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use *;
use PyAstroTime;
use crateframetransform as ft;
use *;
/// Greenwich Mean Sidereal Time
///
/// Notes:
/// * Vallado algorithm 15:
/// * GMST = 67310.5481 + (876600h + 8640184.812866) * tᵤₜ₁ * (0.983104 + tᵤₜ₁ * −6.2e−6)
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate GMST
///
/// Returns:
/// float|numpy.array: GMST at input time[s] in radians
///
/// Equation of Equinoxes
///
/// Greenwich apparant sidereal time, radians
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate GAST
///
/// Returns:
/// float|numpy.array: GAST at input time[s] in radians
/// Earth Rotation Angle
///
///
/// Notes:
/// * See: IERS Technical Note 36, Chapter 5, Equation 5.15
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate Earth Rotation Angle
///
/// Returns:
/// float|numpy.array: Earth Rotation Angle at input time[s] in radians
///
/// Calculation Details
///
/// * Let t be UT1 Julian date
/// * let f be fractional component of t (fraction of day)
/// * ERA = 2𝜋 ((0.7790572732640 + f + 0.00273781191135448 * (t - 2451545.0))
///
/// Rotation from International Terrestrial Reference Frame (ITRF) to the Terrestrial Intermediate Reference System (TIRS)
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from ITRF to TIRS at input time[s]
/// Rotation from Terrestrial Intermediate Reference System to Celestial Intermediate Reference Systems
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from TIRS to CIRS at input time[s]
/// Rotation from Celestial Intermediate Reference System to Geocentric Celestial Reference Frame
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from CIRS to GCRF at input time[s]
///Quaternion representing rotation from the International Terrestrial Reference Frame (ITRF) to the Geocentric Celestial Reference Frame (GCRF)
///
/// Notes:
/// * Uses full IAU2010 Reduction; See IERS Technical Note 36, Chapter 5
/// * Very computationally expensive
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from ITRF to GCRF at input time[s]
///Quaternion representing rotation from the Geocentric Celestial Reference Frame (GCRF) to the International Terrestrial Reference Frame (ITRF)
///
/// Notes:
/// * Uses full IAU2010 Reduction; See IERS Technical Note 36, Chapter 5
/// * Very computationally expensive
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from GCRF to ITRF at input time[s]
/// Approximate rotation from Geocentric Celestrial Reference Frame to International Terrestrial Reference Frame
///
/// Notes:
/// * Uses an approximation of the IAU-76/FK5 Reduction; see Vallado section 3.7.3
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from GCRF to ITRF at input time[s]
/// Approximate rotation from International Terrestrial Reference Frame to Geocentric Celestrial Reference Frame
///
/// Notes:
/// * Uses an approximation of the IAU-76/FK5 Reduction; see Vallado section 3.7.3
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from ITRF to GCRF at input time[s]
/// Rotation from True Equator Mean Equinox (TEME) frame to International Terrestrial Reference Frame (ITRF)
///
/// Notes:
/// * TEME is output frame of SGP4 propagator
/// * This is Equation 3-90 in Vallado
///
/// Args:
/// tm (satkit.time|datetime.datetime|list|numpy.array): Time[s] at which to calculate rotation
///
/// Returns:
/// satkit.quaternion|list: Quaternion or list of quaternions representing rotation from TEME to ITRF at input time[s]
///
/// Get Earth Orientation Parameters at given instant
///
/// Args:
/// tm (satkit.time): Instant at which to query parameters
///
/// Returns:
/// (float, float, float, float, float, float): tuple with following elements:
/// * 0 : (UT1 - UTC) in seconds
/// * 1 : X polar motion in arcsecs
/// * 2 : Y polar motion in arcsecs
/// * 3 : LOD: instantaneous rate of change in (UT1-UTC), msec/day
/// * 4 : dX wrt IAU-2000A nutation, milli-arcsecs
/// * 5 : dY wrt IAU-2000A nutation, milli-arcsecs