Name

CL_gm_eclipseCir — Analytic eclipse calculation for circular orbits

Calling Sequence

   [eclipseS,eclipseE,sun_orb,duration] = CL_gm_eclipseCir(cjd,sma,inc,raan[,er[,mu[,j2]]])
   
   

Description

  • This function computes eclipse duration for circular orbits. Sun's position is defined by date (cjd). (computed with CL_mod_moonSunG50)

    Orbit's node is defined by its right ascension (raan).

    The eclipse is defined as the satellite crossing a cylinder supported on sun's diameter. Calculation is purely geometric: sun-orbit geometry is constant

    eclipseS and eclipseE contain the start and end of eclipse positions : [position on orbit(w+M);right ascension in Gamma50 (Veis);declination in Gamma50 (Veis)]

    sun_orb contains sun's right ascension and declination in orbit frame

    Orbit frame is defined as follows:

    axe X: towards node

    axe Z: orbit's kinetic moment vector

    axe Y assures orthonormal direct frame

    duration contains [total angle of eclipse on orbit;duration] (duration is computed using the meanmotion taking into account J2).

    NOTES:

    - planet is assumed spherical and it is necessarily the earth

    - sun_orb's declination (in orbit frame) is the beta angle (angle between the satellite's orbital plane and the Sun)

  • Last update : 29/2/2008

Parameters

cjd:

CNES julian day (+ut/24, ut in hours) (1xN)

sma:

semi major axis [m] (1xN)

inc:

inclination [rad] (1xN)

raan:

right ascension of ascending node[rad] (1xN)

er:

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

mu:

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

j2:

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

eclipseS:

start of eclipse [position on orbit(w+M);right ascension in Gamma50(Veis);declination in Gamma50(Veis)] [rad] (3xN)

eclipseE:

end of eclipse [position on orbit(w+M);right ascension in Gamma50(Veis);declination in Gamma50(Veis)] [rad] (3xN)

sun_orb:

sun on orbit frame [right ascension;declination (=beta)] [rad] (2xN)

duration:

eclipse duration [angle of position on orbit;duration] [rad;s] (2xN)

Authors

CNES - DCT/SB

See also

CL_gm_betaEclipse, CL_mod_moonSunG50

Examples

//Example 1
cjd=21482;
raan=0;
sma = 1000000+%CL_eqRad;
inc = CL_deg2rad(98);
[eS,eE,s_orb,deltaT] = CL_gm_eclipseCir(cjd,sma,inc,raan)

// Example 2
cjd = CL_dat_cal2cjd(2009,03,21,6); // march 21 2009, 6am
inc = CL_deg2rad(90);
sma = 6978.e3;
raan = 0;
[eS,eE,s_orb,deltaT] = CL_gm_eclipseCir(cjd,sma,inc,raan) // Eclipse position is around 180° of pso...