How does the total mechanical energy (kinetic plus gravitational potential energy) of a satellite in an elliptical orbit vary over one complete orbit?

Understand the Problem

The question asks about the behavior of the total mechanical energy (kinetic plus gravitational potential) of a satellite moving in an elliptical orbit around a planet. Since gravity is a conservative force the total mechanical energy will not change, even though the kinetic and potential energy components will change as the satellite moves.

More Information

As a satellite orbits in an elliptical path, its distance from the planet and its speed change. When the satellite is closer to the planet, its speed increases, increasing kinetic energy but decreasing potential energy. When farther, its speed decreases, decreasing kinetic energy but increasing potential energy. The total mechanical energy, however, remains constant if we assume a non-perturbed orbit.

Tips

A common misconception is that the total energy changes because both kinetic and potential energy are changing. However, these changes are interconnected in such a way that their sum remains constant in the absence of external forces.

Sources

• Energy Relationships for Satellites - The Physics Classroom - physicsclassroom.com
• Energy of an orbiting satellite - Elliptical Orbit & Orbital Mechanics - byjus.com
• 13.5: Satellite Orbits and Energy - Physics LibreTexts - phys.libretexts.org