Question

In case of a satellite orbiting around earth, is it's centripetal acceleration and gravitational acceleration the same?

Answer 1

No, the centripetal acceleration and gravitational acceleration experienced by a satellite orbiting around the Earth are not the same.

Centripetal acceleration refers to the acceleration directed towards the center of the circular path followed by an object in uniform circular motion. It is responsible for keeping the object in its orbit and is always perpendicular to the object's velocity. The centripetal acceleration is given by the equation:

$a_{\text{centripetal}}=\frac{v^2}{r}$

where $v$ is the velocity of the satellite and $r$ is the radius of the circular orbit.

On the other hand, gravitational acceleration is the acceleration due to gravity acting on the satellite. It is the force that pulls the satellite towards the Earth and allows it to remain in orbit. The gravitational acceleration is given by the equation:

$a_{\text{gravitational}}=\frac{GM}{r^2}$

where $G$ is the gravitational constant, $M$ is the mass of the Earth, and $r$ is the distance between the center of the Earth and the satellite.

In an orbit, these two accelerations are not equal, but they are related. The centripetal acceleration is a result of the gravitational force acting on the satellite. The gravitational force provides the necessary centripetal force to keep the satellite in its orbit. Mathematically, the centripetal force is given by:

$F_{\text{centripetal}}=\frac{m{v}^2}{r}$