
175Motion Under a Central Force
© 2010 Taylor & Francis Group, LLC
its drag on a satellite is not very strong; the satellite makes many orbits before its orbital height is
changed appreciably.
Next, we determine the orbit parameters of a satellite from conditions at its closest approach.
From the following two relationships:
r
min
= α/(1 + ε) and α = l
2
/μk
we nd
ε
α
µ
=−
r
l
kr
min min
2
.
If v
0
is the velocity of the satellite at r
min
, then by the conservation of angular momentum, we have
lr
==µθ µ
2
min
and the eccentricity ε can now be expressed as
ε
µ
rv
min 0
2
. (6.52)
If we denote the quantity k/μr
min
by v
c
2
, we see that v
0
= v
c
for a circular ...