Question

If a planet orbits the Sun in an elliptical orbit, the quantities associated with the planet that remain constant are:

• A. Kinetic energy and total energy
• B. Potential energy and angular momentum
• C. Linear speed and angular velocity
• D. Total energy and angular momentum
• E. Kinetic energy and angular velocity

Hint:

In an elliptical orbit, total energy and angular momentum are conserved, while kinetic and potential energies, as well as linear speed and angular velocity, change with position in the orbit.

Answer 1

The Correct Option is D

In an elliptical orbit, the planet experiences a central force due to the Sun, which results in an elliptical trajectory. The key aspects of orbital mechanics that remain constant are:

1. Total Energy: The total energy of the planet (which is the sum of kinetic energy \( K \) and potential energy \( U \)) remains constant in an elliptical orbit. This is because the gravitational force is conservative, and the total energy does not change over time.

2. Angular Momentum: Angular momentum is also conserved in elliptical orbits due to the central force acting along the line connecting the planet and the Sun. Since no external torque acts on the planet, its angular momentum remains constant throughout the orbit.

However:

• Kinetic energy and potential energy vary as the planet moves along its elliptical orbit because the speed of the planet changes depending on its position in the orbit (closer to the Sun, it moves faster; farther, it moves slower).
• Linear speed and angular velocity also change during the orbit because they depend on the planet's distance from the Sun and the shape of the orbit.

Thus, the quantities that remain constant are total energy and angular momentum.

Therefore, the correct answer is:

\[ \boxed{\text{D) Total energy and angular momentum}} \]