Name

CL_man_biElliptic — Total delta V for a bi-elliptic Hohmann transfer

Calling Sequence

   [delta_v,dv1,dv2,dv3,anv1,anv2,anv3]=CL_man_biElliptic(ai,af,rt,[mu])
   
   

Description

  • This function computes the total delta-v requirement for a bi-elliptical Hohmann transfer from a geocentric circular orbit of radius ai to one of radius af. The apogee of the elliptic orbit being rt.

    Output delta-v is the sum of delta-v required to change from orbit 1 to 2, 3 and 4 consecutively. Delta-v impulsions are performed at points A, B and C.

    Impulsions are given in spheric coordinates in the QSW frame : first parameter lambda is the in plane component (pi ~= towards planet and pi/2 = along velocity) second parameter phi is the out of plane component, positive towards the kinetic moment, third parameter is the norm

  • Last update : 09/09/2007

Parameters

ai :

radius of initial circular orbit [m] (1xN)

af :

radius of final circular orbit [m] (1xN)

rt :

radius at position of second maneuver [m] (1xN)

mu :

(optionnal) geocentric gravitational constant [m^3/s^2] (default value is %CL_mu)

delta_v :

total delta-v requirement [m/s] (1xN)

dv1:

delta_v at first maneuver, given in spheric coordinates in QSW frame [lambda;phi;dv] [rad,rad,m/s] (3xN)

dv2:

delta_v at second maneuver, given in spheric coordinates in QSW frame [lambda;phi;dv] [rad,rad,m/s] (3xN)

dv3:

delta_v at third maneuver, given in spheric coordinates in QSW frame [lambda;phi;dv] [rad,rad,m/s] (3xN)

anv1:

true anomaly at first maneuver : initial orbit is circular so this is an arbitrary value of 0 (1xN)

anv2:

true anomaly at second maneuver (either 0 or %pi) [rad] (1xN)

anv3:

true anomaly at third maneuver (either 0 or %pi) [rad] (1xN)

Authors

CNES - DCT/SB

Bibliography

Orbital Mechanics for engineering students, H D Curtis, Chapter 6 (equation 6.4a)

See also

CL_man_hohmann, CL_man_hohmannG

Examples

// 7000 km to 98 000km trough a 280 000 transfer orbit :
ai = 7000.e3;
af = 98000.e3;
rt = 280000.e3;
[delta_v,dv1,dv2,dv3,anv1,anv2,anv3]=CL_man_biElliptic(ai,af,rt)
// Check results :
kep = [ai ; 0 ; %pi/2 ; 0 ; 0 ; anv1];
kep1 = CL_man_applyDv(kep,dv1);
kep1(6) = anv2;
kep2 = CL_man_applyDv(kep1,dv2);
kep2(6) = anv3;
kep3 = CL_man_applyDv(kep2,dv3)

// Same example with Hohmann transfer :
[delta_v,dv1,dv2,anv1,anv2] = CL_man_hohmann(ai,af) // more expensive !