If a body of mass m has to be taken from the surface to the earth to a height h = R, then the amount of energy required is (R = radius of the earth)

The amount of energy required to lift a body of mass m from the surface of the earth to a height h = R (where R is the radius of the earth) can be calculated using the formula for gravitational potential energy.

The formula for gravitational potential energy is:

PE = m * g * h

where: PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

However, because we're dealing with a significant height (equal to the radius of the Earth), we need to consider that the acceleration due to gravity (g) is not constant but decreases with height. Therefore, we need to use the formula for gravitational potential energy for large heights:

PE = - GMm / r

where: G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the distance from the center of the Earth.

When the object is on the surface of the Earth, r = R (the radius of the Earth), and when the object is at height h = R, r = 2R.

The work done (W) on the object to lift it from the surface of the Earth to a height h = R is the change in potential energy:

W = PE_final - PE_initial W = - GMm / (2R) - ( - GMm / R) W = GMm / R

So, the amount of energy required is GMm / R.