CL_man_biElliptic

Description

• This function is deprecated.

  Replacement function: CL_man_dvBiElliptic

• 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" local orbital frame.

  

Parameters

ai :

Semi-major axis of initial circular orbit [m] (1xN or 1x1)

af :

Semi-major axis of final circular orbit [m] (1xN or 1x1)

rt :

Radius at the position of the second maneuver [m] (1xN or 1x1)

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

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)