Acceleration

To determine the acceleration due to gravity at a height of 12800 km from the surface of the earth, we use the formula for gravitational acceleration at a height :

where:

• is the acceleration due to gravity at height .
• is the acceleration due to gravity on the surface.
• is the radius of the earth.

Given:

• Height from the surface: 6400 km, .
• Radius of the earth .

First, calculate the acceleration due to gravity at a height of 6400 km:

Since , we have , thus:

Next, calculate the acceleration due to gravity at a height of 12800 km:

Here, :(since , add to to find the distance from the center as )

Thus, the acceleration due to gravity at a height of 12800 km from the surface of the earth is .