Gravity - change with altitude Does acceleration due to gravity, $g$, which is calculated by Newton's equation, decrease with altitude? Forgive the silly question.
 A: The gravitational force on a small mass $m$ some distance $R$ from the center of a large spherical mass $M$ is given by
$$
|F| = \frac{GMm}{R^2}.
$$
If your distance from the center is some altitude $r$ above the radius of the Earth's surface $R_\oplus$, the force is
$$
|F| = \frac{GMm}{(R_\oplus + r)^2}
= \frac{GMm}{R_\oplus^2} \left( 1 + \frac{r}{R_\oplus} \right)^{-2}
\approx \frac{GMm}{R_\oplus^2} \left( 1 - \frac12 \frac{r}{R_\oplus} \right)
$$
So for $r\ll R_\oplus$, you can say that the gravitational force gets weaker linearly with altitude.  Low-earth orbit has $r/R_\oplus \lesssim 25\%$, so for higher "low" orbits this approximation starts to fail (you could take the next term in the binomial expansion if you wanted).  The atmosphere has $r/R_\oplus \lesssim 1\%$, so all gravitational accelerations in the atmosphere are the same to about three significant figures.
A: Yes, because gravity decreases with the square of distance. The amount that it decreases is very small, however. Interestingly enough, you can measurably weigh more inn one city than in another, due to differing densities and altitudes.
