Why is there a discrepancy between rocket velocity calculations in orbit?

[JM2107]

In the following problem, I got that the velocity is 5609m/s but the answer key says that the velocity of the rocket is 3950m/s. I know both answers can be calculated but I don't understand why the radial distance would be the distance from the rocket to the Earth's surface. I personally think that the velocity of the rocket should be calculated in respect to the center of the mass that is is orbiting around. Could some please tell me if I am right, it would be greatly appreciated. Oh yeah, and I got the correct force which is F=12268.1N. Once again, thanks for any help provided in advance


Here's part of the problem:

1. A 5000 kg rocket orbits the Earth at an altitude above the earth’s surface equal to the radius of the earth[R_earth=6.4*10^6m].
a. Calculate the force exerted on the rocket by the earth.
b. Calculate:
i. the velocity of the rocket

 

[Alexander]

Did you try to equate needed for orbiting centripetal acceleration v²/r to the acceleration of gravity g/4 at that distance? It comes right, v~4 km/sec