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Full Version: Shadow Conditions of Earth Satellites - Kozai orbit propagation
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Accurate predictions of shadow conditions for any type of satellite orbit can be determined by using a combination of one-dimensional minimization and root finding. The algorithm used in this computer program searches for minimum values of the angle between the shadow axis and the satellite’s position vector as a function of time. If this angle lies within the penumbra angle, the algorithm uses Brent's root-finding method to look backward and forward relative to this minimum time to find entrance and exit conditions. This method can also be used to determine entrance and exit relative to the umbra, penumbra and cylindrical shadows.

The information required by the software is "hard-wired" in the source code starting with the initial calendar date and UTC time followed by the classical orbital elements. The type of shadow to model and the simulation duration in days is the next section of user-provided data.

// initial calendar date (month, day, year)

month := 6;

day := 14;

year := 1990;

// initial utc time (hours, minutes, seconds)

uthr := 23.0;

utmin := 0.0;

utsec := 0.0;

// initial orbital elements

// semimajor axis (kilometers)

oev1(1) := 24450.0;

// eccentricity

oev1(2) := 0.725;

// orbital inclination (degrees > radians)

oev1(3) := 18.0 * dtr;

// argument of perigee (degrees > radians)

oev1(4) := 180.0 * dtr;

// raan (degrees > radians)

oev1(5) := 68.0 * dtr;

// true anomaly (degrees > radians)

oev1(6) := 0.0 * dtr;

// type of shadow calculation

// 1 = penumbra shadow

// 2 = umbra shadow

// 3 = cylinder shadow

ishadow := 2;

// simulation duration in days

ndays := 5;

The zipped file for this program, shadow2.zip, can be downloaded from

Reference URL's