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

.