A fourth-order analytical theory for orbit predictions with air drag in terms of KS uniformly regular canonical elements
- Paper number
IAC-08.C1.3.4
- Author
Dr. RAM KRISHAN SHARMA, ISRO, India
- Coauthor
Mr. Xavier James Raj, Indian Space Research Organization (ISRO), India
- Year
2008
- Abstract
An accurate orbit prediction of the Earth’s satellites is an important requirement for mission planning, satellite geodesy, spacecraft navigation, re-entry and orbital lifetime estimates. It has become necessary to use extremely complex force models to match with the present operational requirements and observational techniques. The problem becomes all the more complicated in the near-Earth environment due to the fact that the satellite is influenced by the non-spherical effects of the Earth’s gravitational field as well as the dissipative effects of the Earth’s atmosphere. The effects of the atmosphere are difficult to determine since the atmospheric density, and hence the drag undergoes large modeled fluctuations. Though the accurate ephemeris of a near-Earth satellite can be generated by the numerical integration methods with respect to a complex force model, the analytical solutions, though difficult to obtain for complex force models and limited to relatively simple models, represent a manifold of solutions for a large domain of initial conditions and find indispensable application to mission planning and qualitative analysis. The method of the KS total-energy element equations [1] is a powerful method for numerical solution with respect to different type of perturbing forces. These equations were used systematically by the second author to generate a number of non-singular analytical solutions for low and high eccentricity orbits with air drag perturbation, by keeping the density scale height constant. Using a particular canonical form of the KS equations of motion known as uniformly regular KS canonical equations, where all the 10 canonical elements are constant in the unperturbed two-body problem, the authors have developed third-order non-singular analytical solutions for low eccentricity orbits with air drag using spherical, oblate and oblate diurnally varying atmospheric models with constant density scale height [2, 3, 4]. Also, the authors developed fourth-order non-singular analytical theories for orbit predictions for low and high eccentricity orbits in terms of uniformly regular KS canonical elements and KS elements, respectively, in an oblate atmosphere with scale height dependent on altitude [5]. In this paper, we develop a new non-singular analytical theory for orbit predictions for low eccentricity orbits with oblate diurnally varying atmosphere up to fourth-order terms in eccentricity and c (oblateness parameter) and with variation of scale height with altitude. The analytical solution will be compared with the numerically integrated values as well as with the extended fourth-order theory of Swinerd & Boulton [6]. References 1. Stiefel, E.L. and Scheifele, G., Linear and Regular Celestial Mechanics, Springer, Berlin, 1971. 2. Sharma, R.K. and Xavier James Raj, M., Analytical orbit predictions with oblate atmosphere using K-S uniformly regular canonical elements, 56th IAF, Fukuoka, Japan, IAC-C1.6.0, 10 pages, 2005. 3. Xavier James Raj, M. and Sharma, R.K., Analytical orbit prediction with air drag using KS uniformly regular canonical equations, Planetary and Space Science, 54, 310-316, 2006. 4. Xavier James Raj, M. and Sharma, R.K., Contraction of satellite orbits using KS uniformly regular canonical elements in an oblate diurnally varying atmosphere, Planetary and Space Science, 55, 1388-1397, 2007. 5. Sharma, R.K. and Xavier James Raj, M., Fourth-order theories for orbit predictions for low and high eccentricity orbits in an oblate atmosphere with scale height dependent on altitude, 58th IAF, Hyderabad, India, IAC-07-C1.4.06, 10 pages, 2007. 6. Swinerd, G. G. and Boulton, W. J., Contraction of satellites orbits in an oblate atmosphere with a diurnal density variation, Proc. R. Soc. Lond. A 383, 127-145, 1982.
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