned}{\frac {d\omega \ \ \ }{dt}}=&-8''{,}7194m'-0''{,}0003m''-0''{,}0010m''',\\{\frac {d\omega '\ \ }{dt}}=&6''{,}5036m-0''{,}0004m''-0''{,}0089m'''+0''{,}0080m^{\scriptscriptstyle {\text{IV}}}-0''{,}0005m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\omega ''\ }{dt}}=&-0''{,}2632m-7''{,}8276m'-1''{,}7724m'''+0''{,}4326m^{\scriptscriptstyle {\text{IV}}}+0''{,}0506m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\omega ^{\scriptscriptstyle {\text{IV}}}}{dt}}=&-0{,}0853m-2''{,}6588m'-0''{,}0759m''-6''{,}6908m'''+0''{,}3402m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\omega ^{\scriptscriptstyle {\text{V}}}\ }{dt}}=&-0''{,}0691m-1''{,}3968m'-0''{,}0292m''-0''{,}8696m'''-2''{,}4278m^{\scriptscriptstyle {\text{IV}}}.\end{aligned}}$

Variations annuelles des inclinaisons sur l’écliptique fixe de 1700.

${\begin{aligned}{\frac {d\theta \ \ \ }{dt}}=&0''{,}0963m',\\{\frac {d\theta '\ \ }{dt}}=&-0''{,}0786m+0''{,}0001m''+0''{,}0001m^{\scriptscriptstyle {\text{IV}}},\end{aligned}}$