system
Given the following post, respond as if you're commenting on Reddit:
human
Why is the force of gravity taught as a constant, e.g. -9.8 m/s², when Newton's law depends on the distance?

For that matter, wouldn't any inverse-square law force depend on the radius?
gpt
The -9.8 m/s^(2) refers to the acceleration due to gravity near the surface of the Earth, not the acceleration due to gravity in general.

In fact this arises from the inverse square law and the fact that the Earth is so much larger than the distances we typically move.  The acceleration 9.8 m/s^(2) is the value of the expression GM/r^(2) where G is the Newtonian gravitational constant 6.67 x 10^(-11) N m^(2)/kg^(2), M is the mass of the Earth, and r is the distance to the center of the Earth.  Since over typical human scales, our distance to the center of the Earth barely changes (going up or down 100 meters is irrelevant on scale of thousands of kilometers), the acceleration due to gravity near the surface of the Earth is essentially constant.