$LastChangedDate: 27-Juil-2011 $

# CL_gm_eclipse

Analytical eclipse calculation for elliptical orbits

## Calling Sequence

       [result] = CL_gm_eclipse(sma,ecc,inc,argp,raan,alpha_sun,delta_sun [,er,mu])

## Description

- Computes various results that characterize the portion of the orbit path where the satellite is in the shadow of the planet.

  The eclipsed region is a half cylinder of diameter the planet's diameter, and axis the Sun direction. The calculation is purely geometrical: the Sun direction is supposed constant with respect to the orbit plane.

  result is a structure with the following fields :

  result.start and result.end contain quantities that define the eclipse start and end positions: 'pso': (true) argument of latitude (w+v), 'ra': right ascension, 'decl': declination, tlt: true local time.

  result.sun_orb contains quantities that define the Sun's position ('alpha' and 'delta': spherical coordinates) in a frame tied to the orbit.

  The frame tied to the orbit is defined as follows:

  X-axis: Towards the ascending node

  Z-axis: Parallel to (and same direction as) the angular momentum vector

  Y-axis: Such that the frame is direct.

  result.angle is the total eclipse's length (result.end.pso - result.start.pso)

  result.duration is the duration, computed assuming a keplerian motion.

- Notes:

  - The planet is assumed spherical

## Parameters

sma:

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

ecc:

  Eccentricity (1xN or 1x1)

inc:

  Inclination [rad] (1xN or 1x1)

argp:

  Argument of periapsis [rad] (1xN or 1x1)

raan:

  Right ascension of ascending node [rad] (1xN or 1x1)

alpha_sun:

  Sun right ascension [rad] (1xN or 1x1)

delta_sun:

  Sun declination [rad] (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)

result:

  (structure) Various quantities that define the eclipse [rad,sec] (each field is 1xN)

## Authors

- CNES - DCT/SB

## See also

- CL_gm_betaEclipse

## Examples

    cjd = CL_dat_cal2cjd(2009,03,21,6,0,0);
    sun = CL_mod_moonSunG50(cjd,'s');
    sun_sph = CL_co_car2sph(sun);
    alpha_sun = sun_sph(1,:);
    delta_sun = sun_sph(2,:);
    sma = 2000.e3+%CL_eqRad;
    ecc = 0.1;
    inc = CL_deg2rad(98);
    argp = 0;
    raan = 0;
    [result] = CL_gm_eclipse(sma,ecc,inc,argp,raan,alpha_sun,delta_sun);
    result.start
    result.end
    result.sun_orb
    result.angle
    result.duration