If it requires E joules of energy to raise a mass from the surface of the Earth to an altitude of 6,000 km above the Earth, how much energy is required to raise it from the surface to an altitude of 12,000 km?

To raise the mass to an altitude of 12,000 Km 2E joules are required.

Explanation:

Gravitational Potential Energy

It's the energy stored in an object because of its vertical position or height in a gravitational field.

It can be calculated with the equation:

U=m.g.h

Where:

m = mass of the object

h  = height with respect to a fixed reference

g  = acceleration of gravity, or .

If a mass has a height h1, its potential energy is

If a mass has a height h2, its potential energy is

The ratio of both potential energies is:

Simplifying:

Solving for U2:

Since U1=E:

To raise the mass to an altitude of 12,000 Km 2E joules are required.