Part A :
given
d = 1.5 X 1011 m
t = 9.62 minutes
t = 9.62 X 60
t = 577.2 sec
speed of the particle is v = d / t
v = 1.5 X 1011 / 577.2
v = 2.59 X 108 m/s
v = 2.59 X 108 / 3 X 108
v = 0.8633 c
Part B :
tp =
t / (
1 -
v2 / c2 )
v = 0.8633 c
tp =
577.2 / (
1 -
0.86332 c2 / c2 )
tp =
1143.6696 sec
tp =
1143.6696 / 60
tp =
19.06 min
Part C :
Lp =
L X (
1 -
v2 / c2 )
Lp =
1.5 X 1011 X (
1 -
0.86332 c2 / c2 )
Lp =
1.5 X 1011 X 0.504
Lp =
7.57 X 1010 m
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