Q.What is the variation in acceleration due to gravity with altitude?

[!TLDR] g decreases with increasing altitude h, following $g_h=gR^2/(R+h)^2$, approximately $g_h\approx g(1-2h/R)$ for small h. [!ANSWER] g decreases c …

As an object is raised to height h above a planet's surface, its distance from the planet's centre increases from R to $(R+h)$, so the acceleration due to gravity decreases according to the exact relation $g_h=\dfrac{GM}{(R+h)^2}=\dfrac{gR^2}{(R+h)^2}$. For small heights, where $h\ll R$, the binomial approximation gives the simpler linear form $g_h\approx g\left(1-\dfrac{2h}{R}\right)$, showing g falls off roughly linearly with altitude for modest heights, though the true fall-off is an inverse-square curve that only e …

State the exact inverse-square altitude formula and its small-height linear approximation, bo …

Using the linear approximation $g_h\approx g(1-2h/R)$ even when h is comparable to R, where it becomes noticeably ina …