CL_gm_betaEclipse

Description

• Computes quantities that characterize the portion of the orbit path where the Sun is eclipsed by the planet as seen from the satellite.

  The shadow region is a cylinder whose axis is the (fixed) Sun direction and whose radius is that of the planet (assumed spherical).

  The computed quantities are:

  - half_span: eclipse interval half-length (in true anomaly)

  - mid_pos: anomaly of mid-eclipse, measured from the projection of the Sun direction onto the orbit plane.

  The true anomalies that correspond to the beginning and end of eclipse (resp. tan_beg and tan_end) can then be computed by:

  tan_beg = mid_pos - argsp - half_span

  tan_end = mid_pos - argsp + half_span

  where argsp is the angle between the projection of the Sun direction onto the orbit plane and the direction of the periapsis.

  If the Sun is not eclipsed, half_span is set to 0, and mid_pos to pi (arbitrarily).

  

• Notes:

  - The trajectory of the satellite is an ellipse (no perturbations assumed).

  - If the orbit is circular (ecc = 0), the value of argsp has no impact on the results.

Parameters

sma:

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

betaa:

Sun beta angle (can be positive or negative) [rad] (1xN or 1x1)

ecc:

(optional) Eccentricity. Default value is 0. (1xN or 1x1)

argsp:

(optional) Angle between the Sun direction and the periapsis in the orbit plane. Same sign convention as for the argument of periapsis. Default value is 0. (1xN or 1x1)

er:

(optional) Planet radius (default is %CL_eqRad) [m] (1xN or 1x1)

half_span:

Eclipse interval half-length (in true anomaly) [rad] (1xN)

mid_pos:

Angle from the Sun direction in the orbit plane defining the middle of the eclipse interval [rad] (1xN)

See also

• CL_gm_eclipse

• CL_gm_raan2beta

Authors

• CNES - DCT/SB

Examples

// Example 1 betaa = CL_deg2rad([10,20]); sma = 7.e6; CL_gm_betaEclipse(sma,betaa) CL_gm_betaEclipse(sma,betaa,0) // same // Example 2 cjd = 20050; pos_sun = CL_eph_sun(cjd); pos_sun_sph = CL_co_car2sph(pos_sun); alpha_sun = pos_sun_sph(1); delta_sun = pos_sun_sph(2); raan = %pi/4; inc = CL_deg2rad(98.7); betaa = CL_gm_raan2beta(inc,raan,alpha_sun,delta_sun) sma = 10000.e3; ecc = [0, 0.01]; argsp = 0; [half_span,mid_pos] = CL_gm_betaEclipse(sma,betaa,ecc,argsp)