A comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed (b) angular speed (c) angular momentum (d) kinetic energy (e) potential energy (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

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When a comet orbits the Sun in a highly elliptical orbit, several key aspects of its motion change as it moves through different parts of its orbit.

(a) Linear speed: No, the comet does not have a constant linear speed throughout its orbit. According to Kepler's second law, a comet moves faster when it is closer to the Sun (perihelion) and slower when it is farther away (aphelion).

(b) Angular speed: Similar to linear speed, the angular speed of the comet varies throughout its orbit. It moves faster when closer to the Sun and slower when farther away.

(c) Angular momentum: According to Kepler's second law, the angular momentum of the comet remains constant throughout its orbit. This law states that a line joining a planet and the Sun sweeps out equal areas in equal intervals of time, implying that the angular momentum is conserved.

(d) Kinetic energy: The kinetic energy of the comet varies throughout its orbit due to changes in its linear speed. It has higher kinetic energy when closer to the Sun and lower kinetic energy when farther away.

(e) Potential energy: The potential energy of the comet also varies throughout its orbit due to changes in its distance from the Sun. It has lower potential energy when closer to the Sun and higher potential energy when farther away.

(f) Total energy: The total energy of the comet, which is the sum of its kinetic energy and potential energy, remains constant throughout its orbit. This is because the gravitational force between the comet and the Sun is conservative, and thus the total mechanical energy (kinetic energy + potential energy) is conserved.

In summary, while the linear speed, angular speed, kinetic energy, and potential energy of the comet vary throughout its orbit, the angular momentum remains constant, and the total energy (kinetic energy + potential energy) is conserved.