225
DÉTERMINATION DE L’ORBITE D’APRÈS TROIS OBSERVATIONS COMPLÈTES.
Nous avons ensuite, d’après l’art. 143,
|
![{\displaystyle \log {\frac {\mathrm {R} '\sin \delta '}{b}}..............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97ad38a16bcde10b8c30c1e85ea89cc9ff092cdc) |
9,8648551
|
|
![{\displaystyle \log(\mathrm {P} +a)...............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/defc569a0a1a34b178bb0cf3f641ed4a21546edd) |
0,1914900
|
![{\displaystyle \mathrm {c^{t}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cad68c77647f742f303bffae97fa2c4ea2376ea) |
![{\displaystyle \log \sin(\varepsilon -\sigma )............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd810bca813b974e10513fcc9d438c5ad38c35af) |
0,6103578
|
|
![{\displaystyle \log {\frac {n'r'}{n}}.................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1208f5d6021038aac690f749df7399eda001e21e) |
0,6667029
|
|
![{\displaystyle \log \mathrm {P} ....................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13cbba36142732f7bd271063020d661b7beb633f) |
0,0791018
|
|
![{\displaystyle \log {\frac {n'r'}{n''}}.................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4bb1d8b9164d6a049da1d6ee9b20270f030d26c) |
0,5876011
|
199° 47′ 01,51″ 214° 22′ 06,41″ ; |
9,7516730
|
188° 54′ 32,94″ 203° 29′ 37,84″ ; |
9,6005923
|
De là, nous avons
![{\displaystyle \log p=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dcb85e78f9579275559c9813ae6b207117171ecb)
9,9270735
![{\displaystyle n,\quad \log p''=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c21733d29c38adfad662c05b587802afed345871)
0,0226459
![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b)
et alors
![{\displaystyle \log q=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/203eb710791b3f90f8bd85ee61fd2f2ae2c52c6d)
0,2930977
![{\displaystyle n,\quad \log q''=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf0fc09064b4393f035b48a690db7435b9359c06)
0,2580086
![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b)
d’où l’on déduit
![{\displaystyle {\begin{aligned}\zeta \;&=203^{\circ }17'31''\!,22&\log r\;&=0,3300178\\\zeta ''&=210^{\circ }10'58''\!,88&\log r''&=0,3212819.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76dec1c570f8e067dfaf8d3c1b6d55f16d9c49f4)
Enfin, d’après l’art. 144, nous obtenons
![{\displaystyle {\tfrac {1}{2}}(u''+u)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b32234439ba87b0564ba8fdd0852227f79b8d2a8) |
205° 18′ 10,53″
|
![{\displaystyle {\tfrac {1}{2}}(u''-u)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8bc60316c7d7f41a4897e8fede9dfdbb31fce7d1) |
00−3° 14′ 02,02″
|
![{\displaystyle f'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2327da718662ead42adb628c45b7ec08fa437be6) |
00 3° 48′ 14,06″.
|
|
|
![{\displaystyle \log \sin 2f'......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/23ba7f74feefae5b56ba1d746f4d9a9cc76f27dc) |
9,1218791 |
|
|
![{\displaystyle \log \sin 2f'......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/23ba7f74feefae5b56ba1d746f4d9a9cc76f27dc) |
9,1218791
|
|
![{\displaystyle \log r...........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13e9be81d6ee520aa841620a40cd2a821d306d5f) |
0,3300178 |
|
|
![{\displaystyle \log r''..........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/df96d29f521f728b35930cbdbc8c8157a0ecc1be) |
0,3212819
|
![{\displaystyle \mathrm {c^{t}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cad68c77647f742f303bffae97fa2c4ea2376ea) |
![{\displaystyle \log {\frac {n'r'}{n}}.......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbcb5d683c10c3766378eef23a0d3b00421c80d4) |
9,3332971 |
|
![{\displaystyle \mathrm {c^{t}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cad68c77647f742f303bffae97fa2c4ea2376ea) |
![{\displaystyle \log {\frac {n'r'}{n''}}.......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2d374dc03e428105744a719509695622fabaa6c) |
9,4123989
|
|
![{\displaystyle \log \sin 2f\;......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb0aa2cdc1e0917109898d9943e9c55f2e1283ab) |
8,7851940 |
|
|
![{\displaystyle \log \sin 2f''......}](https://wikimedia.org/api/rest_v1/media/math/render/svg/812540813235a787d9bdd9af74e06e3e057903e6) |
8,8555599
|
3° 29′ 46,03″ |
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4° 06′ 43,28″
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La somme
ne diffère ici de
que de 0″,01.
Maintenant, pour que les temps soient corrigés de l’aberration, il
faut calculer les distances
par les formules de l’art. 145, et