The Earth moves in a nearly perfect circle around the Sun. Assume the speed stays constant. Is the Earth accelerating or not?

http://en.wikipedia.org/wiki/Acceleration

The Earth orbits the Sun due to gravitational acceleration, so yes.

If the speed of the Earth stays constant in its motion around the Sun, then according to the definition of acceleration, the Earth is not accelerating. Acceleration refers to any change in speed or direction. Since the speed remains constant, there is no change, and therefore, no acceleration. However, it's important to note that while the speed is constant, the direction of motion is constantly changing since the Earth moves in a nearly perfect circle, resulting in a centripetal acceleration that keeps the Earth in orbit around the Sun.

To determine whether the Earth is accelerating or not, we need to understand the concept of acceleration. Acceleration is defined as the rate at which an object's velocity changes. Velocity, on the other hand, is a measure of an object's speed in a given direction.

In the case of the Earth orbiting the Sun in a nearly perfect circle, its speed can indeed stay constant. However, there is still a change in the direction of its velocity, as it is constantly changing its direction toward the Sun. This change in direction indicates a change in the Earth's velocity, and therefore acceleration.

Therefore, even if the speed of the Earth remains constant, it is still undergoing acceleration due to the change in its direction. This acceleration is directed towards the Sun, causing the Earth to continually change its direction in its circular orbit.