A planet orbits a star along an elliptical path from point X to point Y, as shown in the figure. In which of the following systems does the total mechanical energy of the system remain constant?
A
The open system containing the planet
B
The open system containing the planet and the star
с
The closed system containing the planet
D
The closed system containing the planet and the star

In the closed system containing the planet and the star the given systems does the total mechanical energy of the system remain constant. Thus correct option of the given question is option D.

Mechanical energy-

Mechanical energy is the energy that is stored by a body because of its motion or its position. This energy can be rotational, transnational or rotational when it is in the moving position.

Energy conservation for an isolated system is a fundamental principle of physics, which states that total energy in a closed and isolated system is constant.

Open system-

An open system is a system that freely exchanges energy and matter with its surroundings. It means energy may enter or leave to this system.The system of star and planet shown in the graph do not fall under the open system as the matter does not transferred from it.Thus option A and B both are incorrect.

Closed system-

Closed system is the physical system in which the transfer of matter not allowed. The system of planet and star is the perfect example which obey the law of conservation of energy. In case of option C it does not include the star in the system. Thus only option D is correct option.

In the closed system containing the planet and the star the given systems does the total mechanical energy of the system remain constant. Thus correct option of the given question is option D.

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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.