Physics

The key is recognizing that gravitational acceleration depends on distance from Earth's center as $g \propto 1/r^2$. When you move to altitude $h$, the distance becomes $R + h$ instead of $R$, so the new gravity is $g' = g_0 R^2/(R+h)^2$. A 2% decrease means $g' = 0.98 g_0$—set up this ratio and solve for $h$ using the approximation that $h \ll R$, which lets you expand and simplify dramatically.

The key is recognizing that gravitational acceleration depends on distance from Earth's center as $g \propto 1/r^2$. When you move to altitude $h$, the distance becomes $R + h$ instead of $R$, so the new gravity is $g' = g_0 R^2/(R+h)^2$. A 2% decrease means $g' = 0.98 g_0$—set up this ratio and solve for $h$ using the approximation that $h \ll R$, which lets you expand and simplify dramatically.