planet - Doesn't gravity attract objects in space until they collide?

There are other formulas at work, but not any other forces.

You need to take into account ont only the force, thus the acceleration, but also the current velocity of a body orbiting another.

To put it simply: if you move a ball sticked to a rope around your head, the only forces are the tension of the rope and gravity towards the floor. Ignoring gravity, the only force is the tension of the rope, but it anyway does not make the ball to orbit your head, it in fact makes the ball to orbit it, due to the speed you put on it.

The gravity for an orbit, like the rope, causes the already moving object to curve its otherwise stright trajectory into an ellipse/circumference, not to fall to center.