RELATIONES INTER LOCOS PLYRES IN ORBITA.

0

a

[1] cosi-p =:} — + —~

/ . C ,c\ . (e+ i)aW - V~cjV - - -

[3] cos i v' = i ^ & + V "cvr) V~ — ' r r~~'

[4] siniv=i^\/Cc — V~(J^jV --

Hinc statim demanant sequentes:

/„ 1 \ . ee — 1

[5] sin.F:=:§a(C—

r.

[ 6 ] sin/=|:a(c— —)/

rr

ee — 17 1

rr

17 ] C03F = ^ ( , + i,_ ( C + ^)) - ^[8] co»/=^(C+-L)—(c+^-^jr

Porro fit per aequ. X art. 21

r =^ e (v + 7 r )— 1

a

a~ =i e ( a + s)

atque liinc

t*] Jf =-=f(c—£-)(«—f)

[ 1 0 ] ~ = i ^ (C+ (c + —~) —2

Haec aequatio 10 cum 8 combinata praebet

r -\-r — (c -f ) cos f. y /rr

[11] « =-f-

*(c_ T ) =

Statuendo itaque perinde vt in ellipsieosj est positiuus vel negatiuusj fit

y/— + v'-

. r v r

2 cos f

— 1 + 2 vel = i