One of my students asked if the graviational force at the Earth's centre is zero. The question was thrown open to the other students and two possible answers were given: zero or infinite! One way of reasoning is to say that the graviational force sums to zero as (assuming uniformity of the Earth) for every force pulling one way is 'cancelled' by and equal and opposite force. But I then imagined modelling the pull of gravity by tension in a rope. Suppose you hold two ropes, one in each hand and the ropes pull in opposite directions with the same magnitude of force. It is true that I wouldn't accelerate as the forces 'cancel' (note the quotation marks), but I certainly wouldn't feel zero force! So the question is: would an observer at Earth's centre feel zero gravity, or would that observer feel the gravitational pull outwards (in all dirctions) towards the surrounding mass?