system
Given the following post, respond as if you're commenting on Reddit:
human
If Newton's Law of Gravitation is only meant for point masses, how come we use it to calculate force of gravity on a massive body like Earth?
gpt
For extended bodies, the force law holds for each infinitesimal piece, and so the total force is the sum (i.e., integral) of each of these infinitesimal forces.

For a spherically symmetric object *A* (this means the object is a sphere and its mass density depends only on the distance from the center), it turns out that the gravitational force from *A* on any other object *B* that is *exterior* to *A* is just the gravitational force on *B* as if all of the mass of *A* were concentrated at its center. In other words, spherically symmetric objects act as if they were point masses, but only on their exterior. This can be proved using the divergence theorem from advanced calculus, and in physics it typically goes by the name of Gauss's Law.