# How does the gravitational force exerted by a proton on an electron compare to the gravitational force exerted by an electron on a proton?

Sep 26, 2014

They are equal in magnitude.

Two bodies always exert forces on each other that are equal in magnitude and opposite by direction by Newton's Third Law. Therefore, in this case, the gravitational force exerted by an electron on a proton and that of a proton on an electron are equal in magnitude.

You can always calculate the magnitude of this force by using the relation:

${F}_{\setminus \textrm{G r a v i t a t i o n a l}} = G \setminus \frac{{m}_{e} {m}_{p}}{{r}^{2}}$

Also note that in a similar way, Newton's Third Law applies to electrostatic force - which is another kind of elementary force being exerted on both the electron and proton. Since the charges are opposite, the forces are attractive and also opposite.

You can calculate the magnitude of electrostatic force using this relation:

${F}_{\setminus \textrm{E \le c t r o s t a t i c}} = \setminus \frac{1}{4 \setminus \pi \setminus {\epsilon}_{0}} \setminus \frac{| {q}_{p} {q}_{e} |}{{r}^{2}}$