How does the conservation of mechanical energy explain why a planet in an elliptical orbit changes speed?
The conservation of mechanical energy explains why a planet in an elliptical orbit changes speed by considering the interplay between gravitational potential energy and kinetic energy.
The conservation of mechanical energy states that the total mechanical energy of a system is constant as long as no external forces, such as friction or air resistance, are acting on it. In the case of a planet in orbit, we can analyze the changes in its mechanical energy to understand the variation in speed.
As a planet moves in its elliptical orbit around the Sun or any other massive body, it experiences changes in gravitational potential energy and kinetic energy. Gravitational potential energy is the energy associated with the position of an object in a gravitational field, while kinetic energy is the energy associated with the motion of an object.
When a planet is closer to the massive body (i.e., at perihelion), it has a lower gravitational potential energy due to the stronger gravitational pull. As the planet moves farther away (i.e., at aphelion), its gravitational potential energy increases since the gravitational pull weakens. The change in potential energy is accompanied by a change in kinetic energy to keep the total mechanical energy constant.
According to the law of conservation of mechanical energy, as the planet moves closer to the massive body, its kinetic energy must increase. This means that the planet speeds up, as kinetic energy is directly proportional to the square of the velocity. Conversely, as the planet moves away and its potential energy increases, the kinetic energy must decrease to maintain the constant total energy. Therefore, the planet slows down.
In summary, the conservation of mechanical energy explains that a planet in an elliptical orbit changes its speed because it undergoes variations in kinetic energy to compensate for changes in gravitational potential energy.