Not really. It might seem so, but angular momentum figures in. I've written computer simulations which only modify the accelerations of bodies based upon their separation and then recalculate their positions and loop. I've used a coordinate system based upon an absolute center and one based upon one of the bodies. Initial conditions have slight relative motions(2D simulation)and a random separation. They don't meet. They orbit.
My daughter did a similar project for one of her physics classes where she could adjust the different parameters and there are conditions in which the orbit becomes so distorted that it does fail.
Back to our regularly scheduled programming.
Now Andrew, I know that you didn’t mean to convey the idea that gravity could have accelerated the planets into orbit... (black holes are snorting indignantly)