12.69:
a) The period of the asteroid is
m
10
3
Inserting
.
11
a
2
2
3
×
=
GM
π
T
for a gives
m
10
5
and
y
84
.
2
11
×
gives a period of 6.11 y.
b) If the period is
.
m
10
90
.
4
then
,
93
.
5
11
×
=
a
y
c) This happens because
,
5
2
4
.
0
=
another ratio of integers. So once every 5 orbits

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