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By Chao, Chia-Chun

Even supposing a great number of texts at the rules and purposes of astrodynamics were released, a booklet is required to summarize the perturbation theories and regulate, or station preserving, algorithms for realizing the dynamics, balance, and upkeep of these orbits. This e-book used to be written to fulfill that desire. It summarizes, in acceptable technical and mathematical aspect, perturbation theories and station retaining algorithms for varied different types of project orbits and constellations. house challenge designers/analysts and structures engineers will positioned this e-book to nice use.
- facts and data showing during this ebook are for informational reasons merely. AIAA and the writer aren't chargeable for any harm or harm as a result of use or reliance, nor do AIAA and the writer warrant that use or reliance could be unfastened from privately owned rights

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3 Generalized Equations of Variation in Terms of F and G Functions Substituting the spherical potential function, Vl, (Eq. [4. 6) Zlr,,,, = Sl,,sin[(I- 2 p ) w + ( I - 2p + q ) M + rn(R - 0 ) ] + Cl,,cos[(I- 2 p ) w + ( I - 2p + q ) M + rn( R - 0 ) ] for I - rn =odd number. 4 Equilibrium Longitudes for 24-Hour Orbits As discussed in K a ~ l a , ~a. 'cross section of Earth along its equatorial plane is slightly ellipse-shaped. It is represented by the tesseral harmonics C22,S22,C,,, S31, . . C44,S44, .

XXXI (l), 99-1 15 (January-March 1983). Gunning and C. Chao, “A PC Based Tool for Molniya Orbit Analysis,” AIAA 963657, presented at the AIAA/AAS Astrodynamics Specialist Conference (San Diego, CA, 29-3 1 July 1996). 5 Application of Averaged Equations to Orbit Analysis This chapter provides examples of long-term orbit variations caused by perturbing sources such as solar-radiation pressure, lunisolar attractions, and Earth gravity harmonics (zonal only). The theme of these examples is to illustrate the application of those averaged equations discussed in Chapter 3 to orbit analysis of a particular type of Earth mission orbit, such as GEO (geosynchronous), H E 0 (highly elliptical), M E 0 (medium Earth), or LEO (low Earth) orbits.

The resonance effect from these tesseral harmonics induces a very slow motion (around 860 days in length) in longitude oscillation around the stable equilibrium points of a 24-hour orbit. Thus, periodic stationkeeping maneuvers are required to maintain the satellite in a given tolerance band. 3, one can derive the equation for predicting the long-term oscillation of longitude of a 24-hour satellite induced by the resonant tesseral harmonics. , ( I - 2 p ) d o / d t + ( I - 2p + q ) d M / d t + r n ( d Q / d t - d O / d t ) 0 .

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