A planet of mass m moves round the sun of mass M in a circular orbit of radius r with - Physics - Gravitation

Question

A planet of mass m moves round the sun of mass M in a circular
orbit of radius r with angular speed omega Another planet of mass
2m moves round the sun in circular orbit of radius 4rwith angular
speed omega' Find the ratio of omega / omega'

Vaibhav T. · Accepted Answer

Dear Student,

When centripetal force is provided by gravitational force then,GMmr2=mω2rω2=GMr3  
 (1)Similarly,ω'2=GM4r3  ω'2=GM64r3
 (2)ω2ω'2=GMr3GM64r3ωω'2=64r3r3ωω'=4rr32ωω'=432ωω'=23ωω'=8

A planet of mass m moves round the sun of mass M in a circular orbit of radius r with angular speed omega. Another planet of mass 2m moves round the sun in circular orbit of radius 4rwith angular speed omega'. Find the ratio of omega / omega'.

A planet of mass m moves round the sun of mass M in a circular orbit of radius r with angular speed omega. Another planet of mass 2m moves round the sun in circular orbit of radius 4rwith angular speed omega^'. Find the ratio of omega / omega^'.