What is the gravitational field strength at a place 220km above the earth's surface?

Question

How would you calculate this without knowing the mass of the second object?

Answer 1

Gravitational field stength is the acceleration a mass would feel if it were there, and this acceleration doesn't depend in mass, as Galileo discovered.
At 220km from the earth's surface, you are 6375+220 = 6595 km from earth's center, since the radius of earth is 6375 km. Now use Newton's law of gravitation:
F=GMm/r^2 but we want a which is F/m
->a=GM/r^2
a=G(5.9742*10^24)/(6595000)^2
a=9.16581912
or a =9.17 m/s2

Answer 2

The gravitational field strength is given in terms force per unit mass. Think about it as using a test mass of mass m to see how strong the gravitational field is at a point.

Start with F = GMm/r^2.
divide by m to get the force per unit mass
F/m = GM/r^2
The gravitational field strength is then GM/r^2
The units will be in newtons per kilogram.

Since F = ma, F/m = a
So you can see that the gravitational field strength will be the same as the acceleration. But you should still use N/kg as your units.

Answer 3

As others have said, it's just the gravitational acceleration and is independent of the mass of the 2nd body. It can be computed very simply. Since it's inversely proportional to radius,
g1(elevated) = g0(surface)*(r0/r1)^2
Using 9.81 for g0, g1 = 9.8*(6375/6595)^2 = 9.1664 m/s^2.