This is a really dumb question but I can't seem to make sense out of this...
For a conservative force, we have [itex]\vec{F}=-\nabla \phi[/itex], where [itex]\phi[/itex] stands for the potential. So let's take the gravitational potential, given by:
[tex]\phi=-G_N \frac{M}{r}.[/tex]
Then, by the previous formula: [itex]\vec{F_g}=-G_N \frac{M}{r^2}\hat{e_r}[/itex]...but this is the expression for the gravitational field (force per unit mass) not the gravitational force... What am I doing wrong?
Thank you very much.
For a conservative force, we have [itex]\vec{F}=-\nabla \phi[/itex], where [itex]\phi[/itex] stands for the potential. So let's take the gravitational potential, given by:
[tex]\phi=-G_N \frac{M}{r}.[/tex]
Then, by the previous formula: [itex]\vec{F_g}=-G_N \frac{M}{r^2}\hat{e_r}[/itex]...but this is the expression for the gravitational field (force per unit mass) not the gravitational force... What am I doing wrong?
Thank you very much.