# Is the equation $g=GM_Em/R_E^2$ in Tipler incorrect?

I was reading my textbook (Tipler et al.), and I am unsure of one of the expressions they used. On page 374, it says (near Figure 11-10) that $$g = GM_Em/{R_E}^2$$. Is this even dimensionally correct? I got a units of $$m/s^2$$ on the left hand side and Newtons on the left hand side. I don't think that they are in agreement. Do they mean to say $$g = GM_E/{R_E}^2$$?

It can either be $$F_g =G \frac {M_E m}{R_E^2}$$ Here they might have misprinted $$F_g$$ as $$g$$.
$$g = G \frac {M_E}{R_E^2}$$ Here they probably mistyped the $$m$$ over there.
Yes, this is certainly an error. The gravitational acceleration is $$g = G M_E/R_E^2$$, consistent with the preceding sentence of the text. It would be inconsistent (and a violation of the equivalence principle) for $$g$$ to depend on $$m$$.