223
DÉTERMINATION DE L’ORBITE D’APRÈS TROIS OBSERVATIONS COMPLÈTES.
Enfin, |
![{\displaystyle \log \left[\operatorname {tang} \beta \sin(\alpha ''-l')-\operatorname {tang} \beta ''\sin(\alpha -l')\right]=\log \mathrm {S} ..}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f61e43bf15a65b0b2140a3d4e217894026fda43) |
8,2033319
|
|
![{\displaystyle \log \mathrm {T} \sin(t+\gamma ')....................................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efe40d1edf162ea138001e1e77680caf4960913c) |
8,4086124
|
d’où |
![{\displaystyle \log \operatorname {tang} (\delta '-\sigma )................................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a5709eb982a80ca64e2460ac3622d3dc54061b2) |
9,7947195
|
31° 56′ 11,81″,
et par suite
0° 23′ 13,12″.
Suivant l’art. 140, nous avons
![{\displaystyle \mathrm {A''D} '-\delta ''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39256bb4233d3bcbafcfe12dbe540b09e7a2402e) |
191° 15′ 18,85″ |
|
![{\displaystyle \log \sin }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b95dc5735b1fc429bcc3bbc8c5ae5b1dcda15448) |
9,2904352![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) |
|
![{\displaystyle \log \cos }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b78175e66de04bc65046138d9f8f34274520a169) |
9,9915661
|
![{\displaystyle \mathrm {AD} '-\delta ={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f4adedeb1a2a664b724c25a81a44aee7b3919ef) |
194° 48′ 30,62″ |
|
»» |
9,4075427![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) |
|
»» |
9,9853301
|
![{\displaystyle \mathrm {A''D} -\delta ''={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5985ccea3ec5d732d903e7432c562c831753ac05) |
198° 39′ 33,17″ |
|
»» |
9,5050667
|
![{\displaystyle \mathrm {A'D} -\delta '+\sigma ={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b199f8850fe99ac4c9987d2c293d5414601973a2) |
200° 10′ 14,63″ |
|
»» |
9,5375909
|
![{\displaystyle \mathrm {AD} ''-\delta ={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81682d5d7a98045770925a017c9ef1817a8db652) |
191° 19′ 08,27″ |
|
»» |
9,2928554
|
![{\displaystyle \mathrm {AD} ''-\delta '+\sigma ={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/45ad6cf8a41d6f5c75c5dd8716bfe6bb8382d2eb) |
189° 17′ 46,06″ |
|
»» |
9,2082723
|
De là, on trouve
![{\displaystyle \log a.............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47411dabe5f10f2944c18c5dc833e224dd4dca6d) |
9,5494437, |
![{\displaystyle \quad a=+}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ae043554a91995dffdcbdf272337d18a7b0f617) |
0,3543592
|
![{\displaystyle \log b.............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3269ee9b55b00a57bf50da7c6736b05f5a87fbd9) |
9,8613533.
|
La formule 13 donnerait
9,8613531, mais nous avons
préféré la première valeur, parce que
est plus
grand que
Il vient ensuite, d’après l’art. 141,
![{\displaystyle 3\log \mathrm {R} '\sin \delta '.....}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8ea75011024e91e8f0b3fa330488ab4e7a51827) |
9,1786252
|
![{\displaystyle \log 2\dots ..........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f3df7af23833b0f47251392cdc505b3d55a654e) |
0,3010300
|
![{\displaystyle \log \sin \sigma ..........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab8ceabbe61f5c15bc45a0feb821529c88b11afb) |
7,8295601
|
|
7,3092153 |
et par suite 2,6907847
|
![{\displaystyle \log b..............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b841ca99c0ffe9f0e64bff521d57f58489fa37a) |
9,8613533
|
![{\displaystyle \log \cos \sigma \,.........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c1948b5423a17eebe6b5ca0aca5e171c32842e1) |
9,9999901
|
|
9,8613632
|
d’où
![{\displaystyle {\frac {b}{\cos \sigma }}={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b084be5aeef0fc10bee76ff5abe59a99ed5d91e3)
0,7267135.
On déduit de là
![{\displaystyle d={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f4ba72c8fe96504e1f0cd46737a24e1d061d1f6)
−1,3625052,
![{\displaystyle \log e={}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed23430e650d14efa68cb8ecdc2e10939616cfd1)
8,3929518
![{\displaystyle n.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e59df02a9f67a5da3c220f1244c99a46cc4eb1c6)
On trouve enfin, au moyen des formules de l’art. 143,
![{\displaystyle \log \varkappa ................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72c76a3c78ef825ac1469365c11c7ee818ad2ba4) |
0,0913394
|
![{\displaystyle \log \varkappa ''...............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38af10a749a2a8476ad860632aa2badf5773e0b5) |
0,5418957
|
![{\displaystyle \log \lambda ................}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c0f0bf295f8808ac2ea269fe7431cb80b32f9336) |
0,1864480
|
![{\displaystyle \log \lambda ''...............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b41fb61dd568d3fa72124b2e5a689ba172fa625) |
0,1592352
|