Final answer:
The correct answer is option d, stating that the satellite in a circular orbit around Earth has an acceleration directed toward the Earth due to the centripetal force provided by Earth's gravity. Option d is the correct answer.
Step-by-step explanation:
The motion of a satellite in a circular orbit around the Earth is a classic problem in physics. Despite the satellite moving at a constant speed, it is indeed accelerating, because its direction is constantly changing as it maintains its circular path. This acceleration is directed towards the center of the Earth, which is consistent with the notion of centripetal acceleration: the required acceleration for an object to move in a circular path.
Addressing the initial statement options:
- No force acts on the satellite: This is incorrect because the gravitational force acts as the centripetal force, which keeps the satellite in orbit.
- The satellite moves at constant speed and hence doesn't accelerate: This is a misunderstanding. While the speed is constant, the velocity is not due to the changing direction, resulting in acceleration towards Earth.
- The satellite has an acceleration directed away from the Earth: This is incorrect; the acceleration is towards the Earth.
- The satellite has an acceleration directed toward the Earth: This is the correct option.
- Work is done on the satellite by the gravitational force: This statement is incorrect because, while gravity does act on the satellite, for work to be done in a physics context, there must be displacement in the direction of the force, and in a circular orbit the displacement is perpendicular to the force of gravity, which means no work is done.
The correct answer is option d, which correctly identifies that the satellite has an acceleration directed toward the Earth.