By Chao, Chia-Chun
Even supposing a large number of texts at the ideas and functions of astrodynamics were released, a publication is required to summarize the perturbation theories and keep an eye on, or station protecting, algorithms for figuring out the dynamics, balance, and upkeep of these orbits. This booklet was once written to satisfy that want. It summarizes, in acceptable technical and mathematical aspect, perturbation theories and station maintaining algorithms for numerous varieties of undertaking orbits and constellations. area undertaking designers/analysts and platforms engineers will placed this ebook to nice use.
- info and knowledge showing during this publication are for informational reasons merely. AIAA and the writer will not be liable for any damage or harm as a result of use or reliance, nor do AIAA and the writer warrant that use or reliance may be unfastened from privately owned rights
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Extra resources for Applied Orbit Perturbation and Maintenance
Then the equations become 59 60 Application of Averaged Equations to Orbit Analysis de/dt dQ/dt = = -gsinQ z - (g/e)cosQ, where g = (3/2)na2( 1 - e2)1’2Fs,pcos2(~/2)and z = dh,,,/dt - dQ/dt. Because e2 = 0 and dhS,,ldt >> dQ/dt, both g and z can be assumed to be positive constants. These equations ( [ 5 . 2 ] )imply that, depending on the initial value of eccentricity, $ may librate about 0 deg. For instance, if $ = 0 and e = g/z, then e and $ will stay constant at their initial values. 3) where K , equal to eO2 - (2g/z)eocos$, is the constant of integration determined from initial conditions.
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.
73 deg. 4. Coefficients and Terms of Resonance for GPS Orbits Tesseral Harmonics Coefficient 7 r;, Terms Inside Braces I P I 4 I c 9 m -0 -0 60 120 180 240 Longitude of ascending node (deg E) 300 Fig. 7. Values of dddt versus longitude of ascending node of a GPS orbit. 2 I I I I I Longitude of ascending node (deg E) Fig. 8. Minimum A V required for GPS longitude stationkeeping. 73. Therefore more terms must be included in the da/dt equations and the Flmp and GI,, series functions. The resonant tesseral series for GPS (Eqs.
Applied Orbit Perturbation and Maintenance by Chao, Chia-Chun