Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/122

jupiter.

${\begin{alignedat}{4}{\frac {d\varpi ^{\rm {iv}}}{dt}}=&20''{,}369659&+&0''{,}000574.\mu &+&0''{,}013364.\mu '&+&0''{,}030362.\mu ''\\&&+&0''{,}006319.\mu '''&+&19''{,}931701.\mu .^{\rm {v}}&+&0''{,}387339.\mu .^{\rm {vi}},\\\\2{\frac {de^{\rm {iv}}}{dt}}=&1''{,}711168&-&0''{,}000024.\mu &+&0''{,}000028.\mu '&+&0''{,}000244.\mu ''\\&&-&{,}000588.\mu '''&+&1''{,}707742.\mu .^{\rm {v}}&+&0''{,}003766.\mu .^{\rm {vi}},\\\\{\frac {d\varphi ^{\rm {iv}}}{dt}}=&-0''{,}241174&+&0''{,}000068.\mu &+&0''{,}000313.\mu '&+&0''{,}000346.\mu '''\\&&-&0''{,}243621.\mu .^{\rm {v}}&+&0''{,}001720.\mu .^{\rm {vi}},\\\\{\frac {d\varphi _{\text{ı}}^{\rm {iv}}}{dt}}=&-0''{,}688820&-&0''{,}029292.\mu &-&0''{,}395414.\mu '&-&0''{,}032856.\mu '''\\&&-&0''{,}232852.\mu .^{\rm {v}}&+&0''{,}001594.\mu .^{\rm {vi}},\\\\{\frac {d\theta ^{\rm {iv}}}{dt}}=&19''{,}926792&+&0''{,}001570.\mu &+&0''{,}018076.\mu '&-&0''{,}030439.\mu ''\\&&-&0''{,}001423.\mu '''&+&20''{,}078923.\mu .^{\rm {v}}&-&0''{,}139915.\mu .^{\rm {vi}},\\\\{\frac {d\theta _{\text{ı}}^{\rm {iv}}}{dt}}=&-45''{,}257336&-&0''{,}976008.\mu &-&39''{,}594863.\mu '&-&0''{,}030439.\mu ''\\&&-&1''{,}201089.\mu '''&-&21''{,}444015.\mu .^{\rm {iv}}&+&18''{,}140621.\mu .^{\rm {v}}\\&&-&0''{,}151543.\mu .^{\rm {vi}}.\end{alignedat}}$

saturne.

${\begin{alignedat}{4}{\frac {d\varpi ^{\rm {v}}}{dt}}=&49''{,}730637&+&0''{,}000068.\mu &+&0''{,}001531.\mu '&+&0''{,}003334.\mu ''\\&&+&0''{,}001697.\mu '''&+&48''{,}737068.\mu .^{\rm {iv}}&+&0''{,}986939.\mu .^{\rm {vi}},\\\\2{\frac {de^{\rm {v}}}{dt}}=&-3''{,}334597&-&0''{,}000000.\mu &+&0''{,}000001.\mu '&+&0''{,}000002.\mu ''\\&&-&0''{,}000048.\mu '''&-&3''{,}394812.\mu .^{\rm {iv}}&+&0''{,}060260.\mu .^{\rm {vi}},\\\\{\frac {d\varphi ^{\rm {v}}}{dt}}=&-0''{,}307841&+&0''{,}000009.\mu &+&0''{,}000055.\mu '&+&0''{,}000043.\mu '''\\&&+&0''{,}298443.\mu .^{\rm {iv}}&+&0''{,}009291.\mu .^{\rm {vi}},\\\\{\frac {d\varphi _{\text{ı}}^{\rm {v}}}{dt}}=&-0''{,}479290&-&0''{,}033813.\mu &-&0''{,}598513.\mu '&-&0''{,}038709.\mu '''\\&&+&0''{,}182639.\mu .^{\rm {iv}}&+&0''{,}009106.\mu .^{\rm {vi}},\\\\{\frac {d\theta ^{\rm {v}}}{dt}}=&-27''{,}794110&+&0''{,}000011.\mu &+&0''{,}000130.\mu '&-&0''{,}003467.\mu ''\\&&-&0''{,}000996.\mu '''&-&26''{,}957559.\mu .^{\rm {iv}}&-&0''{,}832229.\mu .^{\rm {vi}},\\\\{\frac {d\theta _{\text{ı}}^{\rm {v}}}{dt}}=&-58''{,}770060&-&0''{,}342473.\mu &-&18''{,}158175.\mu '&-&0''{,}003467.\mu ''\\&&-&0''{,}436463.\mu '''&-&37''{,}941234.\mu .^{\rm {iv}}&-&1''{,}050744.\mu .^{\rm {v}}\\&&-&0''{,}837504.\mu .^{\rm {vi}}.\end{alignedat}}$