$LastChangedDate: 27-Juil-2011 $

# CL_ex_kepler

Keplerian orbit propagation

## Calling Sequence

       [kep_t2]=CL_ex_kepler(t1,kep_t1,t2 [,mu])

## Description

- Computes the orbital elements kep_t2 at time t2 given the orbital elements kep_t1 at time t1, using a Keplerian model.

  As the model is Keplerian, only the mean anomaly varies.

  There can either be several sets of orbital elements and one final time or one set of orbital elements and multiple final times.

- The orbital elements are the following:

- Notes:

  - This function works for any type of orbit.

## Parameters

t1:

  Initial time [days] (1xP)

kep_t1:

  Keplerian elements at time t1 [sma;ecc;inc;pom;raan;anm] (6xP). P can be > 1 if there is only one final time (i.e. if N==1).

t2:

  Final time [days] (1xN). N can be > 1 if there is only one set of orbital elements (i.e. if P==1).

mu :

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

kep_t2:

  Keplerian elements [sma;ecc;inc;pom;raan;anm] at time t2. (6 x max(P,N))

## Authors

- CNES - DCT/SB

## Bibliography

- 1) Mecanique spatiale, CNES - Cepadues 1995, Tome I

## See also

- CL_ex_secularJ2

- CL_ex_lyddane

- CL_ex_eckHech

- CL_oe_kep2car

- CL_kp_M2v

## Examples

    // Example 1 :
    t1 = 21482.125 // initial time (days, origin = 1950.0)
    kep_t1 = [ 24464560; 0.7311; 0.122138; 3.10686; 1.00681; 0.048363 ]
    T = CL_kp_params('per', kep_t1(1,:)) // orbital period in seconds
    t2 = t1 + (0:1/4:1)*T/86400 // final times (days, origin = 1950.0)
    kep_t2 = CL_ex_kepler(t1, kep_t1, t2)

    // Example 2 :
    t1 = 0.  // initial time (arbitrary origin)
    kep_t1 = [ 7.e6, 0.,  %pi/2,  0., %pi, 0.; ..
    8.e6, 0.1, %pi/2,  0., %pi, 0.  ]'
    t2 = 1. // final time : 1 day later
    kep_t2 = CL_ex_kepler(t1, kep_t1, t2)