$LastChangedDate: 27-Juil-2011 $

# CL_man_biElliptic

Delta V for a bi-elliptic transfer

## Calling Sequence

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

## Description

- Computes the maneuvers of a bi-elliptical transfer from a circular orbit with semi-major axis ai to a circular orbit with semi-major axis af.

  The apogee radius of the elliptical transfer orbit is rt.

  delta-v is the sum of the norms of the velocity increments.

  Velocity increments are expressed in spherical coordinates in the QSW frame: [lambda; phi; dv], where lambda is the in-plane angle (+%pi: towards planet and +%pi/2: ~along velocity), phi is the out-of-plane angle, positive towards the angular momentum vector (the angular momentum vector is perpendicular to the orbit plane and oriented according to right hand rule), dv is the norm of the velocity increment.

## Parameters

ai :

  Semi-major axis of initial circular orbit [m] (1xN)

af :

  Semi-major axis of final circular orbit [m] (1xN)

rt :

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

mu :

  (optional) Gravitational constant [m^3/s^2] (default value is %CL_mu)

delta_v :

  Total |delta-V| (=|dv1|+|dv2|+|dv3]) [m/s] (1xN)

dv1:

  First delta-V, in spherical coordinates in the QSW frame [lambda;phi;dv] [rad,rad,m/s] (3xN)

dv2:

  Second delta-V, in spherical coordinates in the QSW frame [lambda;phi;dv] [rad,rad,m/s] (3xN)

dv3:

  Third delta-V, in spherical coordinates in the QSW frame [lambda;phi;dv] [rad,rad,m/s] (3xN)

anv1:

  True anomaly at the position of the 1st maneuver : initial orbit is circular so this is an arbitrary value of 0 (1xN)

anv2:

  True anomaly at the position of the 2nd maneuver (either 0 or %pi) [rad] (1xN)

anv3:

  True anomaly at the position of the 3rd maneuver (either 0 or %pi) [rad] (1xN)

## Authors

- CNES - DCT/SB

## Bibliography

- 1) 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 through 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 a Hohmann transfer:
    // more expensive !
    [delta_v,dv1,dv2,anv1,anv2] = CL_man_hohmann(ai,af)