$LastChangedDate: 27-Juil-2011 $

# CL_ex_eckHech

Eckstein Hechler orbit propagation analytical model

## Calling Sequence

       [mean_cir_t2,osc_cir_t2] = CL_ex_eckHech(t1,mean_cir_t1,t2 [,er,mu,zonals])

## Description

- Computes the mean orbital elements mean_cir_t2 and the osculating orbital elements osc_cir_t2 at time t2 given the mean orbital elements mean_cir_t1 at time t1.

  Zonals coefficients up to J6 are taken into account.

- The function works in the following cases:

  - 1 initial time and 1 set of initial orbital elements, and N final times.

  - N (or 1) initial times and N sets of initial orbital elements, and N (or 1) final times.

- The orbital elements are the following:

- Warnings :

  - This function does not work for inclinations close to the critical inclinations (63.43494882 deg and 116.5650512 deg)

  - This function nominally works for eccentricities smaller than 5.e-3

  - This function works but with a lesser accuracy for eccentricities between 5.e-3 and 0.1

  - This function does not work for eccentricities greater than 0.1

## Parameters

t1:

  Initial time [days] (1xN or 1x1)

mean_cir_t1:

  Circular adapted mean orbital elements at time t1 [sma;ex;ey;inc;raan;pom+anm] (6xN or 6x1).

t2:

  Final time [days] (1xN or 1x1).

er:

  (optional) Equatorial radius [m] (default is %CL_eqRad)

mu:

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

zonals:

  (optional) Vector of zonal coefficients J1 to Jn (troncated to J6) to be used (default is %CL_j1jn(1:6)) (Nz x 1)

mean_cir_t2:

  Circular adapted mean orbital elements at t2 [sma;ex;ey;inc;raan;pom+anm] (6xN)

osc_cir_t2:

  Circular adapted osculating orbital elements at t2 [sma;ex;ey;inc;raan;pom+anm] (6xN)

## Authors

- CNES - DCT/SB

## Bibliography

- 1) CNES - MSLIB FORTRAN 90, Volume E (me_eck_hech)

## See also

- CL_ex_lyddane

- CL_ex_meanEckHech

## Examples

    // Example 1 : 1 orbit propagated to several times:
    t1 = 12584
    mean_cir_t1 = [42166712;2.9e-3;1.2e-3;CL_deg2rad([97.2;125;5])]
    t2 = 12587:0.2:12588;
    [mean_cir_t2,osc_cir_t2] = CL_ex_eckHech(t1,mean_cir_t1,t2)

    // Example 2 : several orbits propagated to one final time:
    t1 = 12584
    mean_cir_t1 = [42166712;2.9e-3;1.2e-3;CL_deg2rad([97.2;125;5])]
    mean_cir_t1 = [mean_cir_t1,mean_cir_t1*0.95]
    t2 = 12587;
    [mean_cir_t2,osc_cir_t2] = CL_ex_eckHech(t1,mean_cir_t1,t2)