r Pointed to the Satellite from the
Center of the Earth

The work required to place a satellite into orbit needs to be determined.

According to the Newton's Law of Gravitation, the attractive force between the earth and the satellite is:

      F_G = Gm_em_s/r²

where r is pointed from the center of the earth to the satellite. Since r changes with the location of the satellite (from R, the average radius of the earth, to (R + h), the sum of the earth's radius and the altitude of the satellite), integration needs to be used to calculate the work.

First, take an arbitrary location, r, on [R, R + h], as shown on the left. The force applied to overcome the gravitational force is the same as the attractive force between the earth and the satellite at that location.

      F = Gm_em_s/r²

When the satellite moves from r to r + dr, work done by this force is

      dW = Fdr = Gm₁m₂/r² dr

Move the satellite from the earth surface ( r = R) to its orbit ( r = R + h) equals

Substituting the given value into the above equation gives

      R + h = 6.37 x 10⁶ + 650 x 10³ = 7.02 x 10⁶ m

      W = 6.67 x 10^-11(5.98 x 10²⁴)(173)(650 x 10³)
            /((7.02 x 10⁶)(6.37 x 10⁶)
          = 1,003 MW

To move the satellite vertically to its orbit, requires 1,003 MW of work. This does not include work needed to move the rocket used to launch the satellite.