Solution
(a) we know that V
0
=
GM/2R
E
in this problem . Using energy conservatioan, we have
2
1
mv
0
2
−GMm/R
E
=−GMm/r
which yields r= 4R
E
/3. So the multiple of R
E
is 4/3 or 1.33.
(b) Using the equation, we see that in this problem we have K
i
=GMm/2R
E
,
and the above manipulation (using energy conservation) in this case leads to r= 2R_{E}. So the multiple of R_{E} is 2.00.
(c) from escape condition , we see that the mechanical energy =0.