  By using an arithmetic fact, we will firstly prove Saari's conjecture in a
particular case, which is called the Elliptical Type N-Body Problem, and then
we apply it to prove that the variational minimal solution of the planar
Newtonian N-body problem is precisely a relative equilibrium solution whose
configuration minimizes the function $IU^2$, it's worth noticing that we don't
need the hypothesis of Finiteness of Central Configurations. In the Planetary
Restricted Problem (which ignore all the mutual gravitational interactions
between the planets), the corresponding Saari's conjecture is stated and
proved.
