Statistics – Applications
Scientific paper
May 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004agusm.g41c..04x&link_type=abstract
American Geophysical Union, Spring Meeting 2004, abstract #G41C-04
Statistics
Applications
1200 Geodesy And Gravity, 1227 Planetary Geodesy And Gravity (5420, 5714, 6019), 1241 Satellite Orbits, 1243 Space Geodetic Surveys, 1294 Instruments And Techniques
Scientific paper
Future geodetic satellite missions will most probably make use of the concepts of satellite formation flying. Most studies use Hill equations (HE) to describe the relative motion of the chief satellite and deputy satellite. Some underlying assumptions limit the applicability of HE: (1) the Earth is spherically symmetric; (2) the orbit of the Hill frame is rigorously a circle; (3) the relative distance between the satellites is small compared with the radius of the Earth. Under these assumptions, the homogeneous solutions of HE describe relative orbit motion very well. In reality, the situation is much more complicated. The second zonal spherical harmonic of the Earth,J2,produces the primary gravitational perturbations. This J2 force includes secular, long-periodic, and short-periodic components, which consequently will perturb the satellite orbits. Our objective in this presentation is to study the relative motion between arbitrary chief and deputy satellite configurations due to J2 disturbance for geodetic applications. Four different methods, (1) numerical integration of Newton equations; (2) numerical integration of Lagrange Planetary Equations (LPE) in Gauss form, (3) numerical integration of HE; and (4) nontrivial analytical solutions of HE, will be used to analyze the relative motions in the Hill rotating frame. Since this J2 perturbation has a two cycle per revolution (CPR) frequency component, we developed a complementary analytical solutions for the non-homogeneous HE, which combine the homogeneous, resonant and non-resonant solution. Our preliminary results show that numerical integration of Newton equations and LPE can capture all disturbance characteristics, while the numerical or analytical method of HE perform relatively well in the differential mode. Furthermore, one can get any designed shapes of the relative motion by setting specific initial positions and velocities, e.g. 2 by 1 elliptic motion in the orbital plane.
Sneeuw Nico
Tsoi R.
Xu Cenke
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