Theories and Inequalities on the Satellite System

Abstract EN

We define the satellite system without any central, the satellite system with a central, and the satellite system of single point with a central.

For the satellite system without any central S{Γ,ΓN}, we establish the inequality: ∮Γds∮ΓN|PQ|dsQ≤(N|Γ|3/4π2)sin(2π/N).

For the satellite system with a central S{O,Γ,ΓN}, we establish the following inequality under the proper hypothesis: ∮ΓMN[t](r)ds≤(|Γ|2/2π)cos(π/N)(∀t∈]-∞,-2]).

As an application, we get the inequalities ∮ΓρPds≥∮ΓrPds≥2|D(Γ)|, for the satellite system of single point with a central S{O,Γ,P}.

For these results, there are generalized backgrounds in the fields of differential geometry and space science.