60.
(a) For r = R
p
,
v
2
p
=
GM
s
2
R
p
−
1
a
=
6.67
× 10
−11
m
3
/s
2
·kg
1.99
× 10
30
kg
2
8.9
× 10
10
m
−
1
2.7
× 10
12
m
v
p
=
5.4
× 10
4
m/s .
(b) For r = R
a
,
v
2
a
=
GM
s
2
R
a
−
1
a
=
6.67
× 10
−11
m
3
/s
2
·kg
1.99
× 10
30
kg
2
5.3
× 10
12
m
−
1
2.7
× 10
12
m
v
a
=
9.6
× 10
2
m/s .
(c) We appeal to angular momentum conservation:
L = mvr = mv
a
R
a
= mv
p
R
p
= constant
=
⇒
v
a
v
p
=
R
p
R
a
.