379
MÉTHODE D’OLBERS.
Détermination des anomalies vraies.
![{\displaystyle {\begin{aligned}\operatorname {tang} z&=\left({\frac {r}{r''}}\right)^{\frac {1}{2}},&\operatorname {tang} {\frac {1}{4}}(v''\!+v)&=\operatorname {tang} (45^{\circ }\!-z)\operatorname {cotang} {\frac {1}{4}}(v''\!-v).\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a35298464772ca5f1338d53eaaae04feff5b358f)
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1,544824 |
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6° 7′ 17,2″ |
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0.969612
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![{\displaystyle \mathrm {c^{t}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cad68c77647f742f303bffae97fa2c4ea2376ea) |
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0,351337 |
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![{\displaystyle 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/901fc910c19990d0dbaaefe4726ceb1a4e217a0f) |
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1,896161 |
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![{\displaystyle \log \operatorname {tang} (45^{\circ }\!\!-z).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/effe7baebedd4ad16261acb71bcd9febb8f8f102) |
2,775995
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1,948080 |
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![{\displaystyle \log \operatorname {tang} {\frac {v''\!+v}{4}}...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d49b0d7cc830602655cc3cdf921209deb48a1c7) |
1,745607
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![{\displaystyle z={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/849e6b6e731029d74915b222f32df01e36b7f3a2) |
41° 35′ 00″ |
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45° |
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![{\displaystyle {\frac {v''\!+v}{4}}={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb1cc76cfd38c6ee65805bcfaf429a58643aa278) |
29° 6′ 14,0″
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![{\displaystyle 45^{\circ }\!\!-z={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/652c78198b3b4276a5f7c3ecd65e04e1c0b57df4) |
43° 25′ 00″ |
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![{\displaystyle {\frac {v''\!+v}{2}}={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a66c884cd640f24fab485b64b54f0b00a41386b) |
58° 12′ 28″
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![{\displaystyle {\frac {v''\!-v}{2}}={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4dcab36bfefa9bbeb8bed74645ca44966ec67204) |
12° 14′ 34,4″
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![{\displaystyle v''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a566d0b9c4e7ba19d0ba4be3eee23c9ef2b86fb2) |
70° 27′ 02,4″
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![{\displaystyle v\;={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8bb8625fa0ed64b1a8b71a5d6c201bcdca5c12cc) |
45° 57′ 53,6″
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Détermination de la longitude du périhélie dans l’orbite.
![{\displaystyle {\text{☊ }}={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf3680c57552650e754eca70108d9807f70b9da) |
284° 10′ 21,0″ |
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![{\displaystyle {\text{☊ }}={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf3680c57552650e754eca70108d9807f70b9da) |
284° 10′ 21,0″
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![{\displaystyle u={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47c36a2fcc5c45c4e8d31fc2083ac88638b105b8) |
124° 1′ 58,0″ |
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![{\displaystyle u''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/64129d9904fc210ce9571c193054e003087d242c) |
148° 31′ 7,0″
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![{\displaystyle {\text{☊ }}+u={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0818eba78042fc339c3e5e53036d52cf672e9319) |
208° 12′ 19,0″ |
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![{\displaystyle {\text{☊ }}+u''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dac3805367f261c525430c7f3e5a7fecccf584a7) |
232° 41′ 28,0″
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![{\displaystyle v={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43fab2ad337276ceff95169db37b96425158440a) |
245° 47′ 53,6″ |
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![{\displaystyle v''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a566d0b9c4e7ba19d0ba4be3eee23c9ef2b86fb2) |
270° 27′ 2,4″
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![{\displaystyle \pi ={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4cb9aa6235bc0a366cfe1d7706d4649e01842a7) |
162° 14′ 25,4″ |
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![{\displaystyle \pi ={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4cb9aa6235bc0a366cfe1d7706d4649e01842a7) |
162° 14′ 25,6″
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Calcul de la distance périhélie.
On a
![{\displaystyle {\begin{aligned}{\frac {1}{2}}v&=22^{\circ }58'56''\!,8,&{\frac {1}{2}}v''&=35^{\circ }13'31''\!,2,&q&=r\cos ^{2}{\frac {1}{2}}v=r''\cos ^{2}{\frac {1}{2}}v''.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/288a4c0149502eeced382ab4bc666ccd04a50463)
d’où
Distance périhélie ![{\displaystyle q={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8319ff96f795b110daa65b3214c9ddc3997c3a07)
0,29715.