This paper presents simple mathematical mobility models for configuration of Global interconnectivity with LEO satellite systems. The aim of this paper is to investigate on the performance measures of the satellite mobility models regarding optimum Global coverage arc length depending on the satellite locations relative to the four zones (quadrants) of the earth surface. A typical body of the satellite was positioned at a modified height of 780 Km from the earth surface and revolving round the earth in a circle of radius, 7160 Km was carefully studied and analytically parameterized enabling the generation of realistic instantaneous coverage arc lengths data. We compared the minimum required instantaneous arc lengths for the three mobility models that should cover the geographical coverage areas of the earth. The impact of the satellite movements relative to the earth locations was that the instantaneous coverage arc lengths were exponentially varying with time and continuously distributed within the four zones of the earth surface to provide continuous coverage around one polar orbit plane and assuming operations can continue down to an elevation angle of zero degree. The advantage of the derived mobility models is achieving almost 100% global coverage as a result of the dynamic behavior of the satellite playing an important role of providing instantaneous coverage arc lengths. This procedure also allows comparisons among different degrees of built-up zones of the earth surface as well as extra-polation to the different locations on the earth surface.