Question

A planet is in a circular orbit about a remote star, far from any other object in the universe. Which of the following statements is true? a) There is only one force acting on the planet. b) There are two forces acting on the planet and their resultant is zero. c) There are two forces acting on the planet and their resultant is not zero. d) None of the above statements are true.

Short answer

a) There is only one force acting on the planet. b) There are two forces acting on the planet and their resultant is zero. c) There are two forces acting on the planet and their resultant is not zero. d) None of the above statements are true. Answer: c) There are two forces acting on the planet and their resultant is not zero.

Step-by-step solution

Identifying the forces acting on the planet

In a circular orbit, there are two primary forces acting upon the planet: gravity and centripetal force. The force of gravity is the attractive force between the planet and the star, while the centripetal force is the inward pulling force that keeps the planet moving in a circular path. Since these two forces are key players in this scenario, we can eliminate option (a) as it states that there is only one force acting on the planet.

Determine the relationship between the forces

Since the planet is in a circular orbit, the two forces must be in balance to maintain the stable orbit. That is, the gravitational force acting on the planet is what provides the necessary centripetal force to keep the planet in orbit. Mathematically, this can be expressed as: F_gravity = F_centripetal In a stable orbit, these forces are equal in magnitude but in opposite directions. This means that their vector sum will not be zero because they are not acting in the same direction.

Analyze the remaining options

Based on our understanding of the forces acting on the planet, now we need to look at the remaining options: b) There are two forces acting on the planet and their resultant is zero. c) There are two forces acting on the planet and their resultant is not zero. d) None of the above statements are true. Option (b) would be true if the forces were acting in opposite directions. However, this is not the case, as the gravitational force and the centripetal force are not acting in opposite directions, but have a specific relationship to maintain a stable orbit. Therefore, the correct answer is: c) There are two forces acting on the planet and their resultant is not zero.