nn=N[Pi]/180.; k=.01720209895; (* Elements *) t[1]= 35. t[2]= 40. t[3]= 45. q = 0.4255 e = 0.2 om = 293.*nn w = 105.*nn; i = 72.0*nn; dd=.001 p=.5106 n1=0.51024351323596289267 n3=0.50988404891967368740 === (* Sun * Time 1 *) xs[1]= -0.89355708628300 ys[1]= 0.44109863033400; zs[1]= 0.19125554645600; (* Time 2 *) xs[2]= -0.93110826096800; ys[2]= 0.37143971578100; zs[2]= 0.16105220223500; (* Time 3 *) xs[3]= -0.962082097969 ys[3]= 0.29915678619700; zs[3]= 0.12971111376200; === Time 1 ra[1]= 142.094574218177038 degrees = 2.48001816932663654 radians ok dc[1]= 2.06588785641035421 degrees = 0.0360565450713285207 radians ok r0[1]= 1.47077284511113015 AU ok x3= -0.266166523941678256 AU y3= 0.461897960300171472 AU z3= -0.138236049034874209 AU r = 0.550730015024991104 AU th= 111.366647015358588 degrees = 1.94371466732432338 radians ee= 1.748988268502644778 radians (Eccentric anomaly) ok m= 1.55215511242 HP Time 2 ra[2]= 146.007690781125143 degrees = 2.54831493736440517 radians dc[2]= -3.39669019616296452 degrees = -0.0592834275932557908 radians r0[2]= 1.45240816397906087 AU x3= -0.270986191630523221 AU y3= 0.439148484292561214 AU z3= -0.247105509704191916 AU r = 0.572141626030685745 AU th= 122.535231561477764 degrees = 2.1386432404414597 radians ee= 1.95900897925003008 radians (Eccentric anomaly) m = 1.99562800159 hp Time 3 ra[3]= 150.362559347922708 degrees = 2.62432173234662924 radians ok dc[3]= -8.72114488048189251 degrees = -0.152212692707856378 radians ok r0[3]= 1.42842736367098783 AU ok x3= -0.265112136053530011 AU y3= 0.3990476789842281134 AU z3= -0.346297286143571136 AU r = 0.591138989727430619 AU th= 132.9389520420322984 degrees = 2.32022241728430289 radians ok m= ee= 2.16171396043605712 radians (Eccentric anomaly) ok == Matrix dd1=| as[1] xs[1] as[3] | d1 = -0.0596972888321454764 | bs[1],ys[1],bs[3] | | cs[1],zs[1],cs[3] | dd2=| as[1] xs[2] as[3] | d2 = -0.0700500325483139718 | bs[1],ys[2],bs[3] | | cs[1],zs[2],cs[3] | dd3=| as[1] xs[3] as[3] | d2 = -0.0799079587235544952 | bs[1],ys[3],bs[3] | | cs[1],zs[3],cs[3] | ddd=| as[1] as[2] as[3] | dd = 0.000794484222515481341 | bs[1],bs[2],bs[3] | | cs[1],cs[2],cs[3] | === tu1 = 0.08601049475 tu2 = 0.1720209895 tu3 = 0.08601049475 n10 = 0.5 n30 = 0.5 v1 = 0.00184945130178494459 v3 = 0.00184945130178494459 k0 = -0.311408034863969707 l0 = -0.324982044338668529 f = 0.1882538749799898 mm = 0.0210065541837 ll = 0.009311639701 ===== Direction ratio as[1]= -0.78851306922046 bs[1]= 0.61396060828546 cs[1]= 0.036048732880379 as[2]= -0.82765608346983 bs[2]= 0.55809945177728 cs[2]= -0.059248708182304 as[3]= -0.8591226024043 bs[3]= 0.4887924181086 cs[3]= -0.15162561141713 ====== Triangle True values, time 2 rs2 = 1.03086786794706664 Sun to earth distance AU r2 = 0.572141625885 Sun to planet AU r0[2]= 1.45240816397906087 Earth to planet AU angle opposite r2 17.4866899766 degrees = 0.305200315367160168 radians angle opposite ro[2] 130.288933905 degrees = 2.27397087555552301 radians angle opposite rs2 32.2243761189 degrees = 0.562421462675836725 radians ======= Initial approximate values n1 n3 r0[1] r0[2] r0[3] k0 = -0.311408034863969707 l0 = -0.324982044338668529 f = 0.1882538749799898 mm = 0.0210065541837 ll = 0.009311639701 yb = 1.02690269533051981 True Kepler's laws / http://www.alcyone.com/max/physics/kepler/ A proof of Kepler's laws. ======= px = 0.173630530853920976 qx = -0.451038790793390997 py = -0.398586415614684064 qy = 0.885007671582831179 pz = 0.984003926541077156 qz = 0.115435828230097414 ======= HP Calculator programs EQ1 Finds M (Mean anomaly) from Q T E EQ2 Compute eccentric anomaly EE EQ3 Compute RA DC RO E4 Compute abc E5A Time 1 E5B Time 2 E5C Time 3 E6 Initial, Determinates TU123 N10 N30 V1 V3 RC E7 Find EA QA T1A TH1A TH3A E8 XYZ123 Frm RO1A RO3A RA DC E9 Compute RO123A from ABC123 N1A N3A RO123A E10 Real elements E11 Compute N1A N3A from Det and R2A E12 Compute WA OA IA from PQXYZ E13 Prepare to compute YB with F M Y from XYZ31A E14 Compute YB E15 Compute PQXYZ from XYZ13A E16 Find W O I from WA OA IA E17 Long solve Delta RO E18 Compute errors E19 Compute true R TH T RO1A RO3A n1 n3 E20 E8 E13 E14 E7 E15 E12 E16 EQ1 EQ2 EQ3 Find RA DC from RO13A E26 Find RO123A True E27 Compute true N13 E28 Compute PQXYZ from normal elements E30 Compute DX3 DY3 D3Z from true elements E31 find A elements from XYZ DXYZ E32 Find True R TH T2 R2 TH2 EE2 DTH2 DRT2 DRTT2 E33 Compute XYZ3 123 A Det from standard elements