Why does gravity seem to depend on the (inertial) mass?
This is another interesting and profound question: the same quantity, mass, that appears in Newton’s equations of motion, also appears in Newton’s (or Einstein’s) law of gravitation. This is not due to a lack of imagination on Newton’s part: he thought carefully about this coincidence. Because the two are conceptually distinct, let’s separate them. The inertial mass mi is the constant of a body that appears in Newton’s combined first and second law, F = mia. It is the constant that quantifies the body’s reluctance to be accelerated. The gravitational mass mg is the constant of a body that appears in Newton’s law of gravitation, F = − GmgMg/r2. It quantifies the body’s interaction with the gravitational field. Why are they the same? Experimentally, they are the same: Newton and many others since have conducted experiments. Or rather, they are proportional, because we could consider G to include any fixed ratio mi/mg. What sort of experiment? Here’s an example: take a pendulum consisting
