I think there's no other way. You have to observe the fact that the attractive force obeys the inverse square law. That's not measurable with experiments here o

I think there's no other way. You have to observe the fact that the attractive force obeys the inverse square law. That's not measurable with experiments here on earth without extremely advanced modern instruments, so that makes it's effects only really observable on the motion of astronomical bodies. Historically this was the observation that orbits follow elliptical paths. Absent that you'd need some other observation that would lead you to the same conclusion.