Final answer:
The sum of the kinetic and potential energy of a satellite in orbit around the Earth is a constant value, representing the total mechanical energy. This total energy is negative for a satellite in a bound orbit and positive or zero for unbounded orbits. The kinetic to potential energy ratio decreases as the satellite's orbit size increases.
Step-by-step explanation:
As a satellite moves in orbit around the Earth, the sum of the kinetic energy (KE) and potential energy (PE) is known as the total mechanical energy of the satellite, and it is conserved. According to physics principles, a satellite with a negative total energy is in a bound orbit around Earth, which means it is gravitationally bound and will not escape into space unless additional energy is provided.
The choice for gravitational potential energy is so that it is considered zero at infinity and negative at any point within the gravitational field of Earth. This explains why a satellite with zero or positive total energy would not be in a bound orbit, as it would have enough energy to potentially escape the gravitational pull of the Earth.
For a satellite in a circular orbit, the magnitude of the kinetic energy is one-half that of the potential energy. As the size of the orbit increases, the change in potential energy becomes larger, but the orbital speed decreases, affecting the ratio of kinetic energy to potential energy. The conclusion is that satellites closer to Earth require less energy to achieve orbit but require more kinetic energy relative to their potential energy to maintain that orbit.