I equated the equation for centripetal force F=mv^2/r (of the planet) to the force between the two masses (planet and the satellite) to get:
Centripetal acceleration is the acceleration that a body experiences when it is moving in a circular path. It is always directed towards the center of the circle.
The equation for centripetal acceleration is a = v²/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circle.
The expression for centripetal acceleration is derived using the principles of circular motion and Newton's second law of motion. By equating the net force acting on a body in circular motion to its mass times its centripetal acceleration, we can derive the formula a = v²/r.
Centripetal acceleration and tangential acceleration are both components of the total acceleration of a body in circular motion. Centripetal acceleration is directed towards the center of the circle, while tangential acceleration is directed tangentially to the circle. They are related by the equation a² = ac² + at².
Some examples of centripetal acceleration in everyday life include the motion of a car around a curve, a roller coaster on a loop, and a satellite orbiting the Earth. Any object that moves in a circular path experiences centripetal acceleration.