Solar System data for Maple
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Solar System data for Cybernet Waterloo Maple 2023: The Essential Tool for Mathematics.
# PACKAGES with(ScientificErrorAnalysis) : with(Units) : with(ScientificConstants) : # ALIASES alias(l = log10, l100 = log[100], pi[0] = Pi, Q = Quantity, r = sqrt, S_ellipsoid = ellipsoid) : # ASSIGNMENTS pi := pi[0] : # MATHEMATICAL FUNCTIONS E := x -> 10^x : S_ellipse := (a, b) -> pi*a*b : S_spheroid := (a, b) -> S_ellipsoid(a, a, b) : S_circle := r -> S_ellipse(r, r) : S_sphere := r -> S_spheroid(r, r) : # UNITS AddUnit(astronomical_unit, context = astronomy, default = true, conversion = 149597870700*m, prefix = SI) : AddUnit(cubic_centimeter, plural = cubic_centimeters, symbol = cm3, conversion = cm^3) : AddUnit(cubic_meter, plural = cubic_meters, symbol = m3, conversion = m^3) : AddUnit(revolution, spellings = {turn, turns}) : AddUnit(square_centimeter, plural = square_centimeters, symbol = cm2, conversion = cm^2) : AddUnit(square_meter, plural = square_meters, symbol = m2, conversion = m^2) : AddUnit(half_revolution, plural = half_revolutions, spellings = {half_turn, half_turns}, symbol = rev2, conversion = rev/2) : AddUnit(parsec, context = astronomy, default = true, conversion = 648000*AU/pi, prefix = SI) : _AU := Unit(AU) : _cm := Unit(cm) : _cm2 := Unit(cm2) : _cm3 := Unit(cm3) : _d := Unit(d) : _deg := Unit(deg) : _Dpc := Unit(dapc) : _g := Unit(g) : _Gm := Unit(Gm) : _h := Unit(h) : _kg := Unit(kg) : _km := Unit(km) : _lm := Unit(lm) : _lx := Unit(lx) : _m := Unit(m) : _m2 := Unit(m2) : _m3 := Unit(m3) : _min := Unit(min) : _Mm := Unit(Mm) : _pc := Unit(pc) : _rev := Unit(rev) : _rev2 := Unit(rev2) : _s := Unit(s) : _Tm := Unit(Tm) : E_I := _lx : l_A := _AU : l_p := _Dpc : rho_m_CGS := Unit(g/cm3) : theta_rev := _rev : theta_rev2 := theta_rev/2 : (* https://en.wikipedia.org/wiki/astronomical_unit https://en.wikipedia.org/wiki/parsec *) # CONSTANTS ModifyConstant(Newtonian_constant_of_gravitation, symbol = G[N], value = 6.67430E-11, uncertainty = [15, uld], units = N*(m/kg)^2) : AddConstant(gravitational_constant, symbol = K[G], derive = G[N]) : G := Constant(K[G], units) : m_E := -Q(14.18, 0.01) : ## # https://en.wikipedia.org/wiki/gravitational_constant # PHYSICAL FUNCTIONS m := E -> m_E - 5*l100(E/E_I) : q := theta -> 2*((sin(theta)/pi) + (1 - (theta/theta_rev2))*cos(theta))/3 : # SOLAR SYSTEM # https://en.wikipedia.org/wiki/Solar_System_by_size # PLANET TERRA [DISTANCE 0] a_Terra := Q(149598023., 1.)*_km : ## alpha_Terra := Q(152097597., 1.)*_km : ## A_Terra := Q(0.434, 0.001) : ## B_Terra := Q(0.294, 0.001) : ## delta_Terra := Unit(semicircle) : f_Terra := Q(298.257223563, 0.000000001)^(-1) : ## h_Chimborazo := Q(6263.47, 0.01)*_m : ## lambda_Chimborazo := -Q(78.8175, 0.0001)*_deg : ## M_G_Terra := Q(398600441.8, 0.8)*E(6)*Unit(m^3/s^2) : phi_Chimborazo := -Q(1.469167, 0.000001)*_deg : ## P_Terra := 23*_h + 56*_min + Q(4.100, 0.001)*_s : ## r_e_Terra := Q(6378137.0, 0.1)*_m : ## M_Terra := M_G_Terra/G : pi_Terra := 2*a_Terra - alpha_Terra : r_p_Terra := (1 - f_Terra)*r_e_Terra : rho_Terra := delta_Terra/2 : r_Chimborazo := r(((cos(phi_Chimborazo)*r_e_Terra^2)^2 + (sin(phi_Chimborazo)*r_p_Terra^2)^2)/((cos(phi_Chimborazo)*r_e_Terra)^2 + (sin(phi_Chimborazo)*r_p_Terra)^2)) + h_Chimborazo : r_Terra := (2*r_e_Terra + r_p_Terra)/3 : S_Terra := S_spheroid(r_e_Terra, r_p_Terra) : r_max_Terra := r_Chimborazo : r_min_Terra := r_p_Terra : (* https://en.wikipedia.org/wiki/Planet_Terra https://en.wikipedia.org/wiki/Terran_mass https://en.wikipedia.org/wiki/Terran_radius https://en.wikipedia.org/wiki/WGS84 https://en.wikipedia.org/wiki/Terran_extrema#Elevation https://en.wikipedia.org/wiki/Chimborazo *) # TERRAN SATELLITE LUNA [MEAN DISTANCE 0.00253 AU] a_Luna := Q(384399., 1.)*_km : ## alpha_Luna := Q(405400., 100.)*_km : ## alpha_max_Luna := Q(406700., 100.)*_km : ## B_Luna := Q(0.136, 0.001) : ## H_Luna := Q(0.2, 0.1) : ## pi_max_Luna := Q(370400., 100.)*_km : ## P_Luna := 27*_d + 7*_h + 43*_min + Q(11.5, 0.1)*_s : ## r_Luna := Q(1737.4, 0.1)*_km : r_e_Luna := Q(1738.1, 0.1)*_km : ## rho_m_Luna := Q(3.344, 0.005)*rho_m_CGS : alpha_min_Luna := 2*alpha_Luna - alpha_max_Luna : pi_Luna := 2*a_Luna - alpha_Luna : r_p_Luna := 3*r_Luna - 2*r_e_Luna : pi_min_Luna := 2*pi_Luna - pi_max_Luna : S_Luna := S_spheroid(r_e_Luna, r_p_Luna) : Delta_Luna := a_Luna - r_Terra : mu_Luna := 5*l(Delta_Luna*r(a_Terra^2 + a_Luna^2)/l_A^2) : rho_p_Luna := arcsin(r_p_Luna/Delta_Luna) : theta_Luna := arccos((Delta_Luna^2 + a_Luna^2 - r_Terra^2)/(2*Delta_Luna*r(a_Terra^2 + a_Luna^2))) : delta_p_Luna := 2*rho_p_Luna : m_Luna := H_Luna + mu_Luna - 5*l100(q(theta_Luna)) : (* "m_Luna" = -Q(11.10827207886184016890499701474007, 0.10000000016433033743356178579353) ; "delta_p_Luna[arcmin]" = Q(31.57411360436092417450615129791676, 0.00655830180623823709953404706721) ; *) # https://en.wikipedia.org/wiki/Satellite_Luna # CIS-MERCURIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII TO <0.307 AU (MEAN DISTANCES FROM 1.00 AU TO <1.05 AU) ## STAR SOL [ORBITAL RADIUS 0] f_Sol := Q(0.00005, 0.00001) : ## H_Sol := Q(4.83, 0.01) : ## L_Sol := Q(3.75E28, 0.01E28)*_lm : ## M_G_Sol := Q(1.32712442099, 0.00000000010)*E(20)*Unit(m^3/s^2) : ## P_Sol := Q(25.05, 0.01)*_d : ## r_e_Sol := Q(695660., 140.)*_km : M_Sol := M_G_Sol/G : r_p_Sol := (1 - f_Sol)*r_e_Sol : r_Sol := (2*r_e_Sol + r_p_Sol)/3 : S_Sol := S_spheroid(r_e_Sol, r_p_Sol) : Delta_Sol := a_Terra - r_Terra : mu_Sol := 5*l(Delta_Sol/l_p) : rho_e_Sol := arcsin(r_e_Sol/Delta_Sol) : rho_p_Sol := arcsin(r_p_Sol/Delta_Sol) : delta_p_Sol := 2*rho_p_Sol : m_Sol := H_Sol + mu_Sol : (* "m_Sol" = -Q(26.74221593478209323799059756572072, 0.01000000000001053571280042813118) ; "delta_p_Sol[arcmin]" = Q(31.97226489865489735835243772118332, 0.00644233177009254945060053638118) ; *) (* https://en.wikipedia.org/wiki/Star_Sol https://en.wikipedia.org/wiki/Solar_mass https://en.wikipedia.org/wiki/Solar_radius *) # MERCURIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM 0.307 AU TO 0.467 AU (MEAN DISTANCES FROM 1.05 AU TO 1.10 AU) ## PLANET MERCURY [MEAN ORBITAL RADIUS 0.387 AU] a_Mercury := Q(0.387098, 0.000001)*_AU : ## alpha_Mercury := Q(0.466697, 0.000001)*_AU : ## A_Mercury := Q(0.142, 0.001) : ## f_Mercury := Q(0.0009, 0.0001) : ## H_Mercury := -Q(0.4, 0.1) : ## M_Mercury := Q(330.11, 0.02)*E(21)*_kg : P_Mercury := Q(1407.5, 0.1)*_h : ## r_Mercury := Q(2439.7, 1.0)*_km : pi_Mercury := 2*a_Mercury - alpha_Mercury : r_e_Mercury := 3*r_Mercury/(3 - f_Mercury) : r_p_Mercury := (1 - f_Mercury)*r_e_Mercury : S_Mercury := S_spheroid(r_e_Mercury, r_p_Mercury) : Delta_Mercury := r(Delta_Sol^2 + a_Mercury^2) : mu_Mercury := 5*l(a_Mercury*Delta_Mercury/l_A^2) : rho_e_Mercury := arcsin(r_e_Mercury/Delta_Mercury) : rho_o_Mercury := arctan(a_Mercury/Delta_Sol) : rho_p_Mercury := arcsin(r_p_Mercury/Delta_Mercury) : theta_Mercury := arccos((a_Mercury^2 + Delta_Mercury^2 - Delta_Sol^2)/(2*a_Mercury*Delta_Mercury)) : delta_p_Mercury := 2*rho_p_Mercury : Deltarho_Mercury := rho_o_Mercury - rho_e_Sol - rho_e_Mercury : m_Mercury := H_Mercury + mu_Mercury - 5*l100(q(theta_Mercury)) : Deltam_Mercury := m_Mercury - m_Sol : Deltarhostar_Mercury := Deltarho_Mercury/Deltam_Mercury : (* "m_Mercury" = -Q(1.15871898404991463525478168484118, 0.10000000014015777943899626416762) ; "delta_p_Mercury[arcsec]" = Q(6.27049009904340207061754426005796, 0.00260404441715106063666688931206) ; "Deltarhostar_Mercury[arcmin]" = Q(49.00378296634542467885209051967008, 0.19249991723701213429027817394767) ; "Deltarho_Mercury[deg]" = Q(20.89480220156399410431558591885622, 0.00007320283268525235307058882396) ; *) # https://en.wikipedia.org/wiki/Planet_Mercury # TRANS-MERCURIAN/CIS-VENUSIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM >0.467 AU TO <0.718 AU (MEAN DISTANCES FROM >1.10 AU TO <1.23 AU) # VENUSIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM 0.718 AU TO 0.728 AU (MEAN DISTANCES FROM 1.23 AU TO 1.24 AU) ## PLANET VENUS [0.723 AU] a_Venus := Q(0.723332, 0.000001)*_AU : ## alpha_Venus := Q(0.728213, 0.000001)*_AU : ## A_Venus := Q(0.689, 0.001) : ## H_Venus := -Q(4.4, 0.1) : ## M_Venus := Q(4867.5, 0.2)*E(21)*_kg : P_Venus := Q(243.0226, 0.0001)*_d : ## r_Venus := Q(6051.8, 1.0)*_km : f_Venus := 5*pi^2*r_Venus^3/(G*M_Venus*P_Venus^2) : pi_Venus := 2*a_Venus - alpha_Venus : r_e_Venus := 3*r_Venus/(3 - f_Venus) : r_p_Venus := (1 - f_Venus)*r_e_Venus : S_Venus := S_spheroid(r_e_Venus, r_p_Venus) : Delta_Venus := r(Delta_Sol^2 + a_Venus^2) : mu_Venus := 5*l(a_Venus*Delta_Venus/l_A^2) : rho_e_Venus := arcsin(r_e_Venus/Delta_Venus) : rho_o_Venus := arctan(a_Venus/Delta_Sol) : rho_p_Venus := arcsin(r_p_Venus/Delta_Venus) : theta_Venus := arccos((a_Venus^2 + Delta_Venus^2 - Delta_Sol^2)/(2*a_Venus*Delta_Venus)) : delta_p_Venus := 2*rho_p_Venus : Deltarho_Venus := rho_o_Venus - rho_e_Sol - rho_e_Venus : m_Venus := H_Venus + mu_Venus - 5*l100(q(theta_Venus)) : Deltam_Venus := m_Venus - m_Sol : Deltarhostar_Venus := Deltarho_Venus/Deltam_Venus : (* "m_Venus" = -Q(3.76783844204276744429765178948940, 0.10000000005877189598198889050357) ; "delta_p_Venus[arcsec]" = Q(13.52216838023425492461860429518946, 0.00223441326054038937727843844154) ; "Deltarhostar_Venus[deg]" = Q(1.55008437449254005244130967460030, 0.00678066529926617181163588161749) ; "Deltarho_Venus[deg]" = Q(35.61222356518832846317885520610109, 0.00006550205409236586307519845750) ; *) # https://en.wikipedia.org/wiki/Planet_Venus # TRANS-VENUSIAN/CIS-TERRAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM >0.728 AU TO <0.983 AU (MEAN DISTANCES FROM >1.24 AU TO <1.40 AU) # TERRAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM 0.983 AU TO 1.02 AU (MEAN DISTANCES FROM 1.40 AU TO 1.43 AU) # TRANS-TERRAN/CIS-MARTIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM >1.02 AU TO <1.38 AU (MEAN DISTANCES FROM >1.43 AU TO <1.71 AU) # MARTIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM 1.38 AU TO 1.67 AU (MEAN DISTANCES FROM 1.71 AU TO 1.94 AU) # https://en.wikipedia.org/wiki/Martian_System ## PLANET MARS [1.52 AU] a_Mars := Q(227939366., 1.)*_km : ## alpha_Mars := Q(249261000., 1000.)*_km : ## A_Mars := Q(0.170, 0.001) : ## H_Mars := -Q(1.5, 0.1) : ## M_Mars := Q(641.71, 0.03)*E(21)*_kg : P_Mars := Q(1.025957, 0.000001)*_d : ## r_e_Mars := Q(3396.2, 0.1)*_km : r_p_Mars := Q(3376.2, 0.1)*_km : pi_Mars := 2*a_Mars - alpha_Mars : r_Mars := (2*r_e_Mars + r_p_Mars)/3 : S_Mars := S_spheroid(r_e_Mars, r_p_Mars) : Delta_Mars := r(a_Mars^2 + Delta_Sol^2) : mu_Mars := 5*l(a_Mars*Delta_Mars/l_A^2) : rho_e_Mars := arcsin(r_e_Mars/Delta_Mars) : rho_p_Mars := arcsin(r_p_Mars/Delta_Mars) : theta_Mars := arccos((a_Mars^2 + Delta_Mars^2 - Delta_Sol^2)/(2*a_Mars*Delta_Mars)) : delta_p_Mars := 2*rho_p_Mars : m_Mars := H_Mars + mu_Mars - 5*l100(q(theta_Mars)) : (* "m_Mars" = Q(1.32669090715649576766154497789182, 0.10000000000000131818290121219160) ; "delta_p_Mars[arcsec]" = Q(5.10845407354229155894283622100307, 0.00015130780501661998004452404087) ; *) # https://en.wikipedia.org/wiki/Planet_Mars ## MARTIAN SATELLITE PHOBOS alpha_Phobos := Q(9517.58, 0.01)*_km : ## B_Phobos := Q(0.071, 0.012) : d_x_Phobos := Q(25.90, 0.08)*_km : d_y_Phobos := Q(22.60, 0.08)*_km : d_z_Phobos := Q(18.32, 0.06)*_km : pi_Phobos := Q(9234.42, 0.01)*_km : ## P_Phobos := Q(0.31891023, 0.00000001)*_d : ## rho_m_Phobos := Q(1.861, 0.011)*rho_m_CGS : a_Phobos := (alpha_Phobos + pi_Phobos)/2 : r_x_Phobos := d_x_Phobos/2 : r_y_Phobos := d_y_Phobos/2 : r_z_Phobos := d_z_Phobos/2 : r_Phobos := (r_x_Phobos + r_y_Phobos + r_z_Phobos)/3 : r_e_Phobos := (r_x_Phobos + r_y_Phobos)/2 : r_p_Phobos := r_z_Phobos : S_Phobos := S_ellipsoid(r_x_Phobos, r_y_Phobos, r_z_Phobos) : L_Phobos := B_Phobos*L_Sol*S_Phobos/(2*S_sphere(a_Mars)) : Delta_Phobos := Delta_Mars : E_Phobos := L_Phobos/S_sphere(Delta_Phobos) : rho_e_Phobos := arcsin(r_e_Phobos/Delta_Phobos) : rho_o_Phobos := arctan(a_Phobos/Delta_Phobos) : rho_p_Phobos := arcsin(r_p_Phobos/Delta_Phobos) : delta_p_Phobos := 2*rho_p_Phobos : Deltarho_Phobos := rho_o_Phobos - rho_e_Mars - rho_e_Phobos : m_Phobos := m(E_Phobos) : Deltam_Phobos := m_Phobos - m_Mars : Deltarhostar_Phobos := Deltarho_Phobos/Deltam_Phobos : (* "m_Phobos" = Q(14.49456931868745385875982929915521, 0.18384685190994375975648578240774) ; "delta_p_Phobos[arcsec]" = Q(0.01385979483219343599642941121815, 0.00004539234115350043417899383649) ; "Deltarhostar_Phobos[arcsec]" = Q(0.34286305261860027443342251072943, 0.00544926942644971349374476974147) ; "m_Phobos" = simplify(combine(m_Phobos, errors)) ; "delta_p_Phobos[arcsec]" = combine(convert(delta_p_Phobos, units, arcsec), errors) ; "Deltarhostar_Phobos[arcsec]" = combine(convert(simplify(combine(Deltarhostar_Phobos, errors)), units, arcsec), errors) ; *) # https://en.wikipedia.org/wiki/Satellite_Phobos ## MARTIAN SATELLITE DEIMOS a_Deimos := Q(23463.2, 0.1)*_km : ## alpha_Deimos := Q(23470.9, 0.1)*_km : ## B_Deimos := Q(0.068, 0.007) : d_x_Deimos := Q(16.08, 0.16)*_km : d_y_Deimos := Q(11.78, 0.12)*_km : d_z_Deimos := Q(10.22, 0.10)*_km : P_Deimos := Q(30.312, 0.001)*_h : ## rho_m_Deimos := Q(1.465, 0.051)*rho_m_CGS : pi_Deimos := 2*a_Deimos - alpha_Deimos : r_x_Deimos := d_x_Deimos/2 : r_y_Deimos := d_y_Deimos/2 : r_z_Deimos := d_z_Deimos/2 : r_Deimos := (r_x_Deimos + r_y_Deimos + r_z_Deimos)/3 : r_e_Deimos := (r_x_Deimos + r_y_Deimos)/2 : r_p_Deimos := r_z_Deimos : S_Deimos := S_ellipsoid(r_x_Deimos, r_y_Deimos, r_z_Deimos) : L_Deimos := B_Deimos*L_Sol*S_Deimos/(2*S_sphere(a_Mars)) : Delta_Deimos := Delta_Mars : E_Deimos := L_Deimos/S_sphere(Delta_Deimos) : rho_e_Deimos := arcsin(r_e_Deimos/Delta_Deimos) : rho_o_Deimos := arctan(a_Deimos/Delta_Deimos) : rho_p_Deimos := arcsin(r_p_Deimos/Delta_Deimos) : delta_p_Deimos := 2*rho_p_Deimos : Deltarho_Deimos := rho_o_Deimos - rho_e_Mars - rho_e_Deimos : m_Deimos := m(E_Deimos) : Deltam_Deimos := m_Deimos - m_Mars : Deltarhostar_Deimos := Deltarho_Deimos/Deltam_Deimos : (* "m_Deimos" = Q(15.76871438286065425739363427052833, 0.11296045530163542665763375205357) ; "delta_p_Deimos[arcsec]" = Q(0.00773182877647472148082889292215, 0.00007565390192245856746094295290) ; "Deltarhostar_Deimos[arcsec]" = Q(1.05083606782339740834221425763210, 0.01097706248621725194641513470742) ; *) # https://en.wikipedia.org/wiki/Satellite_Deimos # TRANS-MARTIAN/CIS-JOVIAN OBJECTS # OBJECTS WITH MEAN ORBITAL RADII FROM >1.67 AU TO <4.95 AU (MEAN DISTANCES FROM >1.94 AU TO <5.05 AU) ## MINOR PLANET VESTA [2.36 AU] a_Vesta := Q(2.36151, 0.00001)*_AU : ## d_x_Vesta := Q(572.6, 0.1)*_km : ## x-diameter of Vesta d_y_Vesta := Q(557.2, 0.1)*_km : ## y-diameter of Vesta e_Vesta := Q(0.098758, 0.000001) : ## orbital eccentricity of Vesta H_Vesta := Q(3.20, 0.01) : ## r_Vesta := Q(262.7, 0.1)*_km : alpha_Vesta := (1 + e_Vesta)*a_Vesta : pi_Vesta := (1 - e_Vesta)*a_Vesta : r_x_Vesta := d_x_Vesta/2 : # x-radius of Vesta r_y_Vesta := d_y_Vesta/2 : # y-radius of Vesta r_z_Vesta := 3*r_Vesta - r_x_Vesta - r_y_Vesta : # z-radius of Vesta r_e_Vesta := (r_x_Vesta + r_y_Vesta)/2 : r_p_Vesta := r_z_Vesta : Delta_Vesta := r(a_Vesta^2 + Delta_Sol^2) : mu_Vesta := 5*l(a_Vesta*Delta_Vesta/l_A^2) : rho_p_Vesta := arcsin(r_p_Vesta/Delta_Vesta) : theta_Vesta := arccos((a_Vesta^2 + Delta_Vesta^2 - Delta_Sol^2)/(2*a_Vesta*Delta_Vesta)) : delta_p_Vesta := 2*rho_p_Vesta : m_Vesta := H_Vesta + mu_Vesta - 5*l100(q(theta_Vesta)) : (* "m_Vesta" = Q(7.63283683085658473134303750432821, 0.01000001342667624008934552764643) ; "delta_p_Vesta[arcsec]" = Q(0.24000575899974688057125213367208, 0.00033142918084166634228761051955) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Vesta ## MINOR PLANET CERES [2.77 AU] a_Ceres := Q(2.77, 0.01)*_AU : ## e_Ceres := Q(0.116, 0.001) : ## d_x_Ceres := Q(966.2, 0.2)*_km : d_y_Ceres := Q(962.0, 0.2)*_km : H_Ceres := Q(3.34, 0.01) : ## r_Ceres := Q(469.7, 0.1)*_km : alpha_Ceres := (1 + e_Ceres)*a_Ceres : pi_Ceres := (1 - e_Ceres)*a_Ceres : r_x_Ceres := d_x_Ceres/2 : r_y_Ceres := d_y_Ceres/2 : r_z_Ceres := 3*r_Ceres - r_x_Ceres - r_y_Ceres : r_e_Ceres := (r_x_Ceres + r_y_Ceres)/2 : r_p_Ceres := r_z_Ceres : Delta_Ceres := r(a_Ceres^2 + Delta_Sol^2) : mu_Ceres := 5*l(a_Ceres*Delta_Ceres/l_A^2) : rho_p_Ceres := arcsin(r_p_Ceres/Delta_Ceres) : theta_Ceres := arccos((a_Ceres^2 + Delta_Ceres^2 - Delta_Sol^2)/(2*a_Ceres*Delta_Ceres)) : delta_p_Ceres := 2*rho_p_Ceres : m_Ceres := H_Ceres + mu_Ceres - 5*l100(q(theta_Ceres)) : (* "m_Ceres" = Q(8.39950827082026900267119700952730, 0.01751072289545878150502454109850) ; "delta_p_Ceres[arcsec]" = Q(0.41668670115143979115838406964018, 0.00136660544792827098454855175405) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Ceres ## MINOR PLANET PALLAS [2.77 AU] a_Pallas := Q(2.7709176, 0.0000001)*_AU : ## d_x_Pallas := Q(568., 12.)*_km : d_y_Pallas := Q(532., 12.)*_km : e_Pallas := Q(0.2812580, 0.0000001) : ## H_Pallas := Q(4.13, 0.01) : ## r_Pallas := Q(256., 2.)*_km : alpha_Pallas := (1 + e_Pallas)*a_Pallas : pi_Pallas := (1 - e_Pallas)*a_Pallas : r_x_Pallas := d_x_Pallas/2 : r_y_Pallas := d_y_Pallas/2 : r_z_Pallas := 3*r_Pallas - r_x_Pallas - r_y_Pallas : r_e_Pallas := (r_x_Pallas + r_y_Pallas)/2 : r_p_Pallas := r_z_Pallas : Delta_Pallas := r(a_Pallas^2 + Delta_Sol^2) : mu_Pallas := 5*l(a_Pallas*Delta_Pallas/l_A^2) : rho_p_Pallas := arcsin(r_p_Pallas/Delta_Pallas) : theta_Pallas := arccos((a_Pallas^2 + Delta_Pallas^2 - Delta_Sol^2)/(2*a_Pallas*Delta_Pallas)) : delta_p_Pallas := 2*rho_p_Pallas : m_Pallas := H_Pallas + mu_Pallas - 5*l100(q(theta_Pallas)) : (* "m_Pallas" = Q(9.19082708813435298160588213083630, 0.01000000000103284147721498416589) ; "delta_p_Pallas[arcsec]" = Q(0.20406985671405988167035206680037, 0.00972823926941726590643074357439) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Pallas ## MINOR PLANET JUNO [2.67 AU] a_Juno := Q(2.6693661, 0.0000001)*_AU : ## d_x_Juno := Q(288., 5.)*_km : d_y_Juno := Q(250., 5.)*_km : e_Juno := Q(0.2335060, 0.0000001) : ## H_Juno := Q(5.33, 0.01) : ## r_Juno := Q(127., 1.)*_km : alpha_Juno := (1 + e_Juno)*a_Juno : pi_Juno := (1 - e_Juno)*a_Juno : r_x_Juno := d_x_Juno/2 : r_y_Juno := d_y_Juno/2 : r_z_Juno := 3*r_Juno - r_x_Juno - r_y_Juno : r_e_Juno := (r_x_Juno + r_y_Juno)/2 : r_p_Juno := r_z_Juno : Delta_Juno := r(a_Juno^2 + Delta_Sol^2) : mu_Juno := 5*l(a_Juno*Delta_Juno/l_A^2) : rho_p_Juno := arcsin(r_p_Juno/Delta_Juno) : theta_Juno := arccos((a_Juno^2 + Delta_Juno^2 - Delta_Sol^2)/(2*a_Juno*Delta_Juno)) : delta_p_Juno := 2*rho_p_Juno : m_Juno := H_Juno + mu_Juno - 5*l100(q(theta_Juno)) : (* "m_Juno" = Q(10.24259506508462812549996284645253, 0.01000000000109958264789099091065) ; "delta_p_Juno[arcsec]" = Q(0.10834889911856883934725347149900, 0.00448565336978972228854622408676) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Juno ## MINOR PLANET EUNOMIA [2.64 AU] a_Eunomia := Q(2.644, 0.001)*_AU : ## alpha_Eunomia := Q(469., 1.)*_Gm : ## d_Eunomia := Q(231.689, 2.234)*_km : d_x_Eunomia := Q(357., 15.)*_km : d_y_Eunomia := Q(255., 15.)*_km : H_Eunomia := Q(5.41, 0.01) : ## pi_Eunomia := 2*a_Eunomia - alpha_Eunomia : r_Eunomia := d_Eunomia/2 : r_x_Eunomia := d_x_Eunomia/2 : r_y_Eunomia := d_y_Eunomia/2 : r_z_Eunomia := 3*r_Eunomia - r_x_Eunomia - r_y_Eunomia : r_e_Eunomia := (r_x_Eunomia + r_y_Eunomia)/2 : r_p_Eunomia := r_z_Eunomia : Delta_Eunomia := r(a_Eunomia^2 + Delta_Sol^2) : mu_Eunomia := 5*l(a_Eunomia*Delta_Eunomia/l_A^2) : rho_p_Eunomia := arcsin(r_p_Eunomia/Delta_Eunomia) : theta_Eunomia := arccos((a_Eunomia^2 + Delta_Eunomia^2 - Delta_Sol^2)/(2*a_Eunomia*Delta_Eunomia)) : delta_p_Eunomia := 2*rho_p_Eunomia : m_Eunomia := H_Eunomia + mu_Eunomia - 5*l100(q(theta_Eunomia)) : (* "m_Eunomia" = Q(10.28483422230040978047667735761284, 0.01011106892414374647967434666977) ; "delta_p_Eunomia[arcsec]" = Q(0.04051698448581441742339814268632, 0.01085113134768618669737624924284) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Eunomia ## MINOR PLANET FLORA [2.20 AU] a_Flora := Q(2.2014, 0.0001)*_AU : ## e_Flora := Q(0.1449, 0.0001) : ## d_Flora := Q(147.491, 1.025)*_km : d_x_Flora := Q(154., 7.)*_km : d_y_Flora := Q(148., 6.)*_km : H_Flora := Q((6.61 + 6.54)/2, (6.61 - 6.54)/2) : alpha_Flora := (1 + e_Flora)*a_Flora : pi_Flora := (1 - e_Flora)*a_Flora : r_Flora := d_Flora/2 : r_x_Flora := d_x_Flora/2 : r_y_Flora := d_y_Flora/2 : r_z_Flora := 3*r_Flora - r_x_Flora - r_y_Flora : r_e_Flora := (r_x_Flora + r_y_Flora)/2 : r_p_Flora := r_z_Flora : Delta_Flora := r(a_Flora^2 + Delta_Sol^2) : mu_Flora := 5*l(a_Flora*Delta_Flora/l_A^2) : rho_p_Flora := arcsin(r_p_Flora/Delta_Flora) : theta_Flora := arccos((a_Flora^2 + Delta_Flora^2 - Delta_Sol^2)/(2*a_Flora*Delta_Flora)) : delta_p_Flora := 2*rho_p_Flora : m_Flora := H_Flora + mu_Flora - 5*l100(q(theta_Flora)) : (* "m_Flora" = Q(10.73813026189820375955973305242564, 0.03500042845819781959869558554210) ; "delta_p_Flora[arcsec]" = Q(0.08010511445795790139017274159278, 0.00554218942258565176568907533478) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Flora ## MINOR PLANET HYGIEA [3.14 AU] a_Hygiea := Q(3.14178, 0.00001)*_AU : ## d_Hygiea := Q(433., 8.)*_km : # arithmetic mean diameter of Hygiea d_x_Hygiea := Q(450., 10.)*_km : d_y_Hygiea := Q(430., 10.)*_km : e_Hygiea := Q(0.1356, 0.0001) : ## H_Hygiea := Q(5.64, 0.01) : ## alpha_Hygiea := (1 + e_Hygiea)*a_Hygiea : pi_Hygiea := (1 - e_Hygiea)*a_Hygiea : r_Hygiea := d_Hygiea/2 : r_x_Hygiea := d_x_Hygiea/2 : r_y_Hygiea := d_y_Hygiea/2 : r_z_Hygiea := 3*r_Hygiea - r_x_Hygiea - r_y_Hygiea : r_e_Hygiea := (r_x_Hygiea + r_y_Hygiea)/2 : r_p_Hygiea := r_z_Hygiea : Delta_Hygiea := r(a_Hygiea^2 + Delta_Sol^2) : mu_Hygiea := 5*l(a_Hygiea*Delta_Hygiea/l_A^2) : rho_p_Hygiea := arcsin(r_p_Hygiea/Delta_Hygiea) : theta_Hygiea := arccos((a_Hygiea^2 + Delta_Hygiea^2 - Delta_Sol^2)/(2*a_Hygiea*Delta_Hygiea)) : delta_p_Hygiea := 2*rho_p_Hygiea : m_Hygiea := H_Hygiea + mu_Hygiea - 5*l100(q(theta_Hygiea)) : (* "m_Hygiea" = Q(11.20563499791454248138659257274186, 0.01000000832266009892959416072025) ; "delta_p_Hygiea[arcsec]" = Q(0.17522054229889792554791356880918, 0.01164935441328858473338836324759) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Hygiea ## MINOR PLANET INTERAMNIA [3.06 AU] a_Interamnia := Q(457.2, 0.1)*_Gm : ## alpha_Interamnia := Q(528., 1.)*_Gm : ## d_Interamnia := Q(332., 5.)*_km : d_x_Interamnia := Q(362., 8.)*_km : d_y_Interamnia := Q(348., 8.)*_km : H_Interamnia := Q(6.35, 0.01) : ## pi_Interamnia := 2*a_Interamnia - alpha_Interamnia : r_Interamnia := d_Interamnia/2 : r_x_Interamnia := d_x_Interamnia/2 : r_y_Interamnia := d_y_Interamnia/2 : r_z_Interamnia := 3*r_Interamnia - r_x_Interamnia - r_y_Interamnia : r_e_Interamnia := (r_x_Interamnia + r_y_Interamnia)/2 : r_p_Interamnia := r_z_Interamnia : Delta_Interamnia := r(a_Interamnia^2 + Delta_Sol^2) : mu_Interamnia := 5*l(a_Interamnia*Delta_Interamnia/l_A^2) : rho_p_Interamnia := arcsin(r_p_Interamnia/Delta_Interamnia) : theta_Interamnia := arccos((a_Interamnia^2 + Delta_Interamnia^2 - Delta_Sol^2)/(2*a_Interamnia*Delta_Interamnia)) : delta_p_Interamnia := 2*rho_p_Interamnia : m_Interamnia := H_Interamnia + mu_Interamnia - 5*l100(q(theta_Interamnia)) : (* "m_Interamnia" = Q(11.80388141452636749707685857308732, 0.01003894316708003132191797673488) ; "delta_p_Interamnia[arcsec]" = Q(0.12263108537913598384096351160589, 0.00805608158576532978203118768934) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Interamnia ## MINOR PLANET DAVIDA [3.16 AU] a_Davida := Q(3.163, 0.001)*_AU : ## alpha_Davida := Q(3.759, 0.001)*_AU : ## d_x_Davida := Q(357., 2.)*_km : d_y_Davida := Q(294., 2.)*_km : H_Davida := Q(6.43, 0.01) : ## r_Davida := Q(149., 2.)*_km : pi_Davida := 2*a_Davida - alpha_Davida : r_x_Davida := d_x_Davida/2 : r_y_Davida := d_y_Davida/2 : r_z_Davida := 3*r_Davida - r_x_Davida - r_y_Davida : r_e_Davida := (r_x_Davida + r_y_Davida)/2 : r_p_Davida := r_z_Davida : Delta_Davida := r(a_Davida^2 + Delta_Sol^2) : mu_Davida := 5*l(a_Davida*Delta_Davida/l_A^2) : rho_p_Davida := arcsin(r_p_Davida/Delta_Davida) : theta_Davida := arccos((a_Davida^2 + Delta_Davida^2 - Delta_Sol^2)/(2*a_Davida*Delta_Davida)) : delta_p_Davida := 2*rho_p_Davida : m_Davida := H_Davida + mu_Davida - 5*l100(q(theta_Davida)) : (* "m_Davida" = Q(12.02293195994655230783287574310801, 0.01008191813206717803371027836628) ; "delta_p_Davida[arcsec]" = Q(0.10099994012383692749046873656662, 0.00512440688197057315255281660516) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Davida ## MINOR PLANET EUROPA [3.10 AU] a_MPEuropa := Q(3.095, 0.001)*_AU : ## alpha_MPEuropa := Q(3.444, 0.001)*_AU : ## d_y_MPEuropa := Q(330., 8.)*_km : d_z_MPEuropa := Q(249., 10.)*_km : H_MPEuropa := Q(6.66, 0.01) : r_MPEuropa := Q(160., 2.)*_km : pi_MPEuropa := 2*a_MPEuropa - alpha_MPEuropa : r_y_MPEuropa := d_y_MPEuropa/2 : r_z_MPEuropa := d_z_MPEuropa/2 : r_p_MPEuropa := r_z_MPEuropa : r_x_MPEuropa := 3*r_MPEuropa - r_y_MPEuropa - r_z_MPEuropa : r_e_MPEuropa := (r_x_MPEuropa + r_y_MPEuropa)/2 : Delta_MPEuropa := r(a_MPEuropa^2 + Delta_Sol^2) : mu_MPEuropa := 5*l(a_MPEuropa*Delta_MPEuropa/l_A^2) : rho_p_MPEuropa := arcsin(r_p_MPEuropa/Delta_MPEuropa) : theta_MPEuropa := arccos((a_MPEuropa^2 + Delta_MPEuropa^2 - Delta_Sol^2)/(2*a_MPEuropa*Delta_MPEuropa)) : delta_p_MPEuropa := 2*rho_p_MPEuropa : m_MPEuropa := H_MPEuropa + mu_MPEuropa - 5*l100(q(theta_MPEuropa)) : (* "m_MPEuropa" = Q(12.16488561512930766692036021108350, 0.01008506871101465080224973239054) ; "delta_p_MPEuropa[arcsec]" = Q(0.10555479168781255528124559091595, 0.00423926074135274809234793144477) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Europa ## MINOR PLANET EUPHROSYNE [3.16 AU] a_Euphrosyne := Q(472.041, 0.001)*_Gm : ## alpha_Euphrosyne := Q(576.296, 0.001)*_Gm : ## d_Euphrosyne := Q(267.1, 2.6)*_km : d_x_Euphrosyne := Q(294., 6.)*_km : d_z_Euphrosyne := Q(248., 6.)*_km : H_Euphrosyne := Q(6.86, 0.01) : ## pi_Euphrosyne := 2*a_Euphrosyne - alpha_Euphrosyne : r_Euphrosyne := d_Euphrosyne/2 : r_x_Euphrosyne := d_x_Euphrosyne/2 : r_z_Euphrosyne := d_z_Euphrosyne/2 : r_p_Euphrosyne := r_z_Euphrosyne : r_y_Euphrosyne := 3*r_Euphrosyne - r_x_Euphrosyne - r_z_Euphrosyne : r_e_Euphrosyne := (r_x_Euphrosyne + r_y_Euphrosyne)/2 : Delta_Euphrosyne := r(a_Euphrosyne^2 + Delta_Sol^2) : mu_Euphrosyne := 5*l(a_Euphrosyne*Delta_Euphrosyne/l_A^2) : rho_p_Euphrosyne := arcsin(r_p_Euphrosyne/Delta_Euphrosyne) : theta_Euphrosyne := arccos((a_Euphrosyne^2 + Delta_Euphrosyne^2 - Delta_Sol^2)/(2*a_Euphrosyne*Delta_Euphrosyne)) : delta_p_Euphrosyne := 2*rho_p_Euphrosyne : m_Euphrosyne := H_Euphrosyne + mu_Euphrosyne - 5*l100(q(theta_Euphrosyne)) : (* "m_Euphrosyne" = Q(12.44317287649117138441176940298693, 0.01000000369088652491518570875353) ; "delta_p_Euphrosyne[arcsec]" = Q(0.10330378999766332933322444454166, 0.00249928524979132553803200897319) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Euphrosyne ## MINOR PLANET CYBELE [3.43 AU] a_Cybele := Q(3.4283, 0.0001)*_AU : ## alpha_Cybele := Q(3.8102, 0.0001)*_AU : ## d_x_Cybele := Q(297., 1.)*_km : ## d_y_Cybele := Q(291., 1.)*_km : ## H_Cybele := Q(6.58, 0.06) : r_Cybele := Q(131.5, 1.5)*_km : pi_Cybele := 2*a_Cybele - alpha_Cybele : r_x_Cybele := d_x_Cybele/2 : r_y_Cybele := d_y_Cybele/2 : r_z_Cybele := 3*r_Cybele - r_x_Cybele - r_y_Cybele : r_e_Cybele := (r_x_Cybele + r_y_Cybele)/2 : r_p_Cybele := r_z_Cybele : Delta_Cybele := r(a_Cybele^2 + Delta_Sol^2) : mu_Cybele := 5*l(a_Cybele*Delta_Cybele/l_A^2) : rho_p_Cybele := arcsin(r_p_Cybele/Delta_Cybele) : theta_Cybele := arccos((a_Cybele^2 + Delta_Cybele^2 - Delta_Sol^2)/(2*a_Cybele*Delta_Cybele)) : delta_p_Cybele := 2*rho_p_Cybele : m_Cybele := H_Cybele + mu_Cybele - 5*l100(q(theta_Cybele)) : (* "m_Cybele" = Q(12.50127403523052076175137251270059, 0.06000011892223115327399328568700) ; "delta_p_Cybele[arcsec]" = Q(0.07760450134277422006582025772796, 0.00351746656354255675884269856994) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Cybele ## MINOR PLANET SYLVIA [3.48 AU] a_Sylvia := Q(3.48, 0.01)*_AU : ## alpha_Sylvia := Q(3.81, 0.01)*_AU : ## d_x_Sylvia := Q(374., 5.)*_km : d_y_Sylvia := Q(248., 5.)*_km : H_Sylvia := Q(6.94, 0.01) : ## r_Sylvia := Q(137., 2.)*_km : pi_Sylvia := 2*a_Sylvia - alpha_Sylvia : r_x_Sylvia := d_x_Sylvia/2 : r_y_Sylvia := d_y_Sylvia/2 : r_z_Sylvia := 3*r_Sylvia - r_x_Sylvia - r_y_Sylvia : r_e_Sylvia := (r_x_Sylvia + r_y_Sylvia)/2 : r_p_Sylvia := r_z_Sylvia : Delta_Sylvia := r(a_Sylvia^2 + Delta_Sol^2) : mu_Sylvia := 5*l(a_Sylvia*Delta_Sylvia/l_A^2) : rho_p_Sylvia := arcsin(r_p_Sylvia/Delta_Sylvia) : theta_Sylvia := arccos((a_Sylvia^2 + Delta_Sylvia^2 - Delta_Sol^2)/(2*a_Sylvia*Delta_Sylvia)) : delta_p_Sylvia := 2*rho_p_Sylvia : m_Sylvia := H_Sylvia + mu_Sylvia - 5*l100(q(theta_Sylvia)) : (* "m_Sylvia" = Q(12.92262359263233002719760852891304, 0.01545790611721484569335948484881) ; "delta_p_Sylvia[arcsec]" = Q(0.07615933138694830865200241210675, 0.00530773489822125974090227633208) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Sylvia # OBJECTS FROM 4.95 AU TO 5.46 AU # https://en.wikipedia.org/wiki/Jovian_System ## PLANET JUPITER [5.20 AU] a_Jupiter := Q(778.479, 0.001)*E(6)*_km : ## alpha_Jupiter := Q(816.363, 0.001)*E(6)*_km : ## H_Jupiter := -Q(9.4, 0.1) : ## r_Jupiter := Q(69911., 6.)*_km : r_e_Jupiter := Q(71492., 1.)*_km : ## pi_Jupiter := 2*a_Jupiter - alpha_Jupiter : r_p_Jupiter := 3*r_Jupiter - 2*r_e_Jupiter : Delta_Jupiter := r(a_Jupiter^2 + Delta_Sol^2) : mu_Jupiter := 5*l(a_Jupiter*Delta_Jupiter/l_A^2) : rho_e_Jupiter := arcsin(r_e_Jupiter/Delta_Jupiter) : rho_p_Jupiter := arcsin(r_p_Jupiter/Delta_Jupiter) : theta_Jupiter := arccos((a_Jupiter^2 + Delta_Jupiter^2 - Delta_Sol^2)/(2*a_Jupiter*Delta_Jupiter)) : delta_p_Jupiter := 2*rho_p_Jupiter : m_Jupiter := H_Jupiter + mu_Jupiter - 5*l100(q(theta_Jupiter)) : (* "m_Jupiter" = -Q(1.73830381671000556227028870644930, 0.10000000014757641608922524946966) ; "delta_p_Jupiter[arcsec]" = Q(34.73596043427596773054158125657364, 0.00942488364361745501061530983617) ; *) (* https://en.wikipedia.org/wiki/Planet_Jupiter https://en.wikipedia.org/wiki/Jovian_radius *) ## JOVIAN SATELLITE GANYMEDE a_Ganymede := Q(1070400., 100.)*_km : ## alpha_Ganymede := Q(1071600., 100.)*_km : ## H_Ganymede := -Q(2.1, 0.1) : ## M_Ganymede := Q(1.4819E23, 0.0001E23)*_kg : ## P_Ganymede := Q(7.15455296, 0.00000001)*_d : ## r_Ganymede := Q(2634.1, 0.3)*_km : f_Ganymede := 5*pi^2*r_Ganymede^3/(G*M_Ganymede*P_Ganymede^2) : pi_Ganymede := 2*a_Ganymede - alpha_Ganymede : r_e_Ganymede := 3*r_Ganymede/(3 - f_Ganymede) : r_p_Ganymede := (1 - f_Ganymede)*r_e_Ganymede : Delta_Ganymede := Delta_Jupiter : mu_Ganymede := mu_Jupiter : theta_Ganymede := theta_Jupiter : m_Ganymede := H_Ganymede + mu_Ganymede - 5*l100(q(theta_Ganymede)) : rho_e_Ganymede := arcsin(r_e_Ganymede/Delta_Ganymede) : rho_o_Ganymede := arctan(a_Ganymede/Delta_Ganymede) : rho_p_Ganymede := arcsin(r_p_Ganymede/Delta_Ganymede) : delta_p_Ganymede := 2*rho_p_Ganymede : Deltam_Ganymede := m_Ganymede - m_Jupiter : Deltarho_Ganymede := rho_o_Ganymede - rho_e_Jupiter - rho_e_Ganymede : Deltarhostar_Ganymede := Deltarho_Ganymede/Deltam_Ganymede : (* "m_Ganymede" = Q(5.56169618328999443772971129355070, 0.10000000014757641608922524946966) ; "delta_p_Ganymede[arcsec]" = Q(1.37055888756817142236020299136268, 0.00015602888848075965397025110211) ; "Deltarhostar_Ganymede[arcsec]" = Q(35.51076836366765051490838190026062, 0.68795184202561440051734333115850) ; # typical apparent angular separation between Jupiter and Ganymede in arcseconds *) # https://en.wikipedia.org/wiki/Satellite_Ganymede ## JOVIAN SATELLITE IO alpha_Io := Q(423400., 100.)*_km : ## d_x_Io := Q(3660.0, 0.1)*_km : ## d_y_Io := Q(3637.4, 0.1)*_km : ## e_Io := Q(0.0040313019, 0.0000000001) : ## H_Io := -Q(1.7, 0.1) : ## r_Io := Q(1821.6, 0.5)*_km : a_Io := alpha_Io/(1 + e_Io) : r_x_Io := d_x_Io/2 : r_y_Io := d_y_Io/2 : pi_Io := (1 - e_Io)*a_Io : r_z_Io := 3*r_Io - r_x_Io - r_y_Io : r_e_Io := (r_x_Io + r_y_Io)/2 : r_p_Io := r_z_Io : Delta_Io := Delta_Jupiter : mu_Io := mu_Jupiter : theta_Io := theta_Jupiter : m_Io := H_Io + mu_Io - 5*l100(q(theta_Io)) : rho_e_Io := arcsin(r_e_Io/Delta_Io) : rho_o_Io := arctan(a_Io/Delta_Io) : rho_p_Io := arcsin(r_p_Io/Delta_Io) : delta_p_Io := 2*rho_p_Io : Deltam_Io := m_Io - m_Jupiter : Deltarho_Io := rho_o_Io - rho_e_Jupiter - rho_e_Io : Deltarhostar_Io := Deltarho_Io/Deltam_Io : (* "m_Io" = Q(5.96169618328999443772971129355070, 0.10000000014757641608922524946966) ; "delta_p_Io[arcsec]" = Q(0.94509247584531856397869472774157, 0.00078146279752450389474911704927) ; "Deltarhostar_Io[arcsec]" = Q(11.77257705164285011143090892401942, 0.21624617158762520257614985905805) ; *) # https://en.wikipedia.org/wiki/Satellite_Io ## JOVIAN SATELLITE EUROPA alpha_Europa := Q(676938., 1.)*_km : H_Europa := -Q(1.4, 0.1) : ## pi_Europa := Q(664862., 1.)*_km : P_Europa := Q(3.551181, 0.000001)*_d : ## r_Europa := Q(1560.8, 0.5)*_km : rho_m_Europa := Q(3.013, 0.005)*rho_m_CGS : # mass density of Europa a_Europa := (alpha_Europa + pi_Europa)/2 : f_Europa := 15*pi/(4*G*rho_m_Europa*P_Europa^2) : r_e_Europa := 3*r_Europa/(3 - f_Europa) : r_p_Europa := (1 - f_Europa)*r_e_Europa : Delta_Europa := Delta_Jupiter : mu_Europa := mu_Jupiter : theta_Europa := theta_Jupiter : m_Europa := H_Europa + mu_Europa - 5*l100(q(theta_Europa)) : rho_e_Europa := arcsin(r_e_Europa/Delta_Europa) : rho_o_Europa := arctan(a_Europa/Delta_Europa) : rho_p_Europa := arcsin(r_p_Europa/Delta_Europa) : delta_p_Europa := 2*rho_p_Europa : Deltam_Europa := m_Europa - m_Jupiter : Deltarho_Europa := rho_o_Europa - rho_e_Jupiter - rho_e_Europa : Deltarhostar_Europa := Deltarho_Europa/Deltam_Europa : (* "m_Europa" = Q(6.26169618328999443772971129355070, 0.10000000014757641608922524946966) ; "delta_p_Europa[arcsec]" = Q(0.81189815241567765908912650686141, 0.00026009293358495852460525514356) ; "Deltarhostar_Europa[arcsec]" = Q(19.44484172459110603555367826343083, 0.34373948960095394790134236218824) ; *) # https://en.wikipedia.org/wiki/Satellite_Europa ## JOVIAN SATELLITE CALLISTO a_Callisto := Q(1882700., 100.)*_km : ## alpha_Callisto := Q(1897000., 1000.)*_km : ## H_Callisto := -Q(1.2, 0.1) : ## M_Callisto := Q(1.075938, 0.000137)*E(23)*_kg : P_Callisto := Q(16.6890184, 0.0000001)*_d : ## r_Callisto := Q(2410.3, 1.5)*_km : f_Callisto := 5*pi^2*r_Callisto^3/(G*M_Callisto*P_Callisto^2) : pi_Callisto := 2*a_Callisto - alpha_Callisto : r_e_Callisto := 3*r_Callisto/(3 - f_Callisto) : r_p_Callisto := (1 - f_Callisto)*r_e_Callisto : Delta_Callisto := Delta_Jupiter : mu_Callisto := mu_Jupiter : theta_Callisto := theta_Jupiter : m_Callisto := H_Callisto + mu_Callisto - 5*l100(q(theta_Callisto)) : rho_e_Callisto := arcsin(r_e_Callisto/Delta_Callisto) : rho_o_Callisto := arctan(a_Callisto/Delta_Callisto) : rho_p_Callisto := arcsin(r_p_Callisto/Delta_Callisto) : delta_p_Callisto := 2*rho_p_Callisto : Deltam_Callisto := m_Callisto - m_Jupiter : Deltarho_Callisto := rho_o_Callisto - rho_e_Jupiter - rho_e_Callisto : Deltarhostar_Callisto := Deltarho_Callisto/Deltam_Callisto : (* "m_Callisto" = Q(6.46169618328999443772971129355070, 0.10000000014757641608922524946966) ; "delta_p_Callisto[arcsec]" = Q(1.25427350347426642675638474805951, 0.00078050028046557492289097560308) ; "Deltarhostar_Callisto[arcsec]" = Q(57.39576350007012942652619005337320, 0.98988151890278566360998667023612) ; *) # https://en.wikipedia.org/wiki/Satellite_Callisto ## JOVIAN SATELLITE AMALTHEA a_Amalthea := Q(181365.84, 0.02)*_km : d_y_Amalthea := Q(146., 1.)*_km : ## d_z_Amalthea := Q(128., 1.)*_km : ## e_Amalthea := Q(0.00319, 0.00004) : H_Amalthea := Q(7.1, 0.1) : ## r_Amalthea := Q(83.5, 2.0)*_km : alpha_Amalthea := (1 + e_Amalthea)*a_Amalthea : pi_Amalthea := (1 - e_Amalthea)*a_Amalthea : r_y_Amalthea := d_y_Amalthea/2 : r_z_Amalthea := d_z_Amalthea/2 : r_x_Amalthea := 3*r_Amalthea - r_y_Amalthea - r_z_Amalthea : r_p_Amalthea := r_z_Amalthea : r_e_Amalthea := (r_x_Amalthea + r_y_Amalthea)/2 : Delta_Amalthea := Delta_Jupiter : mu_Amalthea := mu_Jupiter : theta_Amalthea := theta_Jupiter : m_Amalthea := H_Amalthea + mu_Amalthea - 5*l100(q(theta_Amalthea)) : rho_e_Amalthea := arcsin(r_e_Amalthea/Delta_Amalthea) : rho_o_Amalthea := arctan(a_Amalthea/Delta_Amalthea) : rho_p_Amalthea := arcsin(r_p_Amalthea/Delta_Amalthea) : delta_p_Amalthea := 2*rho_p_Amalthea : Deltam_Amalthea := m_Amalthea - m_Jupiter : Deltarho_Amalthea := rho_o_Amalthea - rho_e_Jupiter - rho_e_Amalthea : Deltarhostar_Amalthea := Deltarho_Amalthea/Deltam_Amalthea : (* "m_Amalthea" = Q(14.76169618328999443772971129355070, 0.10000000014757641608922524946966) ; "delta_p_Amalthea[arcsec]" = Q(0.03330538982107127545949707493194, 0.00026019836124831152741581751483) ; "Deltarhostar_Amalthea[arcsec]" = Q(1.73119566103922151302229033050228, 0.01483814740695499028346560402053) ; *) # https://en.wikipedia.org/wiki/Satellite_Amalthea ## MINOR PLANET HEKTOR [5.26 AU] a_Hektor := Q(5.2571, 0.0001)*_AU : ## alpha_Hektor := Q(5.3824, 0.0001)*_AU : ## d_y_Hektor := Q(195., 1.)*_km : ## d_z_Hektor := Q(195., 1.)*_km : ## H_Hektor := Q((7.49 + 7.20)/2, (7.49 - 7.20)/2) : r_Hektor := Q(231., 4.)*_km : pi_Hektor := 2*a_Hektor - alpha_Hektor : r_y_Hektor := d_y_Hektor/2 : r_z_Hektor := d_z_Hektor/2 : r_p_Hektor := r_z_Hektor : r_x_Hektor := 3*r_Hektor - r_y_Hektor - r_z_Hektor : r_e_Hektor := (r_x_Hektor + r_y_Hektor)/2 : Delta_Hektor := r(a_Hektor^2 + Delta_Sol^2) : mu_Hektor := 5*l(a_Hektor*Delta_Hektor/l_A^2) : rho_p_Hektor := arcsin(r_p_Hektor/Delta_Hektor) : theta_Hektor := arccos((a_Hektor^2 + Delta_Hektor^2 - Delta_Sol^2)/(2*a_Hektor*Delta_Hektor)) : delta_p_Hektor := 2*rho_p_Hektor : m_Hektor := H_Hektor + mu_Hektor - 5*l100(q(theta_Hektor)) : (* "m_Hektor" = Q(15.04979718436456361732166846445311, 0.14500002234084386565156635296445) ; "delta_p_Hektor[arcsec]" = Q(0.05024240751701347821378486670496, 0.00025765502274339468201926977493) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Hektor ## JOVIAN SATELLITE HIMALIA a_Himalia := Q(11388690., 10.)*_km : ## d_Himalia := Q(139.6, 1.7)*_km : d_e_Himalia := Q(150., 20.)*_km : e_Himalia := Q(0.1537860, 0.0000001) : ## H_Himalia := Q((8.0 + 7.9)/2, (8.0 - 7.9)/2) : ## alpha_Himalia := (1 + e_Himalia)*a_Himalia : pi_Himalia := (1 - e_Himalia)*a_Himalia : r_Himalia := d_Himalia/2 : r_e_Himalia := d_e_Himalia/2 : r_p_Himalia := 3*r_Himalia - 2*r_e_Himalia : Delta_Himalia := Delta_Jupiter : mu_Himalia := mu_Jupiter : theta_Himalia := theta_Jupiter : m_Himalia := H_Himalia + mu_Himalia - 5*l100(q(theta_Himalia)) : rho_e_Himalia := arcsin(r_e_Himalia/Delta_Himalia) : rho_o_Himalia := arctan(a_Himalia/Delta_Himalia) : rho_p_Himalia := arcsin(r_p_Himalia/Delta_Himalia) : delta_p_Himalia := 2*rho_p_Himalia : Deltam_Himalia := m_Himalia - m_Jupiter : Deltarho_Himalia := rho_o_Himalia - rho_e_Jupiter - rho_e_Himalia : Deltarhostar_Himalia := Deltarho_Himalia/Deltam_Himalia : (* "m_Himalia" = Q(15.61169618328999443772971129355070, 0.05000000029515283152508654522397) ; "delta_p_Himalia[arcsec]" = Q(0.03091156492768177288211157418880, 0.01049219026926923726078653481865) ; "Deltarhostar_Himalia[arcmin]" = Q(2.82852350825220569978499677313469, 0.01822700598489195322575862687473) ; *) # https://en.wikipedia.org/wiki/Satellite_Himalia ## MINOR PLANET PATROCLUS [5.21 AU] a_Patroclus := Q(5.209, 0.001)*_AU : ## alpha_Patroclus := Q(5.937, 0.001)*_AU : ## d_Patroclus := Q(113., 3.)*_km : d_x_Patroclus := Q(127., 1.)*_km : ## d_y_Patroclus := Q(117., 1.)*_km : ## H_Patroclus := Q(8.18, 0.01) : ## pi_Patroclus := 2*a_Patroclus - alpha_Patroclus : r_Patroclus := d_Patroclus/2 : r_x_Patroclus := d_x_Patroclus/2 : r_y_Patroclus := d_y_Patroclus/2 : r_z_Patroclus := 3*r_Patroclus - r_x_Patroclus - r_y_Patroclus : r_e_Patroclus := (r_x_Patroclus + r_y_Patroclus)/2 : r_p_Patroclus := r_z_Patroclus : Delta_Patroclus := r(a_Patroclus^2 + Delta_Sol^2) : mu_Patroclus := 5*l(a_Patroclus*Delta_Patroclus/l_A^2) : rho_p_Patroclus := arcsin(r_p_Patroclus/Delta_Patroclus) : theta_Patroclus := arccos((a_Patroclus^2 + Delta_Patroclus^2 - Delta_Sol^2)/(2*a_Patroclus*Delta_Patroclus)) : delta_p_Patroclus := 2*rho_p_Patroclus : m_Patroclus := H_Patroclus + mu_Patroclus - 5*l100(q(theta_Patroclus)) : (* "m_Patroclus" = Q(15.84591171574793968583357341733392, 0.01003291033671434292663026382652) ; "delta_p_Patroclus[arcsec]" = Q(0.02469509428973840153563866783146, 0.00236824669029864616029185117284) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Patroclus ## MINOR PLANET DEIPHOBUS [5.13 AU] a_Deiphobus := Q(5.1276, 0.0001)*_AU : ## alpha_Deiphobus := Q(5.3511, 0.0001)*_AU : ## H_Deiphobus := Q(8.47, 0.10) : P_Deiphobus := Q(58.699, 0.002)*_h : r_Deiphobus := Q(59.1, 0.8)*_km : pi_Deiphobus := 2*a_Deiphobus - alpha_Deiphobus : r_e_Deiphobus := r_Deiphobus : r_p_Deiphobus := r_Deiphobus : Delta_Deiphobus := r(a_Deiphobus^2 + Delta_Sol^2) : mu_Deiphobus := 5*l(a_Deiphobus*Delta_Deiphobus/l_A^2) : rho_p_Deiphobus := arcsin(r_p_Deiphobus/Delta_Deiphobus) : theta_Deiphobus := arccos((a_Deiphobus^2 + Delta_Deiphobus^2 - Delta_Sol^2)/(2*a_Deiphobus*Delta_Deiphobus)) : delta_p_Deiphobus := 2*rho_p_Deiphobus : m_Deiphobus := H_Deiphobus + mu_Deiphobus - 5*l100(q(theta_Deiphobus)) : (* "m_Deiphobus" = Q(16.06932286884668920373380074406197, 0.10000003396380407669762080260838) ; "delta_p_Deiphobus[arcsec]" = Q(0.03119592991975441002813284063167, 0.00042228033797147025246844848579) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Deiphobus ## MINOR PLANET AUTOMEDON [5.11 AU] a_Automedon := Q(5.1079, 0.0001)*_AU : ## alpha_Automedon := Q(5.2417, 0.0001)*_AU : ## d_Automedon := Q(113.11, 2.25)*_km : H_Automedon := Q(8.59, 0.21) : P_Automedon := Q(10.212, 0.002)*_h : pi_Automedon := 2*a_Automedon - alpha_Automedon : r_Automedon := d_Automedon/2 : r_e_Automedon := r_Automedon : r_p_Automedon := r_Automedon : Delta_Automedon := r(a_Automedon^2 + Delta_Sol^2) : mu_Automedon := 5*l(a_Automedon*Delta_Automedon/l_A^2) : rho_p_Automedon := arcsin(r_p_Automedon/Delta_Automedon) : theta_Automedon := arccos((a_Automedon^2 + Delta_Automedon^2 - Delta_Sol^2)/(2*a_Automedon*Delta_Automedon)) : delta_p_Automedon := 2*rho_p_Automedon : m_Automedon := H_Automedon + mu_Automedon - 5*l100(q(theta_Automedon)) : (* "m_Automedon" = Q(16.17305686476238942515956247929105, 0.21000001629160069136202923394229) ; "delta_p_Automedon[arcsec]" = Q(0.02996344457369331875582789687127, 0.00059603731390660725449324159370) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Automedon # OBJECTS FROM >5.46 AU TO <9.04 AU (TRANS-JOVIAN/CIS-SATURNIAN OBJECTS) ## MINOR PLANET HIDALGO [5.74 AU] a_Hidalgo := Q(5.7410, 0.0001)*_AU : ## alpha_Hidalgo := Q(9.5345, 0.0001)*_AU : ## H_Hidalgo := Q(10.77, 0.01) : ## P_Hidalgo := Q(10.063, 0.0003)*_h : r_Hidalgo := Q(26.225, 1.8)*_km : pi_Hidalgo := 2*a_Hidalgo - alpha_Hidalgo : r_e_Hidalgo := r_Hidalgo : r_p_Hidalgo := r_Hidalgo : Delta_Hidalgo := r(a_Hidalgo^2 + Delta_Sol^2) : mu_Hidalgo := 5*l(a_Hidalgo*Delta_Hidalgo/l_A^2) : rho_p_Hidalgo := arcsin(r_p_Hidalgo/Delta_Hidalgo) : theta_Hidalgo := arccos((a_Hidalgo^2 + Delta_Hidalgo^2 - Delta_Sol^2)/(2*a_Hidalgo*Delta_Hidalgo)) : delta_p_Hidalgo := 2*rho_p_Hidalgo : m_Hidalgo := H_Hidalgo + mu_Hidalgo - 5*l100(q(theta_Hidalgo)) : (* "m_Hidalgo" = Q(18.84818002547999101178940642580149, 0.01000027385662396845914808525405) ; "delta_p_Hidalgo[arcsec]" = Q(0.01240988568141543165620003604288, 0.00085177482951875781914261933263) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Hidalgo # OBJECTS FROM 9.04 AU TO 10.1 AU # https://en.wikipedia.org/wiki/Saturnian_System ## PLANET SATURN [9.58 AU] a_Saturn := Q(1433.53, 0.01)*E(6)*_km : ## alpha_Saturn := Q(1514.50, 0.01)*E(6)*_km : ## H_Saturn := -Q(9.7, 0.1) : ## r_Saturn := Q(58232., 6.)*_km : r_e_Saturn := Q(60268., 1.)*_km : ## pi_Saturn := 2*a_Saturn - alpha_Saturn : r_p_Saturn := 3*r_Saturn - 2*r_e_Saturn : Delta_Saturn := r(a_Saturn^2 + Delta_Sol^2) : mu_Saturn := 5*l(a_Saturn*Delta_Saturn/l_A^2) : rho_e_Saturn := arcsin(r_e_Saturn/Delta_Saturn) : rho_p_Saturn := arcsin(r_p_Saturn/Delta_Saturn) : theta_Saturn := arccos((a_Saturn^2 + Delta_Saturn^2 - Delta_Sol^2)/(2*a_Saturn*Delta_Saturn)) : delta_p_Saturn := 2*rho_p_Saturn : m_Saturn := H_Saturn + mu_Saturn - 5*l100(q(theta_Saturn)) : (* "m_Saturn" = Q(0.57255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Saturn[arcsec]" = Q(15.50155238988204008916521483000060, 0.00518472722483855099308881751717) ; *) # https://en.wikipedia.org/wiki/Planet_Saturn ## SATURNIAN SATELLITE TITAN a_Titan := Q(1221870., 10.)*_km : ## alpha_Titan := Q(1257060., 10.)*_km : ## d_x_Titan := Q(5150., 1.)*_km : ## d_y_Titan := Q(5149., 1.)*_km : ## H_Titan := -Q(1.3, 0.1) : ## r_Titan := Q(2574.73, 0.09)*_km : pi_Titan := 2*a_Titan - alpha_Titan : r_x_Titan := d_x_Titan/2 : r_y_Titan := d_y_Titan/2 : r_z_Titan := 3*r_Titan - r_x_Titan - r_y_Titan : r_e_Titan := (r_x_Titan + r_y_Titan)/2 : r_p_Titan := r_z_Titan : Delta_Titan := Delta_Saturn : mu_Titan := mu_Saturn : theta_Titan := theta_Saturn : m_Titan := H_Titan + mu_Titan - 5*l100(q(theta_Titan)) : rho_e_Titan := arcsin(r_e_Titan/Delta_Titan) : rho_o_Titan := arctan(a_Titan/Delta_Titan) : rho_p_Titan := arcsin(r_p_Titan/Delta_Titan) : delta_p_Titan := 2*rho_p_Titan : Deltam_Titan := m_Titan - m_Saturn : Deltarho_Titan := rho_o_Titan - rho_e_Saturn - rho_e_Titan : Deltarhostar_Titan := Deltarho_Titan/Deltam_Titan : (* "m_Titan" = Q(8.97255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Titan[arcsec]" = Q(0.73692193340719991710505630630207, 0.00021669832907642627346932493452) ; "Deltarhostar_Titan[arcsec]" = Q(19.74607544580030777903561762084300, 0.33244254467873484264161990623461) ; *) # https://en.wikipedia.org/wiki/Satellite_Titan ## SATURNIAN SATELLITE RHEA a_Rhea := Q(527040., 10.)*_km : ## d_x_Rhea := Q(1532.4, 0.1)*_km : ## d_y_Rhea := Q(1525.6, 0.1)*_km : ## e_Rhea := Q(0.001, 0.001) : ## H_Rhea := Q(0.1, 0.1) : ## r_Rhea := Q(763.5, 0.5)*_km : alpha_Rhea := (1 + e_Rhea)*a_Rhea : pi_Rhea := (1 - e_Rhea)*a_Rhea : r_x_Rhea := d_x_Rhea/2 : r_y_Rhea := d_y_Rhea/2 : r_z_Rhea := 3*r_Rhea - r_x_Rhea - r_y_Rhea : r_e_Rhea := (r_x_Rhea + r_y_Rhea)/2 : r_p_Rhea := r_z_Rhea : Delta_Rhea := Delta_Saturn : mu_Rhea := mu_Saturn : theta_Rhea := theta_Saturn : m_Rhea := H_Rhea + mu_Rhea - 5*l100(q(theta_Rhea)) : rho_e_Rhea := arcsin(r_e_Rhea/Delta_Rhea) : rho_o_Rhea := arctan(a_Rhea/Delta_Rhea) : rho_p_Rhea := arcsin(r_p_Rhea/Delta_Rhea) : delta_p_Rhea := 2*rho_p_Rhea : Deltam_Rhea := m_Rhea - m_Saturn : Deltarho_Rhea := rho_o_Rhea - rho_e_Saturn - rho_e_Rhea : Deltarhostar_Rhea := Deltarho_Rhea/Deltam_Rhea : (* "m_Rhea" = Q(10.37255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Rhea[arcsec]" = Q(0.21795480321487650682411881357703, 0.00042980599496238972464770136247) ; "Deltarhostar_Rhea[arcsec]" = Q(6.80508179582836468507372121085158, 0.09820255934579165730148994742245) ; *) # https://en.wikipedia.org/wiki/Satellite_Rhea ## SATURNIAN SATELLITE TETHYS a_Tethys := Q(294619., 1.)*_km : ## d_x_Tethys := Q(1076.8, 0.1)*_km : ## d_y_Tethys := Q(1057.4, 0.1)*_km : ## e_Tethys := Q(0.0001, 0.0001) : ## H_Tethys := Q(0.7, 0.1) : ## r_Tethys := Q(531.1, 0.6)*_km : alpha_Tethys := (1 + e_Tethys)*a_Tethys : pi_Tethys := (1 - e_Tethys)*a_Tethys : r_x_Tethys := d_x_Tethys/2 : r_y_Tethys := d_y_Tethys/2 : r_z_Tethys := 3*r_Tethys - r_x_Tethys - r_y_Tethys : r_e_Tethys := (r_x_Tethys + r_y_Tethys)/2 : r_p_Tethys := r_z_Tethys : Delta_Tethys := Delta_Saturn : mu_Tethys := mu_Saturn : theta_Tethys := theta_Saturn : m_Tethys := H_Tethys + mu_Tethys - 5*l100(q(theta_Tethys)) : rho_e_Tethys := arcsin(r_e_Tethys/Delta_Tethys) : rho_o_Tethys := arctan(a_Tethys/Delta_Tethys) : rho_p_Tethys := arcsin(r_p_Tethys/Delta_Tethys) : delta_p_Tethys := 2*rho_p_Tethys : Deltam_Tethys := m_Tethys - m_Saturn : Deltarho_Tethys := rho_o_Tethys - rho_e_Saturn - rho_e_Tethys : Deltarhostar_Tethys := Deltarho_Tethys/Deltam_Tethys : (* "m_Tethys" = Q(10.97255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Tethys[arcsec]" = Q(0.15060777078353936958328461033092, 0.00051559033714760237453069776937) ; "Deltarhostar_Tethys[arcsec]" = Q(3.21743745926362053024065345333835, 0.04375139160808692700368132047223) ; *) # https://en.wikipedia.org/wiki/Satellite_Tethys ## SATURNIAN SATELLITE DIONE a_Dione := Q(377396., 1.)*_km : ## d_x_Dione := Q(1128.8, 0.1)*_km : ## d_y_Dione := Q(1122.6, 0.1)*_km : ## e_Dione := Q(0.0022, 0.0001) : ## H_Dione := Q(0.8, 0.1) : ## r_Dione := Q(561.4, 0.4)*_km : alpha_Dione := (1 + e_Dione)*a_Dione : pi_Dione := (1 - e_Dione)*a_Dione : r_x_Dione := d_x_Dione/2 : r_y_Dione := d_y_Dione/2 : r_z_Dione := 3*r_Dione - r_x_Dione - r_y_Dione : r_e_Dione := (r_x_Dione + r_y_Dione)/2 : r_p_Dione := r_z_Dione : Delta_Dione := Delta_Saturn : mu_Dione := mu_Saturn : theta_Dione := theta_Saturn : m_Dione := H_Dione + mu_Dione - 5*l100(q(theta_Dione)) : rho_e_Dione := arcsin(r_e_Dione/Delta_Dione) : rho_o_Dione := arctan(a_Dione/Delta_Dione) : rho_p_Dione := arcsin(r_p_Dione/Delta_Dione) : delta_p_Dione := 2*rho_p_Dione : Deltam_Dione := m_Dione - m_Saturn : Deltarho_Dione := rho_o_Dione - rho_e_Saturn - rho_e_Dione : Deltarhostar_Dione := Deltarho_Dione/Deltam_Dione : (* "m_Dione" = Q(11.07255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Dione[arcsec]" = Q(0.15985260353973199230071418225082, 0.00034405881740133794177925899052) ; "Deltarhostar_Dione[arcsec]" = Q(4.31459794823945150913122275162896, 0.05811203877422532617936832835619) ; *) # https://en.wikipedia.org/wiki/Satellite_Dione ## SATURNIAN SATELLITE IAPETUS a_Iapetus := Q(3560820., 10.)*_km : ## d_e_Iapetus := Q(1492.0, 0.1)*_km : ## e_Iapetus := Q(0.0276812, 0.0000001) : ## H_Iapetus := Q(1.2, 0.1) : ## r_Iapetus := Q(735.6, 1.5)*_km : alpha_Iapetus := (1 + e_Iapetus)*a_Iapetus : pi_Iapetus := (1 - e_Iapetus)*a_Iapetus : r_e_Iapetus := d_e_Iapetus/2 : r_p_Iapetus := 3*r_Iapetus - 2*r_e_Iapetus : Delta_Iapetus := Delta_Saturn : mu_Iapetus := mu_Saturn : theta_Iapetus := theta_Saturn : m_Iapetus := H_Iapetus + mu_Iapetus - 5*l100(q(theta_Iapetus)) : rho_e_Iapetus := arcsin(r_e_Iapetus/Delta_Iapetus) : rho_o_Iapetus := arctan(a_Iapetus/Delta_Iapetus) : rho_p_Iapetus := arcsin(r_p_Iapetus/Delta_Iapetus) : delta_p_Iapetus := 2*rho_p_Iapetus : Deltam_Iapetus := m_Iapetus - m_Saturn : Deltarho_Iapetus := rho_o_Iapetus - rho_e_Saturn - rho_e_Iapetus : Deltarhostar_Iapetus := Deltarho_Iapetus/Deltam_Iapetus : (* "m_Iapetus" = Q(11.47255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Iapetus[arcsec]" = Q(0.20458843511226902868318177339965, 0.00128829854976685114003929729950) ; "Deltarhostar_Iapetus[arcsec]" = Q(45.94974603703071302821657543147788, 0.59617215427379328200360359653064) ; *) # https://en.wikipedia.org/wiki/Satellite_Iapetus ## SATURNIAN SATELLITE ENCELADUS a_Enceladus := Q(237948., 1.)*_km : ## d_x_Enceladus := Q(513.2, 0.1)*_km : ## d_y_Enceladus := Q(502.8, 0.1)*_km : ## e_Enceladus := Q(0.0047, 0.0001) : ## H_Enceladus := Q(2.1, 0.1) : ## r_Enceladus := Q(252.1, 0.2)*_km : alpha_Enceladus := (1 + e_Enceladus)*a_Enceladus : pi_Enceladus := (1 - e_Enceladus)*a_Enceladus : r_x_Enceladus := d_x_Enceladus/2 : r_y_Enceladus := d_y_Enceladus/2 : r_z_Enceladus := 3*r_Enceladus - r_x_Enceladus - r_y_Enceladus : r_e_Enceladus := (r_x_Enceladus + r_y_Enceladus)/2 : r_p_Enceladus := r_z_Enceladus : Delta_Enceladus := Delta_Saturn : mu_Enceladus := mu_Saturn : theta_Enceladus := theta_Saturn : m_Enceladus := H_Enceladus + mu_Enceladus - 5*l100(q(theta_Enceladus)) : rho_e_Enceladus := arcsin(r_e_Enceladus/Delta_Enceladus) : rho_o_Enceladus := arctan(a_Enceladus/Delta_Enceladus) : rho_p_Enceladus := arcsin(r_p_Enceladus/Delta_Enceladus) : delta_p_Enceladus := 2*rho_p_Enceladus : Deltam_Enceladus := m_Enceladus - m_Saturn : Deltarho_Enceladus := rho_o_Enceladus - rho_e_Saturn - rho_e_Enceladus : Deltarhostar_Enceladus := Deltarho_Enceladus/Deltam_Enceladus : (* "m_Enceladus" = Q(12.37255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Enceladus[arcsec]" = Q(0.07106786295239866916707875073391, 0.00017291979637375408067431564187) ; "Deltarhostar_Enceladus[arcsec]" = Q(2.15179943912031054487107143454406, 0.02578902650984734230204713538220) ; *) # https://en.wikipedia.org/wiki/Satellite_Enceladus ## SATURNIAN SATELLITE MIMAS a_Mimas := Q(185539., 1.)*_km : ## alpha_Mimas := Q(189176., 1.)*_km : ## d_x_Mimas := Q(415.6, 0.1)*_km : ## d_y_Mimas := Q(393.4, 0.1)*_km : ## H_Mimas := Q(3.2, 0.1) : ## r_Mimas := Q(198.2, 0.3)*_km : pi_Mimas := 2*a_Mimas - alpha_Mimas : r_x_Mimas := d_x_Mimas/2 : r_y_Mimas := d_y_Mimas/2 : r_z_Mimas := 3*r_Mimas - r_x_Mimas - r_y_Mimas : r_e_Mimas := (r_x_Mimas + r_y_Mimas)/2 : r_p_Mimas := r_z_Mimas : Delta_Mimas := Delta_Saturn : mu_Mimas := mu_Saturn : theta_Mimas := theta_Saturn : m_Mimas := H_Mimas + mu_Mimas - 5*l100(q(theta_Mimas)) : rho_e_Mimas := arcsin(r_e_Mimas/Delta_Mimas) : rho_o_Mimas := arctan(a_Mimas/Delta_Mimas) : rho_p_Mimas := arcsin(r_p_Mimas/Delta_Mimas) : delta_p_Mimas := 2*rho_p_Mimas : Deltam_Mimas := m_Mimas - m_Saturn : Deltarho_Mimas := rho_o_Mimas - rho_e_Saturn - rho_e_Mimas : Deltarhostar_Mimas := Deltarho_Mimas/Deltam_Mimas : (* "m_Mimas" = Q(13.47255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Mimas[arcsec]" = Q(0.05440999092730954230055700203374, 0.00025839005804347227331836101420) ; "Deltarhostar_Mimas[arcsec]" = Q(1.38747650075467716353848480625963, 0.01521077145701885952452955552338) ; *) # https://en.wikipedia.org/wiki/Satellite_Mimas ## SATURNIAN SATELLITE HYPERION a_Hyperion := Q(1481009., 1.)*_km : ## d_x_Hyperion := Q(360.2, 0.1)*_km : ## d_y_Hyperion := Q(266.0, 0.1)*_km : ## e_Hyperion := Q(0.1230061, 0.0000001) : ## H_Hyperion := Q(4.8, 0.1) : ## r_Hyperion := Q(135., 4.)*_km : alpha_Hyperion := (1 + e_Hyperion)*a_Hyperion : pi_Hyperion := (1 - e_Hyperion)*a_Hyperion : r_x_Hyperion := d_x_Hyperion/2 : r_y_Hyperion := d_y_Hyperion/2 : r_z_Hyperion := 3*r_Hyperion - r_x_Hyperion - r_y_Hyperion : r_e_Hyperion := (r_x_Hyperion + r_y_Hyperion)/2 : r_p_Hyperion := r_z_Hyperion : Delta_Hyperion := Delta_Saturn : mu_Hyperion := mu_Saturn : theta_Hyperion := theta_Saturn : m_Hyperion := H_Hyperion + mu_Hyperion - 5*l100(q(theta_Hyperion)) : rho_e_Hyperion := arcsin(r_e_Hyperion/Delta_Hyperion) : rho_o_Hyperion := arctan(a_Hyperion/Delta_Hyperion) : rho_p_Hyperion := arcsin(r_p_Hyperion/Delta_Hyperion) : delta_p_Hyperion := 2*rho_p_Hyperion : Deltam_Hyperion := m_Hyperion - m_Saturn : Deltarho_Hyperion := rho_o_Hyperion - rho_e_Saturn - rho_e_Hyperion : Deltarhostar_Hyperion := Deltarho_Hyperion/Deltam_Hyperion : (* "m_Hyperion" = Q(15.07255038571874078781874233218398, 0.10000000451603721412085625782896) ; "delta_p_Hyperion[arcsec]" = Q(0.02630340960662670083182860600264, 0.00343467242165088144583621978208) ; "Deltarhostar_Hyperion[arcsec]" = Q(14.02056243983688647178377446750300, 0.13674534221215688026302749258630) ; *) # https://en.wikipedia.org/wiki/Satellite_Hyperion # OBJECTS FROM >10.1 AU TO <18.3 AU (TRANS-SATURNIAN/CIS-URANIAN OBJECTS) ## MINOR PLANET CHIRON [13.7 AU] a_Chiron := Q(13.70, 0.01)*_AU : ## alpha_Chiron := Q(18.87, 0.01)*_AU : ## d_x_Chiron := Q(126., 22.)*_km : d_y_Chiron := Q(109., 19.)*_km : H_Chiron := Q(5.82, 0.07) : r_Chiron := Q(108., 5.)*_km : pi_Chiron := 2*a_Chiron - alpha_Chiron : r_x_Chiron := d_x_Chiron/2 : r_y_Chiron := d_y_Chiron/2 : r_e_Chiron := (r_x_Chiron + r_y_Chiron)/2 : r_z_Chiron := 3*r_Chiron - r_x_Chiron - r_y_Chiron : r_p_Chiron := r_z_Chiron : Delta_Chiron := r(a_Chiron^2 + Delta_Sol^2) : mu_Chiron := 5*l(a_Chiron*Delta_Chiron/l_A^2) : rho_p_Chiron := arcsin(r_p_Chiron/Delta_Chiron) : theta_Chiron := arccos((a_Chiron^2 + Delta_Chiron^2 - Delta_Sol^2)/(2*a_Chiron*Delta_Chiron)) : delta_p_Chiron := 2*rho_p_Chiron : m_Chiron := H_Chiron + mu_Chiron - 5*l100(q(theta_Chiron)) : (* "m_Chiron" = Q(17.63604251252176021164966209378857, 0.07007117811947587461367193142235) ; "delta_p_Chiron[arcsec]" = Q(0.04145485746331596473850709669715, 0.00419309091790719538504353352979) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Chiron ## MINOR PLANET CHARIKLO [15.8 AU] a_Chariklo := Q(15.822, 0.001)*_AU : ## alpha_Chariklo := Q(18.545, 0.001)*_AU : ## d_Chariklo := Q(248., 18.)*_km : d_x_Chariklo := Q(287.6, 0.1)*_km : ## d_y_Chariklo := Q(270.4, 0.1)*_km : ## H_Chariklo := Q(7.08, 0.04) : pi_Chariklo := 2*a_Chariklo - alpha_Chariklo : r_Chariklo := d_Chariklo/2 : r_x_Chariklo := d_x_Chariklo/2 : r_y_Chariklo := d_y_Chariklo/2 : r_e_Chariklo := (r_x_Chariklo + r_y_Chariklo)/2 : r_z_Chariklo := 3*r_Chariklo - r_x_Chariklo - r_y_Chariklo : r_p_Chariklo := r_z_Chariklo : Delta_Chariklo := r(a_Chariklo^2 + Delta_Sol^2) : mu_Chariklo := 5*l(a_Chariklo*Delta_Chariklo/l_A^2) : rho_p_Chariklo := arcsin(r_p_Chariklo/Delta_Chariklo) : theta_Chariklo := arccos((a_Chariklo^2 + Delta_Chariklo^2 - Delta_Sol^2)/(2*a_Chariklo*Delta_Chariklo)) : delta_p_Chariklo := 2*rho_p_Chariklo : m_Chariklo := H_Chariklo + mu_Chariklo - 5*l100(q(theta_Chariklo)) : (* "m_Chariklo" = Q(19.51930512161033945691756897821987, 0.04000093620864061183463165943067) ; "delta_p_Chariklo[arcsec]" = Q(0.01617654092053944915957064921768, 0.00469643132201623463795327286118) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Chariklo ## MINOR PLANET ECHECLUS [10.7 AU] a_Echeclus := Q(1.5977, 0.0001)*_Tm : ## alpha_Echeclus := Q(2.3253, 0.0001)*_Tm : ## H_Echeclus := Q(9.6, 0.1) : ## P_Echeclus := Q(26.802, 0.001)*_h : ## r_Echeclus := Q(32.3, 0.8)*_km : pi_Echeclus := 2*a_Echeclus - alpha_Echeclus : r_e_Echeclus := r_Echeclus : r_p_Echeclus := r_Echeclus : Delta_Echeclus := r(a_Echeclus^2 + Delta_Sol^2) : mu_Echeclus := 5*l(a_Echeclus*Delta_Echeclus/l_A^2) : rho_p_Echeclus := arcsin(r_p_Echeclus/Delta_Echeclus) : theta_Echeclus := arccos((a_Echeclus^2 + Delta_Echeclus^2 - Delta_Sol^2)/(2*a_Echeclus*Delta_Echeclus)) : delta_p_Echeclus := 2*rho_p_Echeclus : m_Echeclus := H_Echeclus + mu_Echeclus - 5*l100(q(theta_Echeclus)) : (* "m_Echeclus" = Q(20.34004719911454839673586545627010, 0.10000036469031411572198479484748) ; "delta_p_Echeclus[arcsec]" = Q(0.00830361297686538016293725621772, 0.00020566288623618534911234353881) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Echeclus # OBJECTS FROM 18.3 AU TO 20.1 AU # https://en.wikipedia.org/wiki/Uranian_System ## PLANET URANUS [19.2 AU] a_Uranus := Q(2.870972, 0.000001)*E(9)*_km : ## alpha_Uranus := Q(3.00639, 0.00001)*E(9)*_km : ## H_Uranus := -Q(7.2, 0.1) : ## r_Uranus := Q(25362., 7.)*_km : r_e_Uranus := Q(25559., 4.)*_km : pi_Uranus := 2*a_Uranus - alpha_Uranus : r_p_Uranus := 3*r_Uranus - 2*r_e_Uranus : Delta_Uranus := r(a_Uranus^2 + Delta_Sol^2) : mu_Uranus := 5*l(a_Uranus*Delta_Uranus/l_A^2) : rho_e_Uranus := arcsin(r_e_Uranus/Delta_Uranus) : rho_p_Uranus := arcsin(r_p_Uranus/Delta_Uranus) : theta_Uranus := arccos((a_Uranus^2 + Delta_Uranus^2 - Delta_Sol^2)/(2*a_Uranus*Delta_Uranus)) : delta_p_Uranus := 2*rho_p_Uranus : m_Uranus := H_Uranus + mu_Uranus - 5*l100(q(theta_Uranus)) : (* "m_Uranus" = Q(6.07566286366347679257073679618727, 0.10000000001139527653151332569451) ; "delta_p_Uranus[arcsec]" = Q(3.58278864666254600705199067401579, 0.00322465424272568625089808008416) ; *) # https://en.wikipedia.org/wiki/Planet_Uranus ## URANIAN SATELLITE TITANIA a_Titania := Q(436282., 1.)*_km : ## e_Titania := Q((0.0012 + 0.0011)/2, (0.0012 - 0.0011)/2) : H_Titania := Q(0.8, 0.1) : ## P_Titania := Q(8.706234, 0.000001)*_d : ## r_Titania := Q(788.4, 0.6)*_km : rho_m_Titania := Q(1.711, 0.005)*rho_m_CGS : alpha_Titania := (1 + e_Titania)*a_Titania : f_Titania := 15*pi/(4*G*rho_m_Titania*P_Titania^2) : pi_Titania := (1 - e_Titania)*a_Titania : r_e_Titania := 3*r_Titania/(3 - f_Titania) : r_p_Titania := (1 - f_Titania)*r_e_Titania : Delta_Titania := Delta_Uranus : mu_Titania := mu_Uranus : theta_Titania := theta_Uranus : m_Titania := H_Titania + mu_Titania - 5*l100(q(theta_Titania)) : rho_e_Titania := arcsin(r_e_Titania/Delta_Titania) : rho_o_Titania := arctan(a_Titania/Delta_Titania) : rho_p_Titania := arcsin(r_p_Titania/Delta_Titania) : delta_p_Titania := 2*rho_p_Titania : Deltam_Titania := m_Titania - m_Uranus : Deltarho_Titania := rho_o_Titania - rho_e_Uranus - rho_e_Titania : Deltarhostar_Titania := Deltarho_Titania/Deltam_Titania : (* "m_Titania" = Q(14.07566286366347679257073679618727, 0.10000000001139527653151332569451) ; "delta_p_Titania[arcsec]" = Q(0.11311787954626297260931258939715, 0.00008608668467046508139287980732) ; "Deltarhostar_Titania[arcsec]" = Q(3.67647800949878493761923795134417, 0.06499157403987822788726778637065) ; *) # https://en.wikipedia.org/wiki/Satellite_Titania ## URANIAN SATELLITE OBERON a_Oberon := Q(583449., 1.)*_km : ## e_Oberon := Q(0.0014, 0.0001) : ## H_Oberon := Q(1.0, 0.1) : ## M_Oberon := Q(3.1104, 0.0749)*E(21)*_kg : P_Oberon := Q(13.46323, 0.00001)*_d : ## r_Oberon := Q(761.4, 2.6)*_km : alpha_Oberon := (1 + e_Oberon)*a_Oberon : f_Oberon := 5*pi^2*r_Oberon^3/(G*M_Oberon*P_Oberon^2) : pi_Oberon := (1 - e_Oberon)*a_Oberon : r_e_Oberon := 3*r_Oberon/(3 - f_Oberon) : r_p_Oberon := (1 - f_Oberon)*r_e_Oberon : Delta_Oberon := Delta_Uranus : mu_Oberon := mu_Uranus : theta_Oberon := theta_Uranus : m_Oberon := H_Oberon + mu_Oberon - 5*l100(q(theta_Oberon)) : rho_e_Oberon := arcsin(r_e_Oberon/Delta_Oberon) : rho_o_Oberon := arctan(a_Oberon/Delta_Oberon) : rho_p_Oberon := arcsin(r_p_Oberon/Delta_Oberon) : delta_p_Oberon := 2*rho_p_Oberon : Deltam_Oberon := m_Oberon - m_Uranus : Deltarho_Oberon := rho_o_Oberon - rho_e_Uranus - rho_e_Oberon : Deltarhostar_Oberon := Deltarho_Oberon/Deltam_Oberon : (* "m_Oberon" = Q(14.27566286366347679257073679618727, 0.10000000001139527653151332569451) ; "delta_p_Oberon[arcsec]" = Q(0.10925161184677567929378465308338, 0.00037301044387582188752287261056) ; "Deltarhostar_Oberon[arcsec]" = Q(4.87471261646566058486147247230308, 0.08407177540752068353245743857333) ; *) # https://en.wikipedia.org/wiki/Satellite_Oberon ## URANIAN SATELLITE ARIEL a_Ariel := Q(190930., 10.)*_km : ## d_x_Ariel := Q(1162.2, 0.1)*_km : ## d_y_Ariel := Q(1155.8, 0.1)*_km : ## e_Ariel := Q(0.0012, 0.0001) : ## H_Ariel := Q(1.0, 0.1) : ## r_Ariel := Q(578.9, 0.6)*_km : alpha_Ariel := (1 + e_Ariel)*a_Ariel : pi_Ariel := (1 - e_Ariel)*a_Ariel : r_x_Ariel := d_x_Ariel/2 : r_y_Ariel := d_y_Ariel/2 : r_z_Ariel := 3*r_Ariel - r_x_Ariel - r_y_Ariel : r_e_Ariel := (r_x_Ariel + r_y_Ariel)/2 : r_p_Ariel := r_z_Ariel : Delta_Ariel := Delta_Uranus : mu_Ariel := mu_Uranus : theta_Ariel := theta_Uranus : m_Ariel := H_Ariel + mu_Ariel - 5*l100(q(theta_Ariel)) : rho_e_Ariel := arcsin(r_e_Ariel/Delta_Ariel) : rho_o_Ariel := arctan(a_Ariel/Delta_Ariel) : rho_p_Ariel := arcsin(r_p_Ariel/Delta_Ariel) : delta_p_Ariel := 2*rho_p_Ariel : Deltam_Ariel := m_Ariel - m_Uranus : Deltarho_Ariel := rho_o_Ariel - rho_e_Uranus - rho_e_Ariel : Deltarhostar_Ariel := Deltarho_Ariel/Deltam_Ariel : (* "m_Ariel" = Q(14.27566286366347679257073679618727, 0.10000000001139527653151332569451) ; "delta_p_Ariel[arcsec]" = Q(0.08289718844725035764207005820529, 0.00025849061923228592021946747355) ; "Deltarhostar_Ariel[arcsec]" = Q(1.44187758929507632324055750318897, 0.02486753029939671366677538643819) ; *) # https://en.wikipedia.org/wiki/Satellite_Ariel ## URANIAN SATELLITE UMBRIEL a_Umbriel := Q(265982., 1.)*_km : ## e_Umbriel := Q(0.0039, 0.0001) : ## H_Umbriel := Q(1.7, 0.1) : ## M_Umbriel := Q(1.2885, 0.0225)*E(21)*_kg : P_Umbriel := Q(4.1445, 0.0001)*_d : ## r_Umbriel := Q(584.7, 2.8)*_km : alpha_Umbriel := (1 + e_Umbriel)*a_Umbriel : f_Umbriel := 5*pi^2*r_Umbriel^3/(G*M_Umbriel*P_Umbriel^2) : pi_Umbriel := (1 - e_Umbriel)*a_Umbriel : r_e_Umbriel := 3*r_Umbriel/(3 - f_Umbriel) : r_p_Umbriel := (1 - f_Umbriel)*r_e_Umbriel : Delta_Umbriel := Delta_Uranus : mu_Umbriel := mu_Uranus : theta_Umbriel := theta_Uranus : m_Umbriel := H_Umbriel + mu_Umbriel - 5*l100(q(theta_Umbriel)) : rho_e_Umbriel := arcsin(r_e_Umbriel/Delta_Umbriel) : rho_o_Umbriel := arctan(a_Umbriel/Delta_Umbriel) : rho_p_Umbriel := arcsin(r_p_Umbriel/Delta_Umbriel) : delta_p_Umbriel := 2*rho_p_Umbriel : Deltam_Umbriel := m_Umbriel - m_Uranus : Deltarho_Umbriel := rho_o_Umbriel - rho_e_Uranus - rho_e_Umbriel : Deltarhostar_Umbriel := Deltarho_Umbriel/Deltam_Umbriel : (* "m_Umbriel" = Q(14.97566286366347679257073679618727, 0.10000000001139527653151332569451) ; "delta_p_Umbriel[arcsec]" = Q(0.08385160362351262155812196045128, 0.00040082861537367097403363882051) ; "Deltarhostar_Umbriel[arcsec]" = Q(1.93346204648142576237158757219608, 0.03072281560793002091014997642387) ; *) # https://en.wikipedia.org/wiki/Satellite_Umbriel ## URANIAN SATELLITE MIRANDA a_Miranda := Q(129858., 1.)*_km : ## d_y_Miranda := Q(468.4, 0.1)*_km : ## d_z_Miranda := Q(465.8, 0.1)*_km : ## z-diameter of Miranda e_Miranda := Q((0.0014 + 0.0013)/2, (0.0014 - 0.0013)/2) : H_Miranda := Q(3.5, 0.1) : ## r_Miranda := Q(235.8, 0.7)*_km : alpha_Miranda := (1 + e_Miranda)*a_Miranda : pi_Miranda := (1 - e_Miranda)*a_Miranda : r_y_Miranda := d_y_Miranda/2 : r_z_Miranda := d_z_Miranda/2 : r_p_Miranda := r_z_Miranda : r_x_Miranda := 3*r_Miranda - r_y_Miranda - r_z_Miranda : r_e_Miranda := (r_x_Miranda + r_y_Miranda)/2 : Delta_Miranda := Delta_Uranus : mu_Miranda := mu_Uranus : theta_Miranda := theta_Uranus : m_Miranda := H_Miranda + mu_Miranda - 5*l100(q(theta_Miranda)) : rho_e_Miranda := arcsin(r_e_Miranda/Delta_Miranda) : rho_o_Miranda := arctan(a_Miranda/Delta_Miranda) : rho_p_Miranda := arcsin(r_p_Miranda/Delta_Miranda) : delta_p_Miranda := 2*rho_p_Miranda : Deltam_Miranda := m_Miranda - m_Uranus : Deltarho_Miranda := rho_o_Miranda - rho_e_Uranus - rho_e_Miranda : Deltarhostar_Miranda := Deltarho_Miranda/Deltam_Miranda : (* "m_Miranda" = Q(16.77566286366347679257073679618727, 0.10000000001139527653151332569451) ; "delta_p_Miranda[arcsec]" = Q(0.03342003667883763108516358751826, 7.17477037941073331020509725822760E-6) ; "Deltarhostar_Miranda[arcsec]" = Q(0.69777400330276580057478943672589, 0.00922248767367460610015227166141) ; *) # https://en.wikipedia.org/wiki/Satellite_Miranda # OBJECTS FROM >20.1 AU TO <29.8 AU (TRANS-URANIAN/CIS-NEPTUNIAN OBJECTS) ## MINOR PLANET PHOLUS [20.3 AU] a_Pholus := Q(20.348, 0.001)*_AU : ## alpha_Pholus := Q(31.943, 0.001)*_AU : ## d_Pholus := Q(185., 16.)*_km : d_x_Pholus := Q(310., 10.)*_km : ## d_y_Pholus := Q(160., 10.)*_km : ## H_Pholus := Q(7.63, 0.01) : ## pi_Pholus := 2*a_Pholus - alpha_Pholus : r_Pholus := d_Pholus/2 : r_x_Pholus := d_x_Pholus/2 : r_y_Pholus := d_y_Pholus/2 : r_z_Pholus := 3*r_Pholus - r_x_Pholus - r_y_Pholus : r_e_Pholus := (r_x_Pholus + r_y_Pholus)/2 : r_p_Pholus := r_z_Pholus : Delta_Pholus := r(a_Pholus^2 + Delta_Sol^2) : mu_Pholus := 5*l(a_Pholus*Delta_Pholus/l_A^2) : rho_p_Pholus := arcsin(r_p_Pholus/Delta_Pholus) : theta_Pholus := arccos((a_Pholus^2 + Delta_Pholus^2 - Delta_Sol^2)/(2*a_Pholus*Delta_Pholus)) : delta_p_Pholus := 2*rho_p_Pholus : m_Pholus := H_Pholus + mu_Pholus - 5*l100(q(theta_Pholus)) : (* "m_Pholus" = Q(21.15936015268792160276830028168321, 0.01000226925457991631506268972216) ; "delta_p_Pholus[arcsec]" = Q(0.00575271866540404306422914488390, 0.00338665824758939500300617213396) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Pholus # OBJECTS FROM 29.8 AU TO 30.3 AU # https://en.wikipedia.org/wiki/Neptunian_System ## PLANET NEPTUNE [30.1 AU] a_Neptune := Q(30.07, 0.01)*_AU : ## alpha_Neptune := Q(30.33, 0.01)*_AU : ## H_Neptune := -Q(6.9, 0.1) : ## r_Neptune := Q(24622., 19.)*_km : r_e_Neptune := Q(24764., 15.)*_km : pi_Neptune := 2*a_Neptune - alpha_Neptune : r_p_Neptune := 3*r_Neptune - 2*r_e_Neptune : Delta_Neptune := r(a_Neptune^2 + Delta_Sol^2) : mu_Neptune := 5*l(a_Neptune*Delta_Neptune/l_A^2) : rho_e_Neptune := arcsin(r_e_Neptune/Delta_Neptune) : rho_p_Neptune := arcsin(r_p_Neptune/Delta_Neptune) : theta_Neptune := arccos((a_Neptune^2 + Delta_Neptune^2 - Delta_Sol^2)/(2*a_Neptune*Delta_Neptune)) : delta_p_Neptune := 2*rho_p_Neptune : m_Neptune := H_Neptune + mu_Neptune - 5*l100(q(theta_Neptune)) : (* "m_Neptune" = Q(8.32335819540866079443930463229461, 0.10001041194349504232218836697625) ; "delta_p_Neptune[arcsec]" = Q(2.23070004179583191287918377034256, 0.00595007368066530330064252850658) ; *) # https://en.wikipedia.org/wiki/Planet_Neptune ## NEPTUNIAN SATELLITE TRITON a_Triton := Q(354759., 1.)*_km : ## d_x_Triton := Q(2709., 1.)*_km : ## d_y_Triton := Q(2706., 1.)*_km : ## e_Triton := Q(0.000016, 0.000001) : ## H_Triton := -Q(1.2, 0.1) : ## r_Triton := Q(1353.4, 0.9)*_km : alpha_Triton := (1 + e_Triton)*a_Triton : pi_Triton := (1 - e_Triton)*a_Triton : r_x_Triton := d_x_Triton/2 : r_y_Triton := d_y_Triton/2 : r_z_Triton := 3*r_Triton - r_x_Triton - r_y_Triton : r_e_Triton := (r_x_Triton + r_y_Triton)/2 : r_p_Triton := r_z_Triton : Delta_Triton := Delta_Neptune : mu_Triton := mu_Neptune : theta_Triton := theta_Neptune : m_Triton := H_Triton + mu_Triton - 5*l100(q(theta_Triton)) : rho_e_Triton := arcsin(r_e_Triton/Delta_Triton) : rho_o_Triton := arctan(a_Triton/Delta_Triton) : rho_p_Triton := arcsin(r_p_Triton/Delta_Triton) : delta_p_Triton := 2*rho_p_Triton : Deltam_Triton := m_Triton - m_Neptune : Deltarho_Triton := rho_o_Triton - rho_e_Neptune - rho_e_Triton : Deltarhostar_Triton := Deltarho_Triton/Deltam_Triton : (* "m_Triton" = Q(14.02335819540866079443930463229461, 0.10001041194349504232218836697625) ; "delta_p_Triton[arcsec]" = Q(0.12398175472604824986546141934599, 0.00025910859058973356838690285556) ; "Deltarhostar_Triton[arcsec]" = Q(2.64224758794707039093312962142783, 0.06556216913840682144931556866260) ; *) # https://en.wikipedia.org/wiki/Satellite_Triton ## NEPTUNIAN SATELLITE NEREID a_Nereid := Q(5513900., 100.)*_km : ## d_Nereid := Q(357., 13.)*_km : e_Nereid := Q(0.749, 0.001) : ## H_Nereid := Q(4.4, 0.1) : ## M_Nereid := Q(3.57E19, 0.01E19)*_kg : P_Nereid := Q((360.14 + 360.13)/2, (360.14 - 360.13)/2)*_d : alpha_Nereid := (1 + e_Nereid)*a_Nereid : pi_Nereid := (1 - e_Nereid)*a_Nereid : r_Nereid := d_Nereid/2 : f_Nereid := 5*pi^2*r_Nereid^3/(G*M_Nereid*P_Nereid^2) : r_e_Nereid := 3*r_Nereid/(3 - f_Nereid) : r_p_Nereid := (1 - f_Nereid)*r_e_Nereid : Delta_Nereid := Delta_Neptune : mu_Nereid := mu_Neptune : theta_Nereid := theta_Neptune : m_Nereid := H_Nereid + mu_Nereid - 5*l100(q(theta_Nereid)) : rho_e_Nereid := arcsin(r_e_Nereid/Delta_Nereid) : rho_o_Nereid := arctan(a_Nereid/Delta_Nereid) : rho_p_Nereid := arcsin(r_p_Nereid/Delta_Nereid) : delta_p_Nereid := 2*rho_p_Nereid : Deltam_Nereid := m_Nereid - m_Neptune : Deltarho_Nereid := rho_o_Nereid - rho_e_Neptune - rho_e_Nereid : Deltarhostar_Nereid := Deltarho_Nereid/Deltam_Nereid : (* "m_Nereid" = Q(19.62335819540866079443930463229461, 0.10001041194349504232218836697625) ; "delta_p_Nereid[arcsec]" = Q(0.01636042095337454513290444626848, 0.00059578226948070773972540966497) ; "Deltarhostar_Nereid[arcsec]" = Q(22.26063247070067367001643598741367, 0.27869389714240077426127758467827) ; *) # https://en.wikipedia.org/wiki/Satellite_Nereid ## NEPTUNIAN SATELLITE PROTEUS a_Proteus := Q(117647., 1.)*_km : alpha_Proteus := Q(117709., 10.)*_km : d_x_Proteus := Q(424., 1.)*_km : ## d_y_Proteus := Q(396., 1.)*_km : ## H_Proteus := Q(5.0, 0.1) : ## r_Proteus := Q(210., 7.)*_km : pi_Proteus := 2*a_Proteus - alpha_Proteus : r_x_Proteus := d_x_Proteus/2 : r_y_Proteus := d_y_Proteus/2 : r_z_Proteus := 3*r_Proteus - r_x_Proteus - r_y_Proteus : r_e_Proteus := (r_x_Proteus + r_y_Proteus)/2 : r_p_Proteus := r_z_Proteus : Delta_Proteus := Delta_Neptune : mu_Proteus := mu_Neptune : theta_Proteus := theta_Neptune : m_Proteus := H_Proteus + mu_Proteus - 5*l100(q(theta_Proteus)) : rho_e_Proteus := arcsin(r_e_Proteus/Delta_Proteus) : rho_o_Proteus := arctan(a_Proteus/Delta_Proteus) : rho_p_Proteus := arcsin(r_p_Proteus/Delta_Proteus) : delta_p_Proteus := 2*rho_p_Proteus : Deltam_Proteus := m_Proteus - m_Neptune : Deltarho_Proteus := rho_o_Proteus - rho_e_Neptune - rho_e_Proteus : Deltarhostar_Proteus := Deltarho_Proteus/Deltam_Proteus : (* "m_Proteus" = Q(20.22335819540866079443930463229461, 0.10001041194349504232218836697625) ; "delta_p_Proteus[arcsec]" = Q(0.02016410589172042227904459420760, 0.00192585803327830222805574412664) ; "Deltarhostar_Proteus[arcsec]" = Q(0.35690775502102472063479388866598, 0.00424359629468321231014849950464) ; *) # https://en.wikipedia.org/wiki/Satellite_Proteus # OBJECTS FROM >30.3 AU (TRANS-NEPTUNIAN OBJECTS) ## MINOR PLANET PLUTO [39.5 AU] a_Pluto := Q(5.90638, 0.00001)*E(9)*_km : ## alpha_Pluto := Q(7.37593, 0.00001)*E(9)*_km : ## H_Pluto := -Q(0.44, 0.01) : ## M_Pluto := Q(1.3025, 0.0006)*E(22)*_kg : P_Pluto := Q(6.387230, 0.000001)*_d : ## r_Pluto := Q(1188.3, 0.8)*_km : f_Pluto := 5*pi^2*r_Pluto^3/(G*M_Pluto*P_Pluto^2) : pi_Pluto := 2*a_Pluto - alpha_Pluto : r_e_Pluto := 3*r_Pluto/(3 - f_Pluto) : r_p_Pluto := (1 - f_Pluto)*r_e_Pluto : Delta_Pluto := r(a_Pluto^2 + Delta_Sol^2) : mu_Pluto := 5*l(a_Pluto*Delta_Pluto/l_A^2) : rho_p_Pluto := arcsin(r_p_Pluto/Delta_Pluto) : theta_Pluto := arccos((a_Pluto^2 + Delta_Pluto^2 - Delta_Sol^2)/(2*a_Pluto*Delta_Pluto)) : delta_p_Pluto := 2*rho_p_Pluto : m_Pluto := H_Pluto + mu_Pluto - 5*l100(q(theta_Pluto)) : (* "m_Pluto" = Q(15.96523035982724833818197589273473, 0.01000000270071783722829301418027) ; "delta_p_Pluto[arcsec]" = Q(0.08295260356666259287356833204972, 0.00005581146599902704944176035375) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Pluto ## MINOR PLANET ERIS [67.9 AU] a_Eris := Q(10.152, 0.001)*_Tm : ## alpha_Eris := Q(14.579E9, 0.001E9)*_km : ## H_Eris := -Q(1.21, 0.01) : ## M_Eris := Q(1.638, 0.014)*E(22)*_kg : P_Eris := Q(15.786, 0.001)*_d : ## r_Eris := Q(1163., 6.)*_km : f_Eris := 5*pi^2*r_Eris^3/(G*M_Eris*P_Eris^2) : pi_Eris := 2*a_Eris - alpha_Eris : r_e_Eris := 3*r_Eris/(3 - f_Eris) : r_p_Eris := (1 - f_Eris)*r_e_Eris : Delta_Eris := r(a_Eris^2 + Delta_Sol^2) : mu_Eris := 5*l(a_Eris*Delta_Eris/l_A^2) : rho_p_Eris := arcsin(r_p_Eris/Delta_Eris) : theta_Eris := arccos((a_Eris^2 + Delta_Eris^2 - Delta_Sol^2)/(2*a_Eris*Delta_Eris)) : delta_p_Eris := 2*rho_p_Eris : m_Eris := H_Eris + mu_Eris - 5*l100(q(theta_Eris)) : (* "m_Eris" = Q(17.54684332321039258790087965412368, 0.01000914314713612705855749401914) ; "delta_p_Eris[arcsec]" = Q(0.04725252709531487675124121718957, 0.00024380496348191360095251800384) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Eris ## MINOR PLANET ORCUS [39.2 AU] a_Orcus := Q(5.8603, 0.0001)*_Tm : ## alpha_Orcus := Q(7.1907, 0.0001)*_Tm : ## d_Orcus := Q(917., 25.)*_km : # arithmetic mean diameter of Orcus H_Orcus := Q(2.31, 0.03) : M_Orcus := Q(0.548, 0.010)*E(21)*_kg : P_Orcus := Q(10.5, 0.1)*_h : ## pi_Orcus := 2*a_Orcus - alpha_Orcus : r_Orcus := d_Orcus/2 : f_Orcus := 5*pi^2*r_Orcus^3/(G*M_Orcus*P_Orcus^2) : r_e_Orcus := 3*r_Orcus/(3 - f_Orcus) : r_p_Orcus := (1 - f_Orcus)*r_e_Orcus : Delta_Orcus := r(a_Orcus^2 + Delta_Sol^2) : mu_Orcus := 5*l(a_Orcus*Delta_Orcus/l_A^2) : rho_p_Orcus := arcsin(r_p_Orcus/Delta_Orcus) : theta_Orcus := arccos((a_Orcus^2 + Delta_Orcus^2 - Delta_Sol^2)/(2*a_Orcus*Delta_Orcus)) : delta_p_Orcus := 2*rho_p_Orcus : m_Orcus := H_Orcus + mu_Orcus - 5*l100(q(theta_Orcus)) : (* "m_Orcus" = Q(18.68123143958017337049346180397264, 0.03000009144371494305346002455886) ; "delta_p_Orcus[arcsec]" = Q(0.03024609597828289304605407087650, 0.00065659632012301018474429997108) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_Orcus ## MINOR PLANET 78799 [37.4 AU] a_MP78799 := Q(37.360, 0.001)*_AU : ## alpha_MP78799 := Q(46.812, 0.001)*_AU : ## d_MP78799 := Q(565., 73.)*_km : H_MP78799 := Q(5.5, 0.1) : ## pi_MP78799 := 2*a_MP78799 - alpha_MP78799 : r_MP78799 := d_MP78799/2 : r_e_MP78799 := r_MP78799 : r_p_MP78799 := r_MP78799 : Delta_MP78799 := r(a_MP78799^2 + Delta_Sol^2) : mu_MP78799 := 5*l(a_MP78799*Delta_MP78799/l_A^2) : rho_p_MP78799 := arcsin(r_p_MP78799/Delta_MP78799) : theta_MP78799 := arccos((a_MP78799^2 + Delta_MP78799^2 - Delta_Sol^2)/(2*a_MP78799*Delta_MP78799)) : delta_p_MP78799 := 2*rho_p_MP78799 : m_MP78799 := H_MP78799 + mu_MP78799 - 5*l100(q(theta_MP78799)) : (* "m_MP78799" = Q(21.66546091511067362563014692859337, 0.10000006749313359602878018472652) ; "delta_p_MP78799[arcsec]" = Q(0.02084422703000682259866092904451, 0.00269314797486060155406653455300) ; *) # https://en.wikipedia.org/wiki/Minor_Planet_78799 # DEFINITIONS (* ASSIGNMENT DEFINITIONS a_ = orbital semimajor axis (mean orbital radius) of alpha_ = orbital apoapsis or maximum orbital radius of alpha_max_ = maximum orbital apoapsis (maximum orbital radius) of alpha_min_ = minimum orbital apoapsis of A_ = geometric albedo/reflectance of B_ = Bond bolometric albedo/reflectance of d_ = arithmetic mean diameter of d_e_ = (spheroid) equatorial diameter of d_p_ = (spheroid) polar diameter of d_x_ = x-diameter of d_y_ = y-diameter of d_z_ = z-diameter of delta_ = typical-distance mean angular diameter of delta_e_ = typical-distance equatorial angular diameter of delta_o_ = typical-distance orbital angular diameter of delta_p_ = typical-distance polar angular diameter of Delta_ = typical distance from Terra to Deltam_ = typical-distance apparent brightness magnitude difference between orbitee and orbiter Deltarho_ = typical-distance angular separation between orbitee and orbiter Deltarhostar_ = typical-distance apparent angular separation between orbitee and orbiter E_ = typical-distance illuminance from f_ = (spheroidal) flattening/oblateness of h_ = geodetic elevation of H_ = absolute brightness magnitude of l_ = length of lambda_ = geodetic longitude of L_ = mean luminous flux (luminosity) m = typical-distance apparent brightness magnitude of mu_ = typical astronomical distance modulus to M_ = mass of M_G_ = gravitational mass parameter of phi_ = geodetic latitude of pi_ = orbital periapsis or minimum orbital radius of pi_max_ = maximum orbital periapsis of pi_min_ = minimum orbital periapsis (minimum orbital radius) of P_ = sidereal equatorial rotation period of r_ = radius or arithmetic mean radius of r_e_ = (spheroid) equatorial radius of r_max_ = maximum radius of r_min_ = minimum radius of r_p_ = (spheroid) polar radius of r_x_ = x-radius of r_y_ = y-radius of r_z_ = z-radius of rho_ = typical-distance mean angular radius of rho_e_ = typical-distance equatorial angular radius of rho_m_ = mass density of rho_o_ = typical-distance orbital angular radius of rho_p_ = typical-distance polar angular radius of S_ = surface area of t_ = time of theta_ = phase angle of V_ = volume of E_I = international illuminance (lux) G = Newton/Cavendish gravitational constant l_A = astronomical length (for astronomical distance modulus) l_p = dekaparsec length (for astronomical distance modulus) m_E = illuminance to apparent brightness magnitude constant pi = Archimedean pi constant rho_m_CGS = centimeter-gram-second mass density (gram per cubic centimeter) theta_rev = circle/revolution/turn/cycle theta_rev2 = semicircle/half-revolution/half-turn/half-cycle FUNCTION DEFINITIONS E = decimal (base-ten) exponential/antilogarithm l = decimal (base-ten) logarithm l100 = centesimal (base-hundred) logarithm m = apparent brightness magnitude for illuminance q = phase integral r = square root S_circle = circular (planar) area S_ellipse = elliptical (planar) area S_ellipsoid = ellipsoidal surface area S_sphere = spherical surface area S_spheroid = spheroidal surface area UNIT DEFINITIONS _AU = astronomical unit of length _cm = centimeter of length _cm2 = square centimeter of area _cm3 = cubic centimeter of volume _d = day of time _deg = (arc)degree of (planar) angle _Dpc = dekaparsec of length _g = gram of mass _Gm = gigameter of length _h = hour of time _kg = kilogram of mass _km = kilometer of length _lm = lumen of luminous flux _lx = lux of illuminance _m = meter of length _m2 = square meter of area _m3 = cubic meter of volume _min = minute of time _Mm = megameter of length _pc = parsec of length _rev = revolution/turn/cycle of (planar) angle _rev2 = half-revolution/half-turn/half-cycle of (planar) angle _s = second of time _Tm = terameter of length *)