History of Science Department University of Aarhus

96 6. KEPLER BEV GELSEN
N
E M S
ae 2
l
p
a
v
ae 1
Figur 6.3
Betragt Fig. 6.3.
l = a +2NE=a(1 + 2e2 cos v)
Cosinusrelationen pa 4SEP og efterf lgende r kkeudvikling giver
r =(l 2 +(ae1 + ae2) 2 ; 2l(ae1 + ae2)cosv) 1
2
m
=(a 2 +4a 2 e2 cos v +4a 2 e 2
2 cos 2 v + a 2 (e1 + e2) 2 ; 2(e1 + e2)a 2 (1 + 2e2 cos v) cos v) 1
2
= a(1+(e1 + e2) 2 +2(e2 ; e1) cos v ; 4e1e2 cos 2 v)
| {z }
X
1
2 ;1