139
RELATIONS ENTRE PLUSIEURS POSITIONS DANS L’ORBITE.
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Nous avons ensuite,
.
La valeur approchée de
est donc
, à laquelle répond,
dans notre table II,
. On a donc
![{\displaystyle \log {\frac {m^{2}}{y^{2}}}=7,2715132}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f61410456450e43cb1cb878c7256f511cefd140)
,
ou
![{\displaystyle {\frac {m^{2}}{y^{2}}}=0,001868587}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4d770887aaf4343d7611dbbc7bd6c3dc6bdb500)
;
d’où, par la formule 16, on a
: c’est pourquoi,
puisque
se trouve, par la table III, entièrement insensible, les valeurs trouvées pour
,
,
n’exigent aucune correction. Maintenant,
la détermination des éléments se fait de la manière suivante :
C’est pourquoi, d’après les formules 27, 28, 29, 30, on a
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![{\displaystyle \dots }](https://wikimedia.org/api/rest_v1/media/math/render/svg/5411a9d9722322917df8faecb6e01b72e3ecede4) |
7,6916214![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) |
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![{\displaystyle \mathrm {c^{t}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cad68c77647f742f303bffae97fa2c4ea2376ea) |
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![{\displaystyle \dots }](https://wikimedia.org/api/rest_v1/media/math/render/svg/5411a9d9722322917df8faecb6e01b72e3ecede4) |
0,0000052
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9,9992065 |
|
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8,7810188
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9,9999929 |
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7,7579709
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7,6908279![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) |
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7,6916143
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8,7810240 |
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![{\displaystyle \log \mathrm {Q} \cos {\tfrac {1}{2}}(\mathrm {F} +\mathrm {G} )\,...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b55bedf5c6af10dbc5b8093f456907de1e84fe0d) |
7,7579761
|
![{\displaystyle {\tfrac {1}{2}}(\mathrm {F} -\mathrm {G} )\quad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/62b565475caadc1ab02b693a4523e37e1b01bcf3) |
— 4° 38′ 41,54″ |
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![{\displaystyle \log \mathrm {P} =\log \mathrm {R} \cos {\tfrac {1}{2}}\varphi ..}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffef98b5392cc246397935f447a70f36f7b85efe) |
8,7824527
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![{\displaystyle {\tfrac {1}{2}}(\mathrm {F} +\mathrm {G} )\quad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae3e8aac971692b1522c83ff868b7dd503f776aa) |
319° 21′ 38,05″ |
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![{\displaystyle \log \mathrm {Q} =\log \mathrm {R} \sin {\tfrac {1}{2}}\varphi ..}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b310488fe46ad0b20dd3e3b3dbb1dbeeb8b69358) |
7,8778355
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![{\displaystyle \mathrm {F} \,\qquad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a226b82e0e52f0325bde68a96926b040ae0966c4) |
314° 42′ 56,51″ |
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De là ![{\displaystyle \;\;{\tfrac {1}{2}}\varphi \;\;=\;\;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3875ef2c9e370cee5b4b5bea640956b8cc9e0ed2) |
07° 06′ 0,935″
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![{\displaystyle v\,\qquad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/99e223355ea49e3dbd065ffd3ba28ebf8db8facd) |
310° 55′ 29,64″ |
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![{\displaystyle \varphi \;\;=\;\;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd96efdf9160b9ff41555145f39d9e3182a8bc1) |
14° 12′ 1,87″0
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![{\displaystyle v'\qquad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/64daf0012ed6903dff28d05c5aab0be688f7cb8f) |
318° 30′ 23,37″ |
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8,7857960
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![{\displaystyle \mathrm {G} \,\qquad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/541b56d750c96a1ac89bd2974672250a26483af3) |
324° 00′ 19,59″ |
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Pour confirmer le calcul :
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![{\displaystyle \mathrm {E} \,\qquad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ded2d5098169f3825fb15c0239457185acea892) |
320° 52′ 15,53″ |
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0,1500394
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![{\displaystyle \mathrm {E} '\qquad =\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/615bf91b134443d45559315b8653c99940f01791) |
327° 08′ 23,65″ |
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![{\displaystyle \log(l+x)=\log {\frac {m}{y}}..}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ffd89a537dd39a8f1094419768d833728a3b9a3) |
8,6357566
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8,7857960
|