What is the apparent weight of a 2000 kg satellite in a geosynchronous orbit?

Question

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 * 10^{7} m( approx 22,000 miles)

Find the value of g at this altitude.

Answer 1

It's in orbit, so it's in freefall; its apparent weight is by definition zero. The gravitational acceleration is precisely equal to the centripetal acceleration.

Answer 2

2000*4000^2=W*26000^2

w=2000*4000*2/26000^2=47.3 Kg

or  16/676*2000 = 47.3 Kg

well, it's consistent.

Answer 3

The force of gravity is:

F = G mearth msat / r^2

The gravitational acceleration on the satellite is:

g = G mearth / r^2

Look up Newton's G and the mass of the earth.  They give you the mass of the radius of the orbit and the mass of the satellite.  Plugnchug.

Poorcoco's interpretation is valid.  The problem doesn't state what reference frame you are in, so you could say your reference frame is orbiting with the satellite, so the centrifugal force cancels gravity and the apparent weight is zero.  I think they mean for you to work in an inertial frame, though, and actually do the calculation.