A student argues that as a satellite orbits the earth in a circular path, it moves with a constant velocity and therefore has no acceleration. The professor claims that the student is wrong since the satellite must have a centripetal acceleration as it moves in its circular orbit. What is wrong with the student's argument?
constant velocity means constant speed, constant direction. It would fly off in space. It must have a force applied moving it toward the Earth. If it has a Force, it must be accelerating.
Another way to say this is to look at it from an x and y perspective. If you are moving with no acceleration, then there would be no curve to the line. If a satelite is going forward(y), there is no (x) directional changes and thus no acceleration. If it moves around the circle, there is an added (x) direction when means it accelerates in that direction since it started at 0 and is moving to a new velocity in that (x) direction
The student's argument is incorrect because even though the satellite moves with a constant velocity in its circular orbit, it still experiences centripetal acceleration.
Acceleration is defined as any change in velocity, which includes a change in magnitude or direction of velocity. In a circular path, the satellite's velocity is constantly changing because it is always changing direction.
In order for an object to change its direction, it must accelerate towards the center of the circular path. This acceleration is called centripetal acceleration, and it is directed toward the center of the circle at all times.
Although the magnitude of the satellite's velocity remains constant, its direction continuously changes, resulting in a centripetal acceleration. Therefore, the student's argument that the satellite has no acceleration is incorrect.
The student's argument is incorrect because it fails to distinguish between velocity and acceleration. While it is true that a satellite in a circular orbit maintains a constant speed or magnitude of velocity, it still experiences acceleration.
Acceleration is defined as any change in velocity, whether it be a change in magnitude (speed) or direction. In the case of circular motion, the satellite's direction is constantly changing as it orbits the Earth. Therefore, the satellite must experience an acceleration directed towards the center of the circular path, which is known as centripetal acceleration.
To mathematically prove this, we can use the equation for centripetal acceleration:
a = v^2 / r
where "a" represents the centripetal acceleration, "v" is the magnitude of the velocity, and "r" is the radius of the circular path. Since the satellite is constantly changing its direction, its velocity vector is constantly changing, and thus, it experiences acceleration.
Hence, the professor is correct in asserting that the satellite must have centripetal acceleration as it moves in its circular orbit, even though its speed or magnitude of velocity remains constant.