Show that the orbital speed of an artificial satellite increases as the energy of the satellite decreases.

Explanation

Total energy of an artificial satellite `=-(GMm)/(2r)` and its kinetic energy `=+(GMm)/(2r)`. In this case, M= mass of the earth, m=mass of the artificial satellite and r=distance of the satellite from the centre of the earth.
When the total energy of the satellite starts decreasing i.e., the value of `-(GMm)/(2r)` starts falling , the value of the kinetic energy `+(GMm)/(2r)` starts increasing. As the orbital speed is directly proportional to the square root of the kinetic energy , it also increases.