mass in regards to size q?

Question

The radius of Earth is about 6.40 x 10^3 km. A 3.90 x 10^3-N spacecraft travels away from Earth. What is the weight of the spacecraft at 6.40 x 10^3 km away from Earth? What about 1.28 x 10^4 km?

Answer 1

F = GMm/r²

First we have F = 3.90 x 10^3 N when r = 6.40 x 10^3 km or 6.4 x 10^6 m, here we are at the surface of the Earth

hence m = Fr²/GM
= (3.9x10^3)(6.4x10^6)²/(6.67x10^-11)(5.9736×10^24)
= 401 kg

So at 6.40 x 10^3 km from the surface of the earth (here I am going to assume that the distance is with respect to the surface, NOT the center of the Earth), we have:

r = 1.28 x 10^7 m

F = GMm/r² = 975.18 N

At r = 6.40 x 10^3 km + 1.28 x 10^4 km

r = 1.92 x 10^7 m

F = GMm/r² = 433.41 N

Answer 2

wikipedia is your friend
http://en.wikipedia.org/wiki/Gravity

the force of gravity = (Kg M1 M2)/(r^2)

You know the force (3.90 x 10^3-N) at one radius (6.40 x 10^3 k), so you can figure out (Kg M1 M2).

So then all you have to do is plug in the new radius values.