Question

A planet is orbiting the sun in an elliptical orbit. Let U denote the potential energy and K denote the kinetic energy of the planet at an arbitrary point on the orbit. Choose the correct statement.

A. K < |U| always
B. K > |U| always
C. K = |U| always
D. K = |U| for two positions of the planet in the orbit.

Answer 1

The correct option is D: K = |U| for two positions of the planet in the orbit, which occur at the closest and furthest points from the Sun, and this is due to the conservation of angular momentum and energy in elliptical orbits.

Step-by-step explanation:

The correct statement regarding the relationship between potential energy (U) and kinetic energy (K) of a planet in an elliptical orbit is that K = |U| for two positions of the planet in the orbit. In an elliptical orbit, according to Kepler's Second Law and the conservation of angular momentum, the planet's velocity—and therefore its kinetic energy—changes depending on its distance from the sun. At the two points where the planet is at its closest (periapsis) and furthest (apoapsis) from the Sun, energy conservation dictates that the kinetic energy and potential energy follow this relationship. The potential energy is chosen to be negative due to the convention that it is zero at an infinite distance and negative at any finite distance, thus when an object is bound in orbit around another object, the total energy (the sum of kinetic and potential energy) is negative, indicating a bound orbit.