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Gravitation

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Question : 4
Total: 25
One of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22×108 m. Show that the mass of Jupiter is about one-thousandth that of the sun.
Solution:  
For Jupiter’s satellites
Orbital period, TJ=1.769days=1.769×24×60×60s
Radius of the orbit, RJ=4.22×108m
Mass of jupiter, MJ=
4π2RI3
GTI2
 ....(i)
Now, orbital period of Earth around the sun
T=1 year =365.25×24×60×60s
Orbital radius, RS=1.496×1011m
Mass of sun MS=
4π2R3
GTE2
 ....(ii)
Dividing (ii) by (i)
MS
MJ
=
R3
RJ3
×
TJ2
TE2

=
(1.496×1011 )3
(4.22×108)3
×
(1.77×24×60×60)2
(365.25×24×60×60)2
=1046
or
MJ
MS
=
1
1046
≃
1
1000
or MJ=
1
1000
MS
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