$LastChangedDate: 27-Juil-2011 $

# CL_op_frozenOrbit

Eccentricity and argument of periapsis of a frozen orbit

## Calling Sequence

       [ecc,pom] = CL_op_frozenOrbit(sma,inc,[,er,zonals])

## Description

- Computes the eccentricity and argument of periapsis of a "frozen" orbit, so that the mean value of eccentricity and argument of periapsis remain constant over time.

  Freezing the orbit is possible by balancing the effects of harmonic even and odd terms of the potential (J1=0, J2, J3, ...).

  The argument of periapis returned is 90 degrees or -90 degrees. The eccentricity is usually small: of the order of 1.e-3 for the Earth.

  If zonals are limited to J2 and J3, the frozen eccentricity is given by:

  eccg = -0.5*sin(inc)*(Req/sma)*J3/J2

  NB: The relative accuracy decreases as the number of zonal terms increases. The result can be very inaccurate for 40 terms or more.

## Parameters

sma:

  Semi major axis [m] (1xN or 1x1)

inc:

  Inclination [rad] (1xN or 1x1)

er:

  (optional) Equatorial radius [m]. Default is %CL_eqRad.

zonals:

  (optional) Vector of zonal coefficients J1 to Jn (1xNz or Nzx1). Default is %CL_j1jn(1:3).

ecc:

  Mean eccentricity (1xN)

pom:

  Mean argument of periapsis [rad] (1xN)

## Authors

- CNES - DCT/SB

## Examples

    sma = %CL_eqRad + [350.e3, 700.e3];
    inc = CL_deg2rad(98);
    [ecc,pom] = CL_op_frozenOrbit(sma,inc)
    [ecc,pom] = CL_op_frozenOrbit(sma,inc,zonals=%CL_j1jn(1:20))