Does Mechanical Energy of a Planet Change in an Elliptical Orbit?

In summary, the mechanical energy of a planet in an elliptical orbit remains constant despite variations in kinetic and potential energy as the planet moves closer to and farther from the central body. The total mechanical energy, which is the sum of kinetic and potential energy, is determined by the semi-major axis of the orbit. Therefore, while individual energy components fluctuate, the overall mechanical energy does not change for a planet in a stable elliptical orbit.
  • #1
mancity
26
2
Homework Statement
Given an elliptical planetary orbit of a planet and a star, do:
(a) the mechanical energy of the planet change during the orbit? If so, describe the motion.
(b) the mechanical energy of the planet-star system change during the orbit? If so, describe the motion.
Relevant Equations
ME=KE+PE
Obviously the mechanical energy of the total system remains the same.

But I'm having a hard time determining of the ME of the planet is constant or if it is changing.
 
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  • #2
mancity said:
Homework Statement: Given an elliptical planetary orbit of a planet and a star, do:
(a) the mechanical energy of the planet change during the orbit? If so, describe the motion.

But I'm having a hard time determining of the ME of the planet is constant or if it is changing.
What's the precise definition of the ME of a planet that is part of a two-body system?
 

FAQ: Does Mechanical Energy of a Planet Change in an Elliptical Orbit?

Does the mechanical energy of a planet change in an elliptical orbit?

No, the total mechanical energy of a planet in an elliptical orbit remains constant. This is because the mechanical energy, which is the sum of the kinetic and potential energies, is conserved in a closed system according to the law of conservation of energy.

How does the kinetic energy of a planet vary in an elliptical orbit?

The kinetic energy of a planet in an elliptical orbit varies depending on its position in the orbit. It is highest when the planet is closest to the star (at perihelion) and lowest when it is farthest from the star (at aphelion).

How does the potential energy of a planet change in an elliptical orbit?

The gravitational potential energy of a planet in an elliptical orbit also varies with its position. It is most negative (lowest) when the planet is closest to the star (at perihelion) and least negative (highest) when it is farthest from the star (at aphelion).

What is the relationship between kinetic and potential energy in an elliptical orbit?

In an elliptical orbit, as the planet moves closer to the star, its potential energy decreases (becomes more negative) and its kinetic energy increases. Conversely, as the planet moves away from the star, its potential energy increases (becomes less negative) and its kinetic energy decreases. The sum of the kinetic and potential energies remains constant.

Why does the total mechanical energy remain constant in an elliptical orbit?

The total mechanical energy remains constant in an elliptical orbit because the forces involved are conservative. The gravitational force between the planet and the star is a conservative force, meaning that the work done by this force only depends on the initial and final positions of the planet, not on the path taken. This ensures that the total mechanical energy is conserved.

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