Analytical eclipse calculation for elliptical orbits
res = CL_gm_eclipse(sma,ecc,inc,argp,raan,alpha_sun,delta_sun [,er,mu])
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.
res is a structure with the following fields :
res.start and res.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.
res.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.
res.angle is the total eclipse's length (res.end.pso - res.start.pso)
res.duration is the duration, computed assuming a keplerian motion.
Notes:
- The planet is assumed spherical
Semi major axis [m] (1xN or 1x1)
Eccentricity (1xN or 1x1)
Inclination [rad] (1xN or 1x1)
Argument of periapsis [rad] (1xN or 1x1)
Right ascension of ascending node [rad] (1xN or 1x1)
Sun right ascension [rad] (1xN or 1x1)
Sun declination [rad] (1xN or 1x1)
(optional) Equatorial radius [m] (default is %CL_eqRad)
(optional) Gravitational constant [m^3/s^2] (default value is %CL_mu)
(structure) Various quantities that define the eclipse [rad,sec] (each field is 1xN)
CNES - DCT/SB