15TH-Order Harmonics in the Geopotential, from Analysis of Decaying Satellite Orbits.
ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
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A satellite with an initial orbital period greater than about 96 minutes will, as it decays under the action of air drag, pass through 15th-order resonance when successive equator crossings are exactly 24 degrees apart, so that each day the satellite follows a fixed set of 15 ground tracks. If the decay is slow enough, the inclination i of the orbit to the equator changes appreciably as the satellite passes through resonance, because of the build-up of perturbations caused by the tesseral harmonics in the Earths gravitational potential of order 15 and degree 15, 17, 19, 21 ... . Equations between the coefficients of these harmonics can be obtained by analyzing the changes in orbits at a variety of inclinations, offering a method of evaluating 15th-order harmonics almost free of contamination from other harmonics. The paper describes the results so far obtained in these studies, from the satellites Ariel 3 i 80 degrees, Transit 1B i 51 degrees, Cosmos 373 i 63 degrees Cosmos 387 i 74 degrees. A set of values is derived for the coefficients of order 15 and degree 15, 17, 19 and 21. Author
- Spacecraft Trajectories and Reentry