Balanced and frozen orbits of satellites of an earth-like planet

Abstract

The present work is concerned with the design of special types of orbits important for certain applications such as communication, .reconnaissance, etc. These orbits are known as balanced orbits. and frozen orbits. The thesis consists of five chapters.

The 1st chapter is an introduction in which the previous works on the subject are reviewed, and the aim and importance of the work are clarified. In the 2nd chapter, the topics relevant to the problem are proposed, including the Lagrange's planetary equations. The disturbing function e ressing the effects of the earth's oblateD;ess up to the 4 zonal harmonic is formed, and the expressions for the components of force resulting from the Luni-Solar effects are derived. These components are obtained 2

up to •o(r/r0) body.

, where the subscript "D" refers to the disturbing

In chapter 3 , Both the effects of the earth oblateness and the Luni-Solar attractions are averaged over the mean anomaly, and then the equations for the averaged variations of the Keplerian elements are formed. The obtained solution is dubbed "modeJ A".

In chapter 4 , Model A is fmther simplified by averaging over the intermediate angle variables u0 for geocentric distances 4 to 7 earth radii. Then in the resulting equations, stationary values of g (dg/dt = 0) and h (dh/dt = 0), are analyzed numerically to find the required atlas of balanced orbits. This is expressed in terms of 99 graphexpressing the relations between both dhldt and dg/dt and i for different values of a, h, g,and e. and 27 graphs representing the relation between a and i for dhldt = 0 for different values of h, g, and e with 10 three dimensional figures between a , i , and e for the same values of h and g . The three dimensional figures for g are 33 graphs