Io, 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.
Orbital period of I0 , TI0 = 1.769 daysÂ
                   = 1.769 × 24 × 60 × 60 sÂ
Orbital radius of I0 , RI0 = 4.22 × 108 mÂ
Satellite I0Â is revolving around the JupiterÂ
Mass of the Jupiter is given by,Â
MJÂ = 4Ï€2RI03Â / GTI02Â Â Â Â Â Â Â Â Â Â Â Â Â ...(i)Â
where,Â
MJÂ = Mass of Jupiter,Â
G = Universal gravitational constant,
Orbital period of the earth,
Te = 365.25 days
  = 365.25 × 24 × 60 × 60 sÂ
Orbital radius of the Earth,
Re = 1 AU = 1.496 × 1011 mÂ
Mass of sun is given as,Â
Ms = 4Ï€2Re3 / GTe2               ...(ii)Â
Therefore,
Ms /Â
MJÂ =Â
       = Â
Substituting the values,Â
=
 = 1045.04
∴ Ms / MJ  ~ 1000Â
      Ms ~ 1000 × MJÂ
Hence, it can be inferred that the mass of Jupiter is about one-thousandth that of the Sun.
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