Question

The orbit of Pluto is much more eccentric than the orbits of the other planets. That is, instead of being nearly circular, the orbit is noticeably elliptical. The point in the orbit nearest to the Sun is called the perihelion and the point farthest from the Sun is called the aphelion. At perihelion, the mechanical energy of Pluto's orbit has:

A) Its maximum value
B) Its minimum value
C) The same value as at every other point in the orbit
D) The value which depends on the sense of rotation

Answer 1

Hint:The work done by the force depends on the angle between the displacement of the body and the force acting on the body. The change in mechanical energy of the system is equal to the work done by the external force on the system.

Step-by-step solution:
The gravitational force of attraction exerting on the planet due to the gravity of the Sun is always toward the sun. When the planet swings from the closest point, perihelion, to the furthest point, aphelion, the effective displacement is away from the sun, not toward it.

Like the case of circular motion in circular motion, the total amount of mechanical energy of a satellite in elliptical motion also remains constant.

Since the only gravitational force between the Pluto and the Sun force doing work upon the Pluto is an internal (conservative) force, the ${{W}_{ext}}$ term is zero. Hence, mechanical energy is conserved.

Unlike the case of circular motion, the energy of a planet in elliptical motion will change forms. As mentioned above, the force of gravity does work upon Pluto to slow it down as it moves away from the Sun and to speed it up as it moves towards the Sun. So if the speed is changing, the kinetic energy will also be changing. As the gravitational potential energy between Pluto and the sun depends on the distance from the Sun, therefore the potential energy of the system also changes. The net change in mechanical energy of Pluto remains the same at every point in its elliptical orbit.

Hence, the same value as at every other point in the orbit.

Therefore, option C is the correct answer.

Note:
-The mechanical energy of Pluto is equal to the sum of kinetic energy and the gravitational potential energy.
-The mechanical energy of the system remains conserved when work done by external force is zero.