Question

A comet moves in an elliptical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), which of the following results is true?

	Speed of the comet	Angular momentum of the comet/sun system	Gravitational potential energy of the comet/sun system
A	Increases	Increases	Decreases
B	Increases	Constant	Decreases
C	Decreases	Decreases	Increases
D	Increases	Increases	Constant
E	Constant	Constant	Constant

Answer 1

We may analyze this problem using Kepler's laws of planetary motion. These laws apply to planets orbiting the Sun and hold equally well for satellites, comets or other massive central body.

The law of Areas says that a line that connects a comet to the Sun sweeps out equal areas in the plane of comet's orbit in equal intervals of time. This means that when comet is closer, it moves faster when it is farther from the Sun.

As the comet moves from aphelion to perihelion, the speed of comet increases.

In the circular motion, the angular momentum of system is always conserved. So angular momentum of comet/sun system will be constant.

The gravitational potential energy (U) of comet/sun system is given as,

where G is universal gravitational constant, M is mass of sun, m is mass of comet, r is distance between Sun and comet.

As comet moves from aphelion to perihelion, r decreases. This means the magnitude of U increases but it gets farther away from zero. This means that the gravitational potential energy of comet/sun system decreases.

So the correct option is B.