292 



L. EULERI OPERA POSTHUMA. 



Asiron.mech.l 



ALQ=tp, atque inclinatio orbitae ad planum JLN^co. Dcinde ipsius orbitae fi/l/ sit semiparameter 

 =D. excentricitas =</ et semiaxis transversus r = 7-^ — Nunc autem sit anomalia vera BLM=s. 



eritque distantia LM=v-=- — • Ponatur porro angulus qLM=Oj qui vocatur argumentum 



latitudinis, erit pro abside ima B angulus qLB = 6 — Sy ac posita longitudine corporis M in 

 orbita propria =9?, erit, uti supra § 192 vidimus, dcp = da -\- dip cos a. Hinc denique quaerantur 

 duo anguli X et ^, ut sit 



coscr cos(»9^ — i//)-!-sin<7 cos« sin («9^ — ifj) =cosA et sin<7 cos {d- — i//) — cosc» cos6Jsin(»9^ — y.i) = sin^tt, 

 erit A, = angulo MLiV, unde fiet distantia MN=V{vv-\-uu — 2accosA), quae voeetur = w. Hunc 



V sin>i 



V sin-i 



in finem quaeratur angulus v^ ut sittangc = — ^? eritque w = — Quodsi nunc ponamus 



brevitatis gratia 



L 



qv^ dtp sin s 



-^ = /1 et uv^dcpsitkfi(^:^ — -i^ = dP, 



iiVli/ .ir.U »: 



pw^ 



dcp (s\\ 



+-«^a^l sin fi 



qvcQ%X 8in«' 



){v^-',:)-^<i' 



dt 



vv 



erit primo dcp = ^y^gp {L-^ M), ac perturbationes ab actionc corporis N tempusculo dt pii|| 



ductae ex § 192 sequenti modo se habere reperiuntur: 



Primo pro variatione semiparametri /) est dp = — 2nuv^d(f sin fi (—^ jj 



Deinde pro excentricitatis q variatione ob 



'iqdq (1 — qq)dp — Inqv^ dcp iin s 



— — = — 2/iO, erit difFcrentiando 



p f 



?.u 



unde fit dq 



p pp 



— nv^dq> s\ns 



puj' 



^mwdcpfsm /u 



qv co8/i sina" 



7w «V' 



, /1 1 N / cos/? 8in« 



npuvdwl-- -)( 



* ■' \w* W^y \\ -h- q coss 



(2 C08 4 -♦- 9 -f- y cos* *) sin fi' 



(i -*-q cos «)* 



)' 



quae reducitur ad hanc formam 



dq = ni>^dq)\—^ — H— (-- — -3) Ui -h- qcoss) cos A sin 5 — (2cos5-t-gH-gcos**) sin//jY 



Hinc cum sit — — - = , erit — = — 2ndQ; erit pro variatione semiaxis transversi r 



dr 



— 'inqrrv^ d(p sins 

 pw^ 



rt t f . q cos /i sin »\ / 1 1 \ 



— 2nrruvdcp[ sin 11 — -. ) ( -r ^ )i 



'\ ' l -1- q COSS/ \W^ U^/ 







0«., j 'inrrvvdcp /—qvains , \ i . , , . ,. ^ . \\ 



seu dr = — — (^— -^ H u C^— „t) (^ cosA sin5 — [i-^-q coss) sm^)J. 



Praeterea consecuti sumus 



1; 



