# Fourth Order Theories For Orbit Predictions For Low And High Eccentricity Orbits In An Oblate Atmosphere With Scale Height Dependent On Altitude

- Paper number
IAC-07-C1.4.06

- Author
Dr. Ram Krishan Sharma, Indian Space Research Organisation (ISRO), India

- Coauthor
Mr. Xavier James Raj, Indian Space Research Organisation (ISRO), India

- Year
2007

- Abstract
An accurate orbit prediction of the Earth satellites is an important requirement for mission planning, satellite geodesy, spacecraft navigation, reentry and orbital lifetime estimates. The problem becomes more complicated in the near Earth environment as the Earth gravitational field and the Earth atmosphere influence the satellite. 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. It is well known that the KS total energy element equations are a powerful method for numerical solution with respect to different type of perturbing forces. The first author had utilized these equations to generate analytical solutions for orbit predictions for low and high eccentricity orbits with air drag perturbation up to third order terms in e and c, oblateness parameter, with analytical oblate atmospheric model. Using a particular canonical form of the KS equations of motion known as uniformly regular KS canonical equations, the authors have developed third order analytical solutions for low eccentricity orbits with air drag for spherical and oblate atmospheric models. The density scale height H was assumed constant in the above studies. In this paper we shall develop fourth order analytical solutions for orbit predictions with air drag for low and high eccentricity orbits in an oblate atmosphere with variation in H with altitude. For low eccentricity orbits uniformly regular KS canonical elements will be utilized. Terms up to fourth order in e and c will be included. The analytical solution will be compared with the numerically integrated values as well as with the extended fourth order theory of Swinerd and Boulton. For high eccentricity orbits, the KS elements will be used. The series expansions up to fourth order will be generated in terms of a new independent variable, function of e, and c. The effect of fourth order terms and H will be analyzed. MACSYMA and Maxima software will be utilized to carry out the analytical computations

- Abstract document
- Manuscript document
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