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Alpha Centauri Specs Tiffany J Finley 12-10-2003 ASEN 5050, Final Project
alphacentauri_ly = 4.35; % 4.35 light years away au = 149597870; % 1AU = 149,597,870 km c_light = 2.99792458e8; % speed of light = 3e8 m/s lightyear = 9.4605284e15; % 1 light year = 9.5e15 m ac_m = alphacentauri_ly * lightyear; % gives ac distance in meters ac_au = (ac_m/1000)/au; ly_au = (.1*c_light/1000)/au * (3600*24*365); % = 6320 AU/year if traveling at .1c vel_kms = .1*c_light / 1000 % vel in km/s mS = 1.9891e30; % kg mew_Sun = 1.32712428e11; % km3/solar s2 r_Sun = 696000; % km, radius of the Sun rA = r_Sun * 1.23; rB = r_Sun * 0.865; mA = mS * 1.144; mB = mS * .907; ecc = .519; P = 79.9; % years a_closest = 11.2; % AU, radii a_mean = 23.7; a_furthest = 35.6; mtot = mA + mB; Grav = 6.673e-20; % km3/kg.s2 mew_bin = Grav*mtot; % allows for orbit with diameter greater than max separation distance between binary stars % max sep = 35.6, so this orbit is .2 AU beyond r = 35.8*au; v_escape_bin = sqrt(2*mew_bin/r) v_circle_outer = sqrt(mew_bin/r); % Delta V to insert into orbit around binary star total_init_dv = vel_kms - v_circle_outer; T_outer_circle = 2*pi*sqrt(r^3/mew_bin)/(3600*24*365) %%% Next do Hohmann Transfer/Patched Conic into Alpha Centauri A, circular orbits %%%
r_chz = 2*au; % target radius inside continually habitable zone of A ri1 = r; rf1 = a_closest*au + r_chz; % final circ orbit around binary cm atrans1 = (ri1 + rf1)/2 T_trans1 = pi*sqrt(atrans1^3/mew_bin) % half period of transfer ellipse ecc_trans1 = 1 - rf1/atrans1 % eccentricity of transfer orbit vtrans1a = sqrt((2*mew_bin/ri1) - mew_bin/atrans1) vfinal1 = sqrt(mew_bin/rf1); % this would be ending circular orbit around center of mass dv_trans1 = v_circle_outer vtrans1a - %%% But now the s/c needs to be captured into Alpha A orbit from cmcentric system %%% % find speed of Alpha A at perihelion a_alphaA = rf1/(1-ecc) v_alpha_per = sqrt(2*mew_bin/rf1 - mew_bin/a_alphaA) % km/s r_peri_A = rA + r_chz; % radius of orbit around A, instead of around binary cm % v_plus = velocity relative to cm at apoapse of Hohmann transfer v_plus = vtrans1a; v_minus = ri1/(a_closest*au)*v_plus v_inf_alphaA = v_minus - v_alpha_per % eccentricity of transfer past alpha A (if it isnt captured) ecc_trans2 = 1 + (r_peri_A*v_inf_alphaA^2)/(Grav*mA) %del = Grav*mA/v_inf_alphaA^2 * sqrt(ecc_trans2^2 - 1) d_delta2 = 2*asin(1/ecc_trans2); v_theta_plus2 = v_alpha_per - v_inf_alphaA*cos(pi - d_delta2) v_r_plus2 = v_inf_alphaA*sin(pi - d_delta2) Beta = atan(v_r_plus2/v_theta_plus2) Beta_deg = rad2deg(Beta) % new spacecraft velocity v_plus2_helio_cm = sqrt(v_theta_plus2^2 + v_r_plus2^2) % Now find dV for capture into Alpha Centauri orbit v_sc_alpha_per = sqrt(Grav*mA/r_peri_A) dv_trans2 = v_sc_alpha_per - v_plus2_helio_cm...