why gravitational potential energy is negative?
The gravitational potential energy is taken to be zero as a matter of convenience - so that that zero potential energy is at an infinite distance from the centre of a spherical object.why gravitational potential energy is negative?
Actually, as George correctly pointed out, there is no direct connection between the sign of the potential energy and the direction of the force! One could choose the ground such that potential energy would be positive everywhere. It's the change of potential energy that dictates the direction of the force. It's all about the choice of zero of potential (one could even make a choice of zero such that the potential energy is positive for some points and negative for some other points (and zero on some surface). Only a change of potential energy matters, physically. I think it's important to make that clear to the OP!!!In simple terms, if you solve for the force it must be negative for an attractive potential to reflect this. In a repulsive potential the sign must be changed to get the correct direction of the force.