how much time a satellite in an orbit at height 35780 km above the earth surface would take if the mass of the earth would have been four times it's original mass
Answers
The higher the orbit, the slower the tangential velocity. For circular orbits such as are common for satellites, the orbital speed decreases as square root of distance form the center of gravity (that is, center of Earth, not its surface). If this distance doubles, the speed is reduced by square root of 2.
v2r is a constant for circular stable orbits. As an example, if four times the radius, then halve the speed.
You might like to think what this means for navigating a spaceship between orbits. You see on the movies that the producers usually have no idea about nechanics, and think you can just point your rockets in any direction, and that is where you will head.
But if you are following another craft ahead of you in orbit, then the mass of that craft matters. If the mass is different then you don't need to do anything, just wait and you will meet up.. If the mass is the same as yours, then increasing speed to catch it up will in fact put you into a higher orbit above it. Firing a thruster radially to lower your orbit will work but when you stop firing it you are now you are not moving fast enough to maintain orbit and you will keep dropping. So catching up with a ship in your orbit is a bit tricky, first you angle down at the right amount to lose altitude whilst increasing speed, then you reverse that by angling up, but you have to brake by flipping around or firing retros. You can't just point and shoot like some dogfighting ace pilot. Sorry, Hollywood, you goofed again.