Question

An artificial satellite revolves around a planet for which gravitational force varies with the distance from its centre as F=k/r². If its orbital speed is v, then:

a. The satellite will move in an elliptical orbit
b. The satellite will move in a circular orbit
c. The satellite will escape the planet's gravitational pull
d. The satellite's orbit cannot be determined from the given information

Answer 1

An artificial satellite with a gravitational force of F=k/r² and constant speed v will move in a circular orbit due to the balance between gravitational force and inertia that characterizes circular motion.

Step-by-step explanation:

Given that the gravitational force acting on an artificial satellite is inversely proportional to the square of the distance from the planet's center, as described by the formula F=k/r², and knowing that the satellite has an orbital speed v, we can infer its orbital behavior.

According to Kepler's Laws and Newton's laws of motion and gravitation, a satellite in stable orbit must have a balance between the centripetal force required to keep it in orbit and the gravitational force exerted by the planet. In the case of a circular orbit, this balance is constant, meaning the gravitational force providing the centripetal acceleration equals the inertia of the satellite moving at a constant orbital speed v. As such, the satellite would move in circular motion because the inverse-square law for gravity indeed defines conditions for circular orbits when the speed is constant.

Thus, the correct answer is: b. The satellite will move in a circular orbit.