To find the attractions between planets and stuff like that, you use the center of gravity/mass to apply to Newton's equation. So even if those planets collided into each other, you could separate them if you give enough force, because $r$ (distance between the center of gravity/mass of each planet) in the gravitation equation is not $0$ therefore $r^2$ is not $0$. But the problem comes when you put the centers of gravity/mass of two objects on each other. Then $r$ is $0$, $r^2$ is $0$ and when you divide by $r^2$ (in the gravitation equation), you’re dividing by $0$ which means the gravity is infinite; i.e you'll never be able to separate them. Now you might say that there will never be such an instance where the two centers of gravity/mass will never be on each other, but consider this-
Two hoops, one 1/2 in radius of the other, placed on a table such that the circumference of those 2 hoops are parallel (like a train track that goes in perfect circles). The center of mass of the bigger hoop will be at the very center of the area (circle) enclosed by the bigger hoop. The same goes for the second, smaller hoop. The center of mass of each hoop will lie on the same point. So does that mean no matter how much you tried, you'll never be able to separate them? This question has been puzzling me for ages so help would be great.