﻿ 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. from Physics Gravitation Class 11 Manipur Board

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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 days

=  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,

T= 365.25 days

= 365.25 × 24 × 60 × 60 s

Orbital radius of the Earth,

R
= 1 AU = 1.496 × 1011

Mass of sun is given as,

Ms = 4π2Re3 / GTe                           ...(ii)

Therefore,

Ms / MJ  = = Substituting the values,

= = 1045.04

∴ Ms / MJ  ~ 1000

M~ 1000 × M

Hence, it can be inferred that the mass of Jupiter is about one-thousandth that of the Sun.
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