# Relation between gravitational field and gravitational potential

The gravitational field is the negative differential of the gravitational potential. Now the gravitational potential due to a particle at a distance $r$ is $-Gm/r$ where $m$ is the mass of the particle. If I take the negative differential of this potential I get $-Gm/r^2$, which should be the magnitude of the gravitational field due to that particle at a distance $r$.

My question is, why is it coming out to be negative? I know that at a distance $r$ due to a particle the gravitational field is $Gm/r^2$ and it is not negative, so why am I getting a negative sign when I take the differential of the gravitational potential?

• The negative sign shows that it an attractive force ie the gravitational field is directed towards the body creating that field. Gm/r^2 gives you the magnitude of the gravitational field. – Farcher Feb 20 '16 at 9:32

Gravitational field is a vector field and is determined by negative gradient of the gravitational potential. $$\vec g=-\vec\nabla \phi$$
Frome equation above, it is obvious that $|\vec g|=|-\vec\nabla \phi|$ (magnitude of $\vec g$ is equal to magnitude of $-\vec \nabla \phi$) and we know that $|-\vec\nabla \phi|$ is a non-negative quantity.
You have made a mistake by assuming that $|\vec g|=-|\vec\nabla \phi|$