Question
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.
Solution
Orbital period of I0 , TI0 = 1.769 days
= 1.769 × 24 × 60 × 60 s
= 1.769 × 24 × 60 × 60 s
Orbital radius of I0 , RI0 = 4.22 × 108 m
Satellite I0 is revolving around the Jupiter
Mass of the Jupiter is given by,
MJ = 4π2RI03 / GTI02 ...(i)
where,
MJ = Mass of Jupiter,
G = Universal gravitational constant,
Orbital period of the earth,
Te = 365.25 days
= 365.25 × 24 × 60 × 60 s
= 365.25 × 24 × 60 × 60 s
Orbital radius of the Earth,
Re = 1 AU = 1.496 × 1011 m
Mass of sun is given as,
Ms = 4π2Re3 / GTe2 ...(ii)
Therefore,
Ms / MJ =
=
Ms / MJ =
=
Substituting the values,
= 
= 1045.04
∴ Ms / MJ ~ 1000
Ms ~ 1000 × MJ
Hence, it can be inferred that the mass of Jupiter is about one-thousandth that of the Sun.
