When using Kepler's third law of motion to find the period of an orbiting body, why do you combine the altitude of the orbiting body with its radius?
What specifically matters for orbital motion is the separation between the centers of the two bodies. So if you are given the distance between their surfaces, then you also need to add their radii.
Specifically, when studying orbital motion, we study the center-of-mass motion of each body, meaning that we approximate each extended body as a point particle of the same mass. Due to the shell theorem, this approach also accurately accounts for the gravitational force (at least to the extent that the bodies can be approximated as spherical). This is the approximation under which Kepler's laws are valid.
1$\begingroup$ Thank you for this answer, it was very useful. I was a bit confused when examples were given within my textbook which combined the radius with the altitude of the orbiting body in order to form an answer. $\endgroup$– OliverOct 2, 2022 at 13:09