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: a) There is only one force acting on the planet.

Step-by-step solution

Identify the forces acting on the planet

First, let's identify the forces acting on the planet. The main force at play is the gravitational force between the remote star and the planet. This force is directed towards the remote star and keeps the planet in its orbit.

Analyze each statement

Now we will analyze each statement to determine which is true based on the forces acting on the planet: a) There is only one force acting on the planet. If there were only one force acting on the planet, it would be the gravitational force. This statement is true because no other forces are at play as there are no other objects nearby that can influence the planet. b) There are two forces acting on the planet and their resultant is zero. This statement is not true as there is only one force (the gravitational force) acting on the planet. Thus, there cannot be two forces with their resultant being zero. c) There are two forces acting on the planet and their resultant is not zero. Similarly, this statement is not true as there is only one force acting on the planet which is the gravitational force. d) None of the above statements are true. As we established that statement a) is true, this statement is not accurate.

Choose the correct answer

Based on our analysis in Steps 1 and 2, the correct answer is: a) There is only one force acting on the planet.

Key concepts

Gravitational Force

The force that governs the motion of planets and keeps them in orbit is known as the gravitational force. According to Sir Isaac Newton's Law of Universal Gravitation, every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

This force can be described by the formula: \( F = G\frac{m1 \cdot m2}{r^2} \) where \( F \) is the force of gravity, \( G \) represents the gravitational constant (\(6.674 \times 10^{-11} \,\text{N} \cdot \text{m}^2/\text{kg}^2\)), \( m1 \) and \( m2 \) are the masses of the two objects, and \( r \) is the distance between the centers of the two masses.

In our exercise, the planet is kept in a circular orbit around the star solely by this gravitational force, which acts as the centripetal force needed for circular motion.

Circular Motion

Circular motion is the movement of an object along the circumference of a circle or rotation along a circular path. It can involve uniform (at a constant speed) or non-uniform (speed changes) motion. For an object to maintain a circular motion, it must experience a force that acts toward the center of the circle, known as the centripetal force. The gravitational force mentioned earlier serves this purpose in the case of planetary orbits.

The centripetal force needed to make an object perform circular motion is given by the equation: \( F_{centripetal} = \frac{mv^2}{r} \) where \( m \) is the mass of the orbiting object, \( v \) is the orbital speed, and \( r \) is the radius of the orbit. In the orbital context, this centripetal force is provided by the gravitational attraction between the planet and the star.

Orbital Mechanics

The study of the motions of artificial and natural celestial bodies under the influence of gravitational forces is known as orbital mechanics. It relies heavily on the principles of physics and celestial mechanics to predict and understand the orbits of planets, moons, and spacecraft. Kepler's laws of planetary motion describe how celestial bodies orbit in space, and they further clarify the relationship between the orbit's size, shape, and the orbital period.

From the perspective of our exercise, the key takeaway is that the planet's orbit around the star is stable and circular due to the gravitational force acting as the centripetal force, resulting in a balance that keeps the planet in a consistent path, neither falling into the star nor moving away into space.