Abstract
An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.
Highlights
The fact that the Earth is not a true sphere is one of the important causes for the deviation of the orbits of the artificial satellites from undisturbed Keplerian ellipses, the largest perturbations in the motion of such satellites being due to the oblateness of the Earth
If ζ is an osculating element and ζ sp is the short-periodic variation in the corresponding element, the mean element ζ m is related by ζ ζ m ζ sp where ζ sp is the function of mean elements
Sharma [10] utilized the theories of Bhatnagar and Taqvi and Liu to compute the mean elements using the iterative scheme of Gooding [11] and made a comparison between them
Summary
The fact that the Earth is not a true sphere is one of the important causes for the deviation of the orbits of the artificial satellites from undisturbed Keplerian ellipses, the largest perturbations in the motion of such satellites being due to the oblateness of the Earth. By retaining the quadratic terms in h and l, Bhatnagar and Taqvi [8] generated the short periodic expressions: δa, δh, δl, δΩ, δi and δλ0 , where λ0 M ω , to an accuracy of second-order in eccentricity. In this Paper, an analytical theory for calculating the perturbations due to J2 in the orbital elements of a satellite to accuracy up to fourth power in eccentricity is derived.
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