Question

Compare two objects in orbit around the earth. One is a satellitein an orbit relatively close to the earth’s surface, and the other is the moon. Assume both have circular orbits. Which of the orbiting bodies has the largest centripetalacceleration? What is the centripetalacceleration of the moon?How would your answer change if Newton’s law of gravity was wrong and all bodies experienced a constant force independent of distance?

Answer 1

centripetal acceleration is given as

a = v²/r

here "v" = speed of the object in the orbit , r = radius of the circular orbit.

here the centripetal force to move in circle is provided by the gravitational force between earth and object.

hence

F_c = GMm/r²

m = mass of object , M = mass of earth , r = distance of object from center of earth

But F_c = ma

hence

a = GM/r²

hence the centripetal acceleration is inversly related to the square of the distance between the object and earth.

so greater the distance , smaller will be the acceleration . hence centripetal acceleration is greater for the satellite as compared to the