Why are centripetal and gravitational forces equal in orbiting bodies?

[Moolisa]

Homework Statement

How would an FBD of the following look like?

Using elementary newtonian mechanics, find the period of mass m1 in a circular orbit of radius r around a fixed mass m2

Relevant Equations

Centripetal force, Gravitational force

I've solved this problem, I know you equal centripetal force with gravitational force, then rearrange for velocity to find T. My answer is the same as the one in the back of the book. But then I started thinking about it and don't know why they are equal to each other. Arent the forces in the same direction? Centripetal force is directed towards m2(the fixed mass at the center) right? Am I forgetting something fundamental to orbiting bodies?

To be clear, the FBD part isn't in the actual problem, so if this question doesn't make sense/is faulty, that would be why

 

[mfb]

Gravitational force is the centripetal force. "Centripetal force" just means "whatever keeps the object on a circle", it doesn't specify what type of force it is. It could also be a string, an electromagnetic force or something else.

 

[Moolisa]

Well, I feel completely embarrassed. Thank you so much,