$LastChangedDate: 27-Juil-2011 $

# CL_man_hohmann

Delta V for a Hohmann transfer

## Calling Sequence

       [delta_v,dv1,dv2,anv1,anv2] = CL_man_hohmann(ai,af [,mu])

## Description

- Computes the maneuvers of a Hohmann transfer from an initial circular orbit with semi major axis ai to a final circular orbit with semi major axis af.

  The output argument delta_v is the sum of the norms of the velocity increments required (|dv1| + |dv2|).

  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)

mu :

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

delta_v :

  Total delta-v required = |dv1| + |dv2|. [m/s] (1xN)

dv1:

  First velocity increment, in spherical coordinates in the QSW frame [lambda;phi;|dv|] [rad,rad,m/s]. (3xN)

dv2:

  Second velocity increment, in spherical coordinates in the QSW frame [lambda;phi;|dv|]. [rad,rad,m/s] (3xN)

anv1:

  True anomaly at the location of the first velocity increment (in the initial orbit): as the initial orbit is circular, anv1 is set to 0 arbitrarily. (1xN)

anv2:

  True anomaly at the location of the second velocity increment (in the intermediate orbit): %pi if ai < af, 0 otherwise. [rad] (1xN)

## Authors

- CNES - DCT/SB

## See also

- CL_man_biElliptic

## Examples

    // 7200km to 7000km :
    ai = 7200.e3;
    af = 7000.e3;
    [delta_v,dv1,dv2,anv1,anv2] = CL_man_hohmann(ai,af);
    // 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)