The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the earth. The value of f is

The escape velocity is defined as the minimum speed by which a body has to move away from the influence of a planet’s gravitational pull without further propulsion. For Earth, it would depend on how far a distance one moves away from the center of the Earth. The escape velocity is proportional to the square root of the reciprocal of the radius R of the Earth at the surface.

Now consider a platform located at a height equal to the radius of the Earth (R) above its surface. This makes the total distance from the Earth’s center to the platform (2R). Since escape velocity decreases with an increase in distance from the planet’s center, the escape velocity from this platform is less than that from the Earth’s surface.

This, knowing that escape velocity varies in inverse proportion to the distance from the center’s square root, makes escape velocity at a distance of 2R a fraction of the surface escape velocity. The factor f linking between the two velocities can then be calculated as follows, 1/√2 . Therefore, if the escape velocity from earth’s surface is some quantity ‘a’, then from this ‘platform’ it becomes an amount ‘a divided by f’.

This shows that gravity depends on distance, indicating that the escape velocity at altitude varies.