Question

How can an object accelerate towards the center without ever getting any closer to the center?

Answer 1

If the object is making circular motion, it can accelerate towards the center while it is moving around the center.

Explanation:

In circular motion, the object is moving on a circular orbit around the center with velocity v. Then the radial acceleration is

`a_(rad) = (v^2)/(R)`

This is called the centripetal acceleration.

For example, if you tie a ball with a string and rotate the ball circularly you can feel the tension in the string. This tension is equal to
`(mv^2)/(R)` according to Newton's Second Law.