Question

The force to keep an object turning in a circle is given by F = m×V^2/d How much more force is required for a planet to keep a moon in an orbit of the same distance and speed if the moons mass were to double?

Answer 1

Doubling the moon's mass would require doubling the force to maintain the same orbit because the force is directly proportional to the mass of the object in circular motion.

Step-by-step explanation:

The formula F = m\u00d7V^2/d indicates that the force needed to keep an object in circular motion is directly proportional to the object's mass. Therefore, if a moon's mass doubles, the force required to maintain the same circular orbit at the same speed would also double, since all other factors in the formula (the velocity V and the distance d) remain constant.

Newton's universal law of gravitation is essential to understanding this concept, as it explains that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force provides the centripetal force necessary for an object to maintain a circular orbit. If you double the mass of the moon, you would need to double the gravitational force to achieve the same orbital pattern because the centripetal force requirement has doubled.