question_answer

When a satellite moves to a lower orbit in the atmosphere of the earth, it becomes hot. This indicates that there is some dissipation in its mechanical energy. But the satellite spirals down towards the earth with an increasing speed, why?

Answer:

                For a satellite orbiting the earth, Total energy \[=-\] Kinetic energy i.e., \[E=-K\] When the satellite enters the atmosphere of the earth, it dissipates its mechanical energy (which is negative) against atmospheric friction. Energy E becomes more negative. As a result, the kinetic energy of the satellite increases and hence its speed increases. But its orbital speed \[{{\upsilon }_{0}}=\sqrt{GM/(R+h)}\]can increase only if its height h becomes smaller. Hence the satellite moves to a lower orbit with an increased speed. Thus due to the atmospheric friction, the satellite spirals down towards the earth with increasing speed and ultimately bums out in the lower dense atmosphere.