At what height in kilometers above the surface of the Earth is there a 7% difference between the approximate gravitational force mg and the actual gravitational force on an object

There is a 7 % difference between the approximate gravitational force and the actual gravitational force at a height of 240 kilometers.

Explanation:

We can calculate gravity as a function of mass of the Earth (), measured in kilograms, radial distance from center of the planet (), measured in meters, and gravitation constant (), measured in newton-square meters per square kilogram:

(Eq. 1)

And we solve the equation for :

(Eq. 1b)

If we know that , and , the radial distance from the center of the Earth is:

The height above the surface of the Earth is the difference between the value above and the radius of the planet. That is:

()

There is a 7 % difference between the approximate gravitational force and the actual gravitational force at a height of 240 kilometers.