Investigation of Higher Degree Terms of the Solid Tide Potential as a Function of the Satellite Altitude of 1000–6000 km

Abstract

The precise determination of satellite orbit is possible due to our precise knowledge of the theory of satellite motion and as a result of all forces acting on a satellite being known and the high precision of measurement techniques. Forces Caused by distribution of the Earth mass and atmosphere, increase with inversely proportion to satellite altitude (it means gravity field of the Earth, solid and ocean tides, Earth atmosphere). Usually, the gravity field and the tide potential in an external point P(r,ø,λ)of the Earth are described by:

$$ V = \frac{{GM}}{r}\left[ {1 + \sum\limits_{n = 2}^\infty {\sum\limits_{m = 0}^n {{{\left[ {\frac{{{}^aE}}{r}} \right]}^n}{P_{nm}}(\sin \phi )\left[ {\left[ {{C_{nm}} + \Delta {C_{nm}}} \right]\cos m\lambda + \left[ {{S_{nm}} + \Delta {S_{nm}}} \right]\sin m\lambda } \right]} } } \right] $$

(1)

where;

P_nm(sinø) -the associated Legendre function of degree n and order m,

GM -the gravitational constant of the Earth,

r,ø,λ -the distance from the center of mass, latitude, and the longitude to the satellite,

C_nm,S_nm -the coefficients of the gravity field model,

ΔC_nm,ΔS_nm -the corrections to the coefficients of the gravity field caused by solid and ocean tide potential, they are time functions.