![{\displaystyle (2)\left\{{\begin{aligned}367^{\mathrm {m} }{,}468=&56{,}879696.1{,}022486.2\mathrm {A} '{\frac {\mathrm {L} '}{r'^{3}}}+54{,}260856.2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}\\+&3{,}333442.2(\mathrm {A'-B} ).1{,}022486{\frac {\mathrm {L} '}{r'^{3}}}+4{,}685805.2(\mathrm {A-B} ){\frac {\mathrm {L} }{r^{3}}},\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff3d6bb82f147d9c1fb4b29efe8774e1434df860)
![{\displaystyle (3)\left\{{\begin{aligned}160^{\mathrm {m} }{,}850=&56{,}962913.0{,}977514.2\mathrm {A} '{\frac {\mathrm {L} '}{r'^{3}}}-63{,}635484.2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}\\+&3{,}267165.0{,}977514.2(\mathrm {A'-B} ).{\frac {\mathrm {L} '}{r'^{3}}}+4{,}667171.2(\mathrm {A-B} ){\frac {\mathrm {L} }{r^{3}}},\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/404d3ac2af909a9ae3bfda116f8d20833270852d)
![{\displaystyle (4)\left\{{\begin{aligned}203^{\mathrm {m} }{,}948=&63{,}497242.0{,}977514.2\mathrm {A} '{\frac {\mathrm {L} '}{r'^{3}}}-54{,}301142.2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}\\-&3{,}267165.0{,}977514.2(\mathrm {A'-B} ).{\frac {\mathrm {L} '}{r'^{3}}}-4{,}667171.2(\mathrm {A-B} ){\frac {\mathrm {L} }{r^{3}}}.\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ba4c533d61a4accad5639b9be61a98105cf49612)
Dans toutes ces équations, les valeurs
et
sont relatives aux moyennes distances de la Lune et du Soleil à la Terre.
Le système
des équations précédentes donne
![{\displaystyle (5)\qquad 778^{\mathrm {m} }{,}708=120{,}426277.1{,}022486.2\mathrm {A} '{\frac {\mathrm {L} '}{r'^{3}}}+117{,}893323.2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5ced69233b5798952eb89b307d0b678edab3374)
le système des équations
donne
![{\displaystyle (6)\qquad 364^{\mathrm {m} }{,}798=120{,}460155.0{,}977514.2A'{\frac {\mathrm {L} '}{r'^{3}}}-117{,}936626.2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/601899dc4c7198c8701670f7216bde5026501a80)
De ces deux équations on tire
![{\displaystyle 2\mathrm {A} '{\frac {\mathrm {L} '}{r'^{3}}}=4^{\mathrm {m} }{,}74788,\qquad 2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}=1^{\mathrm {m} }{,}64658.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c20dfeb1d3e52ee1811f0e09047a67d1baf4db75)
Le système des équations
donne
![{\displaystyle (7)\left\{{\begin{aligned}43^{\mathrm {m} }{,}891=&6{,}666885.1{,}022486.2\mathrm {A} '{\frac {\mathrm {L} '}{r'^{3}}}\qquad \quad \ \ +9{,}371611.2\mathrm {A} {\frac {\mathrm {L} }{r^{3}}}\\-&6{,}666885.1{,}022486.2\mathrm {{\frac {A'-B}{A'}}A'} {\frac {\mathrm {L} '}{r'^{3}}}-9{,}371611.2\mathrm {{\frac {A-B}{A}}A} {\frac {\mathrm {L} }{r^{3}}}\,;\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f5d73447a9068fb47c74d4c3a7576faabb3f2ed)