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Numerical Example 2 Kepler_Test1 * (Analytic Kepler algorithms compared with Numerical Integration) High Earth Orbit (HEO) , typical 2-Body solutions using the 2009 TLE file Input: (2009_298, isat = 19773) t1 = 0., t2 = 86400. (seconds) Output: kepler1b failed to converge, kepler1a and kepler2 converged to correct answer DerAstro r_eci (t2) (km) v_eci (t2) (km/s) kepler1a 16906.0049 1871.5115 2495.6926 4.125426 3.558097 0.604363 kepler1b 99927.4767 92921.1426 14631.3162 5.642214 7.607469 0.840981 kepler2 16906.0049 1871.5115 2495.6926 4.125426 3.558097 0.604363 Num. Int. (2-Body) r_eci (t1) (km) v_eci (t1) (km/s) 209.011468 30385.859968 4.280644 2.248716032 2.177749649 0.329155365 * 16906.0051 1871.5115 2495.6927 4.125426 3.558097 0.604363 Free download: Kepler_Test computer programs with source code
Numerical Example 3 Analytic Kepler, SGP4, Vinti, Kepler+ algorithms and num. int. (wgs 4x4, . . .) compared with num. int. (wgs 12x12, . . .) Low Earth Orbit (LEO) , typical 2-Body and perturbed solutions using the 2009 TLE file Input: (2009_249, isat = 4382) t1 = 0., t2 = 86400. (seconds) Algorithm r_eci (t2) (km) v_eci (t2) (km/s) kepler2 346.687092 6795.012489 412.914501 sgp4 257.913989 6719.684754 1214.516634 vinti 207.380964 6701.510662 1337.255798 kepler+ 213.326456 6703.763322 1322.957867 num. int. (4x4, . .) num. int. (12x12, . .) r_eci (t1) (km) v_eci (t1) (km/s) 510.306735 6793.878710 0.007287 2.949065600 0.256823630 7.486987267 Output: kepler2 is poor. sgp4 is fair. vinti is reasonable. kepler+ and num. int. (4x4, . .) produced good solutions for SSA purposes. 213.622528 6703.908820 1322.028866 216.109788 6704.762171 1316.193868 2.978862 0.215630 7.472634 3.040136 1.016065 7.361291 3.045054 1.156390 7.334489 3.044552 1.140038 7.337720 3.044515 1.139009 7.337933 3.044353 1.132308 7.339295
Page 1 and 2: Astrodynamics 101 Part 1: Kepler+ A
Page 3 and 4: Astrodynamics 101: Kepler+ Algorith
Page 5 and 6: Destruction Power of Space Debris P
Page 7 and 8: How Many? Then (2009) http://www.uc
Page 9 and 10: How Debris Clouds Look Like? Debris
Page 11 and 12: Orbit Determination of All Space Ob
Page 13 and 14: object v (t 2 ) at t 2 r (t ) 2 Sph
Page 15 and 16: v (t ) object at t r (t) Accelerati
Page 17 and 18: 3. Sun gravity a = r sun v (t ) ob
Page 19 and 20: V Transfer Orbit v t1 1 v 1 t 1 t 2
Page 21 and 22: 3. Equations of Motion Equations fo
Page 23 and 24: Equations of Motion Formulation Who
Page 25 and 26: 4. Analytic Algorithms for Predicti
Page 27 and 28: Kepler Equations of Motion (2-Body)
Page 29 and 30: + Kepler solution (Vinti and other
Page 31 and 32: APL Technical Digest Vol 27, #3 (20
Page 33 and 34: Key SSA Features of Kepler+ SGP4 Ke
Page 35 and 36: Atm. Drag effects SS, ISS Applicati
Page 37 and 38: UNCLASSIFIED Applications of Analyt
Page 39 and 40: Analytic Algorithm Pioneer -- Prof.
Page 41 and 42: Astrodynamics 101 Part 2: Verificat
Page 43 and 44: Reference Trajectory (General) 6. M
Page 45: Numerical Example 1 Kepler_Test1 *
Page 49 and 50: Algorithm SGP4 (analytic) Vinti (an
Page 51 and 52: Algorithm (Reference = WGS84 12x12,
Page 53: UNCLASSIFIED 7. Numerical Examples

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