An New Experimental Formula of Satellite Distances and Its Explanation

In the solar system, there are three satellite systems-those of Jupiter, Saturn and Uranus. In each satellite system, there is a law of satellite distances. An new empiri-mental formuls of this law is obtained, i.e. (1) in this paper, α_n=B₁×Bⁿ, where an is the orbital semi-major axis of n-th satellite, B₁ and Bare constants for each system. Gonorally, the relative error of the value calculated from above formula with the observational value is not more than 10%. However, small satellites have larger errors.