I've imagined this little scenario to help me conceptualize things.
Let's say we have a doughnut-shaped object with a hole whose diameter is greater than that of a sphere. Let's say that the sphere is vertically aligned with the center of the doughnut and is horizontally gravitating towards it according to Newton's law of universal gravitation. What will happen?
1) The sphere will pass through the doughnut, travel a certain distance (but how far) and accelerate back towards the doughnut (and oscillate back and forward).
2) The sphere will stop as it reaches the center of the doughnut. The reasoning behind this is that the distance between the two objects will be zero and hence the acceleration which is inversely proportional to the distance will be infinity (but in both directions?). This doesn't sound right.
3) Something else