$LastChangedDate: 27-Juil-2011 $

# CL_op_repeat2smaInc

Semi major axis and inclination corresponding to (N,P,Q)

## Calling Sequence

       [sma,inc] = CL_op_repeat2smaInc(N,P,Q,ecc,sso,[incInput],[er,mu,j2,rotr_pla,rotr_pla_sun])

## Description

- Computes the semi major axis (and inclination for sunsynchronous orbits) of repeat (also called phased) orbits with given repeat parameters N,P,Q.

  The 3 integers N,P,Q are such that:

  Tc (duration of repeat cycle) = (N*Q+P)*T = Q * Tr, where T is the orbit period (more exactly the mean nodal period), and Tr is the revolution period of the planet with respect to the orbit's (ascending or descending) node.

  Then:

  Q (=Tc/Tr) is the number of planet revolutions per repeat cycle.

  N+P/Q (=Tr/T) is the number of orbits per planet revolutions with respect to the orbit's (ascending or descending) node.

  N*Q+P (= Tc/T) is the (whole) number of orbits per repeat cycle.

  Note that Tr depends on the orbit parameters because the node drifts under the effect of J2.

  If sso = 1, the orbits are sun-synchronous (the inclination is then computed)

  If sso = 0, the function uses incInput as the inclination to be used.

## Parameters

N:

  Values of N (1x1 or 1xNt)

P:

  Values of P (1x1 or 1xNt)

Q:

  Values of Q (1x1 or 1xNt)

ecc:

  Eccentricity (1x1 or 1xNt)

sso:

  1 = sun synchronous orbits, 0 = fixed inclination (1x1)

incInput :

  (mandatory in case sso=0, unused otherwise) inclinations (rad) (1x1 or 1xNt)

er:

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

mu:

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

j2:

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

rotr_pla :

  (optional) rotation rate of the planet (default is %CL_rotrEarth) (1x1)

rotr_pla_sun :

  (optional) mean apparent rotation rate of the Sun around the planet (default is %CL_rotrEarthSun) (1x1)

sma:

  Semi major axis (m). sma is %nan if value cannot be computed. (1xNt)

inc:

  Inclination (rad). inc is %nan if value cannot be computed. (1xNt)

## Authors

- CNES - DCT/SB

## See also

- CL_op_searchRepeatOrbits

- CL_op_repeatGroundTracks

- CL_op_ssoJ2

## Examples

    N = 15;
    P = 3;
    Q = 16;
    ecc = 0.01;
    sso = 0;
    incInput = CL_deg2rad(98);
    [sma,inc] = CL_op_repeat2smaInc(N,P,Q,ecc,sso,incInput)

    N = [15,15];
    P = [3,5];
    Q = [16,6];
    ecc = [0.01, 0.001];
    sso = 1 ;
    [sma,inc] = CL_op_repeat2smaInc(N,P,Q,ecc,sso)