Question
Sat September 12, 2009 By:

one of the satellites of jupiter , has an orbital period of 1.769 days and the radius of the orbit

Expert Reply
Wed November 04, 2009

The time period is, T = 2πR/V,

T2 = 4π2R2/V2 ............(1)

The centripetal force for the satellite's motion is the gravitational force between satellite and Jupiter,

mV2/R = GMm/R2, where m is the mass of the satellite and M is the mass of Jupiter and other symbols have their usual meaning.

V2 = GM/R

Using this V2 in (1),

T2 = 4π2R3/(GM)

M = 4π2R3/(GT2)

M = (4)(3.14)2(4.22x108)3/((6.67x10-11)(1.769x24x3600)2)

= 1.90 x 1027 kg

= 2x1027 kg

Sun's Mass is, 2x1030 kg.

Hence the Jupiter's mass is 1000th that of sun.

Regards,

Team,

TopperLearning.

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