two satellites orbit the earth in stable orbits. satellite a is three times the mass of satellite b. satellite a orbits with a speed vvv at a distance rrr from the center of the earth. satellite b travels at a speed that is greater than vvv . at what distance from the center of the earth does the satellite b orbit?



Answer :

Satellite B's radius will be less than Satellite A's radius.

m = Satellite Mass

v = Satellite Velocity

r = Orbital radius of the satellite

Relating the gravitational and centripetal forces

mv^2/ r= GmM/r^2

v^2/r=GM/r^2

v^2=GM/r

v = sqrtGM/r

As can be shown, the mass of the satellite has no bearing on the relationship between velocity and radius.

This implies that the radius must shrink for v to increase

Here, vb>va

Therefore, satellite b's radius will be smaller than satellite a's radius.

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