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Hohmann vs Bi-elliptic transfer

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% In this example we compare be-elliptic and Hohmann transfer.
% The total speed change that required for spacecraft transfer from
% geocentric circular orbit with radius Ri to a higher altitude Rf
clc;
clear all;
Rf  =  125000;   % [km] Final circular orbit
Ri  =  7200;     % [km] Initial circular orbit
Rb  =  190000;   % [km] Apogee of the transfer ellipse
mu  =  398600;   % [km^3/s^2] Earth’s gravitational parameter

% For initial circular orbit
Vc = (mu/Ri)^0.5;
a   = Rf/Ri;
b   = Rb/Ri;

Hohmann transfer

For Hohmann transfer total speed change

dV_H =Vc*(1/(a)^0.5 -(2/(a*(a+1)))^0.5*(1-a) - 1);
% Semimajor axes of the Hohmann transfer ellipse
a_h = (Rf + Ri)/2;
% Time required for Hohmann transfer
t_H = pi/(mu)^0.5*(a_h^1.5);     %[s]
fprintf('Total speed change = %4.4f [km/s]\n',dV_H);
fprintf('Time required for transfer = %4.2f [hours]\n\n',t_H/3600);
Total speed change = 3.9878 [km/s]
Time required for transfer = 23.49 [hours]

Bi-elliptic transfer

For Bi-elliptic transfer total speed change

dV_BE = Vc*((2*(a+b)/(a*b))^0.5 - (1+1/a^0.5) - ((2/(b +b^2))^0.5*(1-b)));
% Semimajor axes of the first transfer ellipse
a1 = (Ri + Rb)/2;
% Semimajor axes of the second transfer ellipse
a2 = (Rf + Rb)/2;
t_BE = pi/(mu)^0.5*(a1^1.5+a2^1.5);     %[s]
fprintf('Total speed change = %4.4f [km/s]\n',dV_BE);
fprintf('Time required for transfer = %4.2f [hours]\n',t_BE/3600);
Total speed change = 3.9626 [km/s]
Time required for transfer = 129.19 [hours]

 

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