Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/136

110

MÉCANIQUE CÉLESTE.

$+(1+\mu ''')\left\{{\begin{aligned}-0{,}&0000000478\\+0{,}&0000005487.\cos \ \ (n'''t-n''t+\varepsilon '''-\varepsilon '')\\+0{,}&0000080620.\cos 2(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0{,}&0000006475.\cos 3(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0{,}&0000001643.\cos 4(n'''t-n''t+\varepsilon '''-\varepsilon '')\\\end{aligned}}\right\}$

$+(1+\mu ^{\text{ıv}})\left\{{\begin{aligned}-0{,}&0000011581\\+0{,}&0000159384.\cos \ \ (n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\-0{,}&0000090986.\cos 2(n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\-0{,}&0000006550.\cos 3(n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\-0{,}&0000000704.\cos 4(n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\\end{aligned}}\right\}$

$+(1+\mu ^{2}{\rm {{v}\ )\left\{{\begin{aligned}-0{,}&0000000580\\+0{,}&0000010337.\cos \ \ (n^{2}{\rm {{v}t-n''t+\varepsilon ^{2}{\rm {{v}-\varepsilon '')}}}}\\-0{,}&0000003859.\cos 2(n^{2}{\rm {{v}t-n''t+\varepsilon ^{2}{\rm {{v}-\varepsilon '')}}}}\\\end{aligned}}\right\}}}$

Inégalités dépendantes de la première puissance des excentricités.

$\partial \nu ''=(1+\mu ')\left\{{\begin{aligned}0''{,}&234290.\sin(\ \ n't+\varepsilon '-\varpi '')\\-0''{,}&400233.\sin(2n't-\ \ n''t+2\varepsilon '-\varepsilon ''-\varpi '')\\+0''{,}&448083.\sin(2n''t-\ \ n't+2\varepsilon ''-\varepsilon '-\varpi '')\\-0''{,}&521547.\sin(2n''t-\ \ n't+2\varepsilon ''-\varepsilon '-\varpi ')\\-11''{,}&318247.\sin(3n''t-2n't+3\varepsilon ''-2\varepsilon '-\varpi '')\\+3''{,}&661696.\sin(3n''t-2n't+3\varepsilon ''-2\varepsilon '-\varpi ')\\-7''{,}&231346.\sin(4n''t-3n't+4\varepsilon ''-3\varepsilon '-\varpi '')\\+2''{,}&229704.\sin(4n''t-3n't+4\varepsilon ''-3\varepsilon '-\varpi ')\\+0''{,}&667802.\sin(5n''t-4n't+5\varepsilon ''-4\varepsilon '-\varpi '')\\\end{aligned}}\right\}$

$+(1+\mu ''')\left\{{\begin{aligned}-3''{,}&381490.\sin(2n'''t-\ \ n''t+2\varepsilon '''-\varepsilon ''-\varpi '')\\+wt''{,}&597711.\sin(2n'''t-\ \ n''t+2\varepsilon '''-\varepsilon ''-\varpi ''')\\-0''{,}&269754.\sin(3n'''t-2n''t+3\varepsilon '''-2\varepsilon ''-\varpi '')\\+2''{,}&043057.\sin(3n'''t-2n''t+3\varepsilon '''-2\varepsilon ''-\varpi ''')\\-0''{,}&320240.\sin(4n'''t-3n''t+4\varepsilon '''-3\varepsilon ''-\varpi '')\\+2''{,}&491082.\sin(4n'''t-3n''t+4\varepsilon '''-3\varepsilon ''-\varpi ''')\\-0''{,}&416405.\sin(5n'''t-4n''t+5\varepsilon '''-4\varepsilon ''-\varpi ''')\\\end{aligned}}\right\}$

$+(1+\mu ^{\text{ıv}})\left\{{\begin{aligned}0''{,}&932384.\sin(\ \ n^{\text{ıv}}t+\varepsilon ^{\text{ıv}}-\varpi '')\\-7''{,}&839149.\sin(\ \ n^{\text{ıv}}t+\varepsilon ^{\text{ıv}}-\varpi ^{\text{ıv}})\\-4''{,}&605075.\sin(2n^{\text{ıv}}t-\ \ n''t+2\varepsilon ^{\text{ıv}}-\varepsilon ''-\varpi '')\\+1''{,}&871601.\sin(2n^{\text{ıv}}t-\ \ n''t+2\varepsilon ^{\text{ıv}}-\varepsilon ''-\varpi ^{\text{ıv}})\\-1''{,}&677049.\sin(3n^{\text{ıv}}t-2n''t+3\varepsilon ^{\text{ıv}}-2\varepsilon ''-\varpi ^{\text{ıv}})\\-0''{,}&459646.\sin(2n''\ \ t-\ \ n^{\text{ıv}}t+2\varepsilon ''-\varepsilon ^{\text{ıv}}-\varpi '')\\-0''{,}&289022.\sin(2n''\ \ t-\ \ n^{\text{ıv}}t+2\varepsilon ''-\varepsilon ^{\text{ıv}}-\varpi ^{\text{ıv}})\\\end{aligned}}\right\}$