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If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:
When satellite orbits close to a planet, its time period depends upon:
A time period of a satellite is the time taken by the satellite to go once around the earth.
T = 2π(r3/√MG), where r = R + D,
if D is very small wrt to R so D can be neglected .
So T = 2π(√1/Mσ), where σ is density of the planet.
so here clearly we can see if the orbit of the satellite is very close to the planet then its period depends only on the density of the planet.