Page:Gauss - Théorie du mouvement des corps célestes, traduction Dubois, 1864.djvu/396

377

MÉTHODE D’OLBERS.

Détermination des latitudes et longitudes héliocentriques correspondantes des observations extrêmes, de la longitude du nœud et de l’inclinaison.

${\begin{aligned}\sin \lambda &={\frac {\rho \operatorname {tang} \beta }{r}},&\sin \lambda ''&={\frac {\mathrm {M} \rho \operatorname {tang} \beta ''}{r''}}.\end{aligned}}$

$\rho {}=$	0,83268	$\log ={}$	1,920478	$\log ={}$	1,920478
$r={}$	0,35061	$\mathrm {c^{t}} \log ={}$	0,455176	$\log \mathrm {M} ={}$	1,902781
$\beta ={}$	18° 55′ 46,8″	$\;\log \operatorname {tang} ={}$	1,535237	$r''\!={}$0,44531${}\log ={}$	0,351337
$\log \sin \lambda ={}$			1,910891	$\beta ''\!=$ 18° 56′ 1,7″ $\;\log \operatorname {tang} ={}$	1,535340
				$\log \sin \lambda ''\!={}$	1,709936
d’où	$\lambda ={}$54° 32′ 16,0″			$\lambda ''=\!{}$30° 50′ 58,0″

Appliquons maintenant les formules

${\begin{aligned}\sin \varepsilon &={\frac {\rho \sin(\Theta -\alpha )}{r\cos \lambda }},&\sin \varepsilon ''&={\frac {\mathrm {M} \rho \sin(\Theta ''\!-\alpha '')}{r''\cos \lambda ''}},\end{aligned}}$

$\operatorname {tang} \left(\mathrm {L} +{\frac {d\mathrm {L} }{2}}-{\text{☊ }}\right)={\frac {\operatorname {tang} {\dfrac {d\mathrm {L} }{2}}\sin(\lambda ''\!\!+\!\lambda )}{\sin(\lambda ''\!\!-\!\lambda )}},$et$\operatorname {tang} \mathrm {I} ={\frac {\operatorname {tang} \lambda }{\sin(\mathrm {L} \!-\!{\text{☊ }})}},$

nous avons

$\theta -\alpha =5^{\circ }24'35''\!,3$ et $(\Theta ''\!-\alpha '')=10^{\circ }33'33''\!,5$

$\mathrm {c^{t}}$	$\log r$		0,455176	$\mathrm {c^{t}}$	$\log r''$		0,351337
	$\log \rho$		1,920478		$\log \rho$		1,920478
	$\log \sin(\Theta -\alpha ).$		2,974414		$\log \mathrm {M}$		1,902781
$\mathrm {c^{t}}$	$\log \cos \lambda$		0,236449		$\log \sin(\Theta ''\!-\alpha '')$		1,263052
	$\log \sin \varepsilon$		1,586517	$\mathrm {c^{t}}$	$\log \cos \lambda ''$		0,066250
	$\varepsilon ={}$	022° 42′  7,0″			$\log \sin \varepsilon ''$		1,503898
	$\Theta +180^{\circ }\!={}$	271° 35′  2,7″			$\varepsilon ''={}$	218° 36′ 26″
	$\mathrm {L} ={}$	248° 52′ 55,7″			$\Theta ''\!+180^{\circ }\!={}$	276° 20′ 16,4″
	$\mathrm {L} ''={}$	257° 43′ 50,4″			$\mathrm {L} ''={}$	257° 43′ 50,4″
	$\mathrm {L} ''\!-\mathrm {L} ={}$	258° 50′ 54,7″
	${\frac {d\mathrm {L} }{2}}={}$	254° 25′ 27,3″
	$\mathrm {L} +{\frac {d\mathrm {L} }{2}}={}$	253° 18′ 23,0″
	$\lambda ''=\!{}$	230° 50′ 58,0″
	$\lambda ={}$	254° 32′ 16,0″