Potential Gradients

The gravitational potential gradient at a point is the change in gravitational potential per metre, ΔV_g/Δr. Its unit is J kg^-1 m^-1, which is the same as N kg^-1.The gravitational field strength is equal to the negative of the potential gradient, g = -ΔV_g/Δr. The minus sign shows that the field points in the direction in which the potential decreases, towards the mass.On a graph of V_g against r, the gradient of the tangent at any point gives the potential gradient, and so the magnitude of g, at that distance. Because V_g = -GM/r, the curve rises towards zero and becomes less steep further from the planet, showing that the field gets weaker.Lines joining points of equal potential are called equipotentials. No work is done moving a mass along an equipotential, and field lines always cross equipotentials at right angles. Where equipotentials are closer together, the potential gradient and the field strength are greater.