Answer:
The correct answer is Option D, the closed system containing the planet and the star.
Explanation:
To start, we need to define mechanical energy: the energy an object has from its motion and position.
The fundamental principle in physics is that the total energy in a closed system stays constant, even if it transforms. By saying "closed system," we refer to a system isolated from its surroundings. Energy never leaves the system; it only moves from one part to another.
This statement only applies to closed systems, however. An open system that interacts with its environment works differently. Energy may enter and leave the system through interaction with external forces, and this includes mechanical energy. For this reason, Option A and Option B are incorrect.
The remaining two options, C and D, only vary with the objects in the closed system. Option D includes the star; Option C does not.
However, we should take a closer look at Option C. Can an object have potential energy with itself? No, it cannot. It only has potential energy with other bodies. If the system is defined as the planet only, the only type of energy present is kinetic energy. We know a planet orbiting a star has more kinetic energy near and more gravitational potential energy further from its star. Thus it has less kinetic energy further from its star and less mechanical energy. Because of this, Option C is incorrect.
The only answer left is Option D. If we define the planet and star as a closed system, we find no net external force acting on it. Consequently, it obeys the law of conservation of energy. From prior reasoning, we know mechanical energy includes potential energy and kinetic energy and that the amounts of these energies vary with its orbit. As a result, mechanical energy is always conserved and always the same. In the end, the correct answer is Option D.
