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# Tag Archives: Hohmann vs Bi-elliptic transfer

## Hohmann vs Bi-elliptic transfer

Contents

% 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]