Other
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010phdt.......169h&link_type=abstract
ProQuest Dissertations And Theses; Thesis (Ph.D.)--York University (Canada), 2010.; Publication Number: AAT NR68320; ISBN: 97804
Other
Scientific paper
A study of a low-orbit polar satellite around Mars is carried out using Lagrangian mechanics principles and Lagrange's planetary equations in which both conservative and non-conservative forces are modelled. Our work differs from state-of-the-art Newtonian and Gaussian methods and enhances the modelling of the perturbing potentials arising from areopotential anomalies: atmospheric drag, dust drag, solar radiation pressure, relativistic effects, third-body, and solid-body tides on Mars. Because we are interested in analytical/numerical expressions and results, the Lagrangian method constitutes a more suitable analytical approach than does the traditional Gaussian. The resulting system of equations of motion for the satellite provides the time derivatives of the orbital elements as functions of the gravitational harmonic coefficients and all the perturbing effects we considered. When the time derivatives of the orbital elements are available from satellite tracking observations, the equations can be used in a least-squares estimation process to provide, the gravitational field in terms of harmonic coefficients. To understand the utility of the derived equations of motion, we obtain analytical expressions for the gravitational harmonics of degree and order six. These expressions involve, among other variables, the inclination and eccentricity functions and their time derivatives. In particular, the numerical calculation of high-degree/order eccentricity and inclination functions are known to be numerically unstable. To remove such instabilities, we use an effective and efficient transformation that relates the eccentricity functions to Hansen coefficients, using Bessel functions of the first kind. Similarly, the inclination functions are transformed into hypergeometric series. Analytical and numerical tests show that the transformed inclination and eccentricity functions are remarkably stable up to degree/order eighty. This is very important when the Lagrangian method is used to determine the gravitational field with high accuracy and spatial resolution. We study the effects of atmospheric dust on low orbiters by considering a low velocity "fluid" dust medium containing dust particles of radius 1.25 mum, by deriving a velocity-cube dissipation function that represents the energy density dissipated by the satellite per unit time. We have developed a method for determining a satellite's dust drag coefficient provided that its geometrical shape is known. For example, for a cylindrical satellite, we find that Cd = 4. We also calculate an upper bound to the atmospheric dust density of 8.323 x 10-10 kg m-3 at an altitude of 100 km. Local dust storm-clouds in the range of 800 - 1000 km reduce the semi-major axis from a few centimetres up to a few decimetres per day. Similarly, episodic dust clouds of 10 km in length and at low altitudes (65 - 90 km) result in sub-millimetre per day losses in the semi-major axis. The satellite's mass increase due to dust adhesion is modelled by considering the dust as an aerosol moving in an atmospheric fluid. Adhesion affects the semi-major axis by a few millimetres to a few decimetres per year. Other orbital elements are affected only by insignificant amounts.
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