How Do Objects Behave When Dropped from Satellites?

[Amith2006]

Sir,
1)If an object is dropped from a satellite moving close to the Earth will it fall to the Earth or will it move along with the satellite? The answer given in my book is, it will fall to the Earth with an acceleration due to gravity. But how is it so? At the instant it is dropped, it has an orbital velocity. So it should move along with the satellite, isn’t it Sir?
2)It is said that the geostationary satellite is falling freely under gravity while orbiting the earth, then how does it have a constant orbital velocity?

 

[Gokul43201]

Sir,
1)If an object is dropped from a satellite moving close to the Earth will it fall to the Earth or will it move along with the satellite? The answer given in my book is, it will fall to the Earth with an acceleration due to gravity. But how is it so? At the instant it is dropped, it has an orbital velocity. So it should move along with the satellite, isn’t it Sir?

This is a guess, but perhaps the key in in the words "close to earth". A satellite in a Low Earth Orbit usually is orbiting in the Exosphere, where there is some tiny amount of air resistance. If the satellite does not use its rockets to provide periodic boosts, it will gradually lose speed and spiral earthwards.

2)It is said that the geostationary satellite is falling freely under gravity while orbiting the earth, then how does it have a constant orbital velocity?

It does not have a constant velocity - only a constant speed.