RELATIONES INTER LOCOS PLTRE3 IN ORBITA.

9*

Per formulam secundam habemus exactius fqq&v — ■§- A (rr + rr + &RR),designante R radium vectorem anomaliae intermediae i A- r + N' — II respondentem.Tam exprimendo p per r, R, r, N, A r -{-f A, N+A ad normam formulae in art. 82traditae, inuenimus

4 sin \ A 2 sin | A

P~

cos -s

(t + 7 7 ) sinf A — -

IA / 1 1 \

•, atque hinc

■ sin A2 sin | A 2

cos 03

2 sin | A 1

Statuendo itaque

n ~ V 7 1 J P

2 sin | A 2 \J{rr cos 2 a)cos 03

{/ (it' cos 2 03 )

c „ coslA v/(?'/cos2 0>)

(/ j lit jK —— ) "vndc

r ^ ’

COS 03 (1 — —)

yalor approximatus secundus ipsius \/p elicitur

Vp

■ a +

si statuitur 2 a

(

2 a cos £ A 2 cos 2 03 2cosoi (1 —)

p>

:a-f

( 1 ——)*v P

COS I- A COS 2 03COS 01

Y

•J = e. Scribendo itaque n pro s/p, determinabitur

at per aequationem (at — «)(i-

OtJt

•) 2 — e, quae rite euoluta ad quintum gradum

ascenderet. Statuamus at = q + n, ita vt sit q valor approximatus ipsius at , atqueu quantitas perexigua, cuius quadrata altioresque potestates negligere liceat: Quasubstitutione prodit

(q — a) (1— qq^^ fl {(*

Y2 , —«) /

) ‘ /A V 1

( I‘l

Atn i

■-e, siue

sq' — {qq—Kq) (qq—Sy^ (qq — < 5 ) (</ 3 + 5 <f</ — 4 aS) ’ a eo( l ue

_ eq Sj ,-(qq — S) (a qq^ S q — 5 aS)q

71 (qq — S){q^ +^Sq — 4 aS)

lam in problemate nostro habemus valorem approximatum ipsius at, puta =3«,quo in formula praecedente pro q substituto, prodit valor correctus243 « 4 £-f 3 a (pera — $• (gaa + 7 S)

(gaa— S) (27 aa -}- 5§)

^ €

R —--— — y, formula induit formam hancce

17 (1— oflja ' ’

at—

Statuendo itaque

27 aa