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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 $g = GM_E/{R_E}^2$?

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Yes it is incorrect. Most probably it is a typo.

It can either be $$F_g =G \frac {M_E m}{R_E^2}$$ Here they might have misprinted $F_g$ as $g$.

Or

$$g = G \frac {M_E}{R_E^2}$$ Here they probably mistyped the $m$ over there.

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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 $m$.

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