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# Tag Archives: Geocentric circular orbit

## Bi-Elliptic Hohmann Transfer

In this example we calculate the total change in speed required for a bi-elliptic Hohmann transfer from a geocentric circular orbit of 7200 km radius to circular orbit of 125000 km radius. The apogee of the first transfer ellipse is 190000 km.

clc; clear all; R_i = 7200; % [km] R1_a = 190000; % [km] R_f = 125000; % [km] mu = 398600; % [km^3/s^2] Earth’s gravitational parameter % For initial circular orbit V_i = (mu/R_i)^0.5; % Speed at apogee and perigee for the first transfer ellipse V1_a = (2*mu*R_i/(R1_a*(R1_a+R_i)))^0.5; V1_p = (2*mu*R1_a/(R_i*(R1_a+R_i)))^0.5; % Semimajor axes of the first transfer ellipse a1 = (R_i + R1_a)/2; % Speed at apogee and perigee for the second transfer ellipse V2_a = (2*mu*R_f/(R1_a*(R1_a+R_f)))^0.5; V2_p = (2*mu*R1_a/(R_f*(R1_a + R_f)))^0.5; % Semimajor axes of the second transfer ellipse a2 = (R_f + R1_a)/2; % For target circular orbit V_f = (mu/R_f)^0.5; % For bi-elliptic maneuver the total speed change required dV = abs(V_i - V1_p)+ abs(V1_a - V2_a) + abs(V_f - V2_p); %[km/s] % Time required for transfer t_bi = pi/(mu)^0.5*(a1^1.5+a2^1.5); %[s] fprintf('Total speed change = %4.4f [km/s]\n',dV); fprintf('Time required for transfer = %4.2f [hours]\n',t_bi/3600);

Total speed change = 3.9626 [km/s] Time required for transfer = 129.19 [hours]