Statistics – Computation
Scientific paper
May 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987em%26p...38...21s&link_type=abstract
Earth, Moon, and Planets (ISSN 0167-9295), vol. 38, May 1987, p. 21-36.
Statistics
Computation
3
Artificial Satellites, Astrodynamics, Earth Gravitation, Geopotential, Gravitational Fields, Orbit Calculation, Boundary Value Problems, Orbital Mechanics, Trajectory Analysis, Zonal Harmonics
Scientific paper
In this paper, economical and stable recurrence formulas for the earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulas is also established for the initial value problem of the Burdet oscillator for the prediction of artificial satellites in the earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.
Adel Sharaf Mohamed
Arafah M. R.
Awad M. E.
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