I have always had this question in mind. I know expression for gravitational potential is given as


While acceleration due to gravity is given as


So i assume


Is my assumption correct? Even if it is, I am not able to understand this relation intuitively. Initially I thought that this meant that thier (acceleration due to gravity and gravitational potential) directions were different. But Gravitational potential is scalar and cannot have direction. If my assumption is not correct, is there any intuitive relation between $V$ and $g$?

  • $\begingroup$ Acceleration is proportional to the inverse of the distance squared. V and g take different units (V is measured in $J/kg$, or $m^2/s^2$, while acceleration is measured in $m/s^2$), they cannot become equal by simple negation. $\endgroup$ Jun 2 at 15:40
  • 3
    $\begingroup$ What made you think $g\propto 1/r$ rather than $g\propto 1/r^2$? $\endgroup$
    – J.G.
    Jun 2 at 15:45

1 Answer 1


$V \ne -g$. For one thing, the gravitational potential is a scalar while $\vec g$ is a vector field, so they can't be equal. They aren't equal in magnitude either: $$ V = -\frac{GM}{r}$$ $$ \vec g = -\frac{GM}{r^2}\hat r \ \ \Rightarrow \ \ g = |\vec g| = \frac{GM}{r^2}$$ The relation between $V$ and $\vec g$ is $$\vec g = -\vec\nabla V,$$ i.e. $\vec g$ is the negative gradient of $V$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.