261
DÉTERMINATION D’UNE ORBITE D’APRÈS QUATRE OBSERVATIONS.
de là,
pourront être déterminées par les
équations suivantes :
![{\displaystyle \log r\;\sin(v'-\,v\,)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3172e06904ab524b74e65ef9ca2d2dcaeda30f72) |
9,74942, |
|
![{\displaystyle \log r\;\sin(v'\!-v+17^{\circ }\,7'\,5'')={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c369938b97494fb09aa1879c412ed88ed780ddd3) |
0,07500
|
![{\displaystyle \log r'''\sin(v'''\!\!-\!v'')={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4197a2bee3fbc9fbd80b4346a56f50ba74a28ed2) |
9,84729, |
|
![{\displaystyle \log r'''\sin(v'''\!\!-\!v''\!+17^{\circ }\,7'\,5'')={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fc483217f4b4ceb85b677a311b9c4f56d99a83b) |
0,10733 ;
|
d’où nous obtenons
![{\displaystyle v'-v\,={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/01f0380303bef8cb94525e952f93a1328f0474d0) |
14° 14′ 32″, |
![{\displaystyle \log \,r\;={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b23a7d51956591197a26db2aac86ad8f0daa44f0) |
0,35865,
|
![{\displaystyle v'''\!\!-\!v''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27604244ef6c9f587dc22ed41d8ce815aa710009) |
18° 48′ 33″, |
![{\displaystyle \log r'''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ddd6345b6e98f3f1ee40c13629c00445c38dc9f) |
0,33887.
|
Enfin, on trouve
![{\displaystyle \log(n01)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b53b7ade9d9e2925b61072d890afe68a40fa3dc7)
0,00426,
![{\displaystyle \log(n12)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5007fa2797605607db67dcd5d979bcec59af45bb)
0,00599,
![{\displaystyle \log(n23)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff9bb79707f5df7b41f78ed71de0783c00bfda3e)
0,00711,
et de là les valeurs corrigées de ![{\displaystyle \mathrm {P',\,P'',\,Q',\,Q} '',}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8bb5e42ebdff96ad3eea296012ebddef71e790fc)
![{\displaystyle \log \mathrm {P} '={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf924f5d2780617a2f798aae5127a4d5a7f59722) |
0,05944, |
|
![{\displaystyle \log \mathrm {Q} '={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8237a7ba314b1a1d5cb0171afb46cd145295b417) |
9,60374,
|
![{\displaystyle \log \mathrm {P} ''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0ec4281ff516446351d053ace4d5e4df3115e1) |
9,97219, |
|
![{\displaystyle \log \mathrm {Q} ''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efb3f039d52abcfc5897c7d06a6326271334e665) |
9,69581,
|
sur lesquelles la seconde hypothèse sera établie. Ses principaux résultats
sont les suivants :
|
|
|
|
|
|
|
![{\displaystyle c'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eddbde36c942164e886f073c58e5e28e21886973) |
− 7,67820, |
![{\displaystyle \log d'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d42910d13a099138f95f6eab8ba97064f2e32934) |
0,045736 ,
|
![{\displaystyle c''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1fe40e4062b6a4b843ffd6e1cbe8428a91a6f3a) |
+ 2,21061, |
![{\displaystyle \log d''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f5b272917edfaffd28f38eac2d48c351968b8a7) |
0,126054,
|
![{\displaystyle x'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/251285494246bda63044cb6a38c6b06d83d498f7) |
2,03308, |
![{\displaystyle z'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/699d6632c1f7067981e640a976207d7967968d48) |
23° 47′ 54″, |
![{\displaystyle \log r'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a8c1f6fc2b3c01bdbdd02219a0661e91973f6e7) |
0,346747,
|
![{\displaystyle x''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2264e78b127e4ae0a6a0439b9b8b4ff7b098f16) |
1,94290, |
![{\displaystyle z''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb78276c57993c7b68335420711da823c6f0d275) |
27° 12′ 25″, |
![{\displaystyle \log r''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84ba0210b0ffa76a5684b095c26c99a3ef6ab3e4) |
0,339373,
|
![{\displaystyle \mathrm {C'C} ''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f986cc0759e1ac1c18e7996495b59cf758425202) |
17° 8′ 0″,
|
![{\displaystyle v'-v\,={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/01f0380303bef8cb94525e952f93a1328f0474d0) |
14° 21′ 36″, |
![{\displaystyle \log r\;={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d395d15eaece84259163eb52e34d50e6aa013f4) |
0,354687,
|
![{\displaystyle v'''\!\!-\!v''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27604244ef6c9f587dc22ed41d8ce815aa710009) |
18° 50′ 43″, |
![{\displaystyle \log r'''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ddd6345b6e98f3f1ee40c13629c00445c38dc9f) |
0,334564,
|
![{\displaystyle \log(n01)={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b53b7ade9d9e2925b61072d890afe68a40fa3dc7) |
0,004359, |
0,006102, 0,007280.
|
De là se déduisent de nouveau les valeurs corrigées de
![{\displaystyle \log \mathrm {P} '={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf924f5d2780617a2f798aae5127a4d5a7f59722) |
0,059426, |
|
![{\displaystyle \log \mathrm {Q} '={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8237a7ba314b1a1d5cb0171afb46cd145295b417) |
9,604749,
|
![{\displaystyle \log \mathrm {P} ''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/848d417cb2b2d9827a1b291558b9dae79c8a4039) |
9,972249, |
|
![{\displaystyle \log \mathrm {Q} ''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efb3f039d52abcfc5897c7d06a6326271334e665) |
9,697564,
|
au moyen desquelles, si nous procédons à la troisième hypothèse,
résultent les nombres suivants :
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![{\displaystyle c'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eddbde36c942164e886f073c58e5e28e21886973) |
− 7,67815, |
![{\displaystyle \log d'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d42910d13a099138f95f6eab8ba97064f2e32934) |
0,045729 ,
|
![{\displaystyle c''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1fe40e4062b6a4b843ffd6e1cbe8428a91a6f3a) |
+ 2,21076, |
![{\displaystyle \log d''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f5b272917edfaffd28f38eac2d48c351968b8a7) |
0,126082,
|
![{\displaystyle x'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/251285494246bda63044cb6a38c6b06d83d498f7) |
2,03255, |
![{\displaystyle z'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/699d6632c1f7067981e640a976207d7967968d48) |
23° 48′ 14″, |
![{\displaystyle \log r'={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a8c1f6fc2b3c01bdbdd02219a0661e91973f6e7) |
0,346653,
|
![{\displaystyle x''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2264e78b127e4ae0a6a0439b9b8b4ff7b098f16) |
1,94235, |
![{\displaystyle z''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb78276c57993c7b68335420711da823c6f0d275) |
27° 12′ 49″, |
![{\displaystyle \log r''\!={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84ba0210b0ffa76a5684b095c26c99a3ef6ab3e4) |
0,339276,
|
![{\displaystyle \mathrm {C'C} ''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f986cc0759e1ac1c18e7996495b59cf758425202) |
17° 8′ 4″,
|