$LastChangedDate: 27-Juil-2011 $

# CL_ex_secularJ2

Secular J2 orbit propagation

## Calling Sequence

       [kep_t2] = CL_ex_secularJ2(t1,kep_t1,t2 [,er,mu,j2])

## Description

- Propagation of Keplerian orbital elements kep_t1 to the time t2 including the secular J2 effects only.

  The secular effects of J2 consist in drifts on periapsis argument, right ascension of ascending node and mean anomaly.

  See CL_op_driftJ2 for more details.

  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:

## Parameters

t1:

  Initial time [days] (1xP)

kep_t1:

  Keplerian orbital elements [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).

kep_t2:

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

er:

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

mu:

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

j2:

  (optional) (Unnormalized) zonal coefficient (second zonal harmonic) (default is %CL_j2)

## Authors

- CNES - DCT/SB

## See also

- CL_ex_kepler

- CL_ex_lyddane

- CL_ex_eckHech

- CL_op_driftJ2

## Examples

    // propagation of one satellite to several times:
    dga = 7070 * 1000;
    ecc = 0.001;
    inc = CL_deg2rad(98);
    pom = CL_deg2rad(90);
    gom = 0;
    anm = 0;
    t1 = 21915;
    t2 = t1:0.1:t1+1;
    kep_t1=[dga;ecc;inc;pom;gom;anm];
    [kep_t2] = CL_ex_secularJ2(t1, kep_t1, t2);

    // propagation of 2 element sets to one final time:
    t2 = t1+1;
    t1=[t1,t1+0.5];
    kep_t1=[kep_t1,[dga+100*1000;ecc+0.1;inc;pom;gom;anm]];
    [kep_t2] = CL_ex_secularJ2(t1, kep_t1, t2);