A rover operating on Mars measures changes in gravitational pull as it climbs a steep hill of height ∆z, where ∆z is much smaller than R_Mars (the radius of Mars). Use the binomial expansion
(1 ± x)ⁿ = 1 ± nx + (n(n-1)/2) x² ± ...
to derive the formula approximating the change in acceleration due to gravity in Mars $\Delta g_{\text{Mars }}$, where $g_{Mars}$ is the gravitational acceleration at Mars's surface.

• A. $-4g_{Mars}\frac{\Delta z}{R_{\text{Mars }}}$
• B. $-3g_{Mars}\frac{\Delta z}{R_{\text{Mars }}}$
• C. $-2g_{Mars}\frac{\Delta z}{R_{\text{Mars }}}$
• D. $-g_{Mars}\frac{\Delta z}{R_{\text{Mars }}}$

Answer: (C)