# Convert coordinates from TEME to GCRF The TEME (True Equator, Mean Equinox) and GCRF (Geocentric Celestial Reference Frame) are both ECI frames of reference, i.e., Earth-centered inertial coordinate frames, where the origin is placed at the center of mass of Earth and the coordinate frame is fixed with respect to the stars (and therefore not fixed with respect to the Earth surface in its rotation). The difference between the two resides in the fact that in the GCRF frame, the X-axis and Z-axis are aligned respectively with the mean equinox and rotation axis of Earth at 12:00 Terrestrial Time on the 1st of January, 2000, while in the TEME frame they are aligned with the mean equinox and rotation axis at the time of the corresponding TLE. Due to the change of the direction of the vernal equinox and the rotation axis over time, coordinates in the two frames differ slightly. The function implement 2 algorithms. The default one applies first a transformation to ITRF using the algorithm implemented by David A. Vallado in the teme2ecef routine, followed by a transformation to GCRF using nutation-precesion-bias and polar motion matrices (transformation for velocity takes into account variations in Earth's rotation speed through length of day data provided by IERS). The second one follows the same procedure implemented by NAIF in the SPICE routine ZZTEME, and is provided for cases where users aim to reproduce SPICE's output. This function requires the `asteRiskData` package, which can be installed by running `install.packages('asteRiskData',repos='https://rafael-ayala.github.io/drat/')` ```r TEMEtoGCRF(position_TEME, velocity_TEME, dateTime, SPICEAlgorithm, ephemerisTime) ``` ## Arguments - `position_TEME`: Vector with the X, Y and Z components of the position of an object in TEME frame, in m. - `velocity_TEME`: Vector with the X, Y and Z components of the velocity of an object in TEME frame, in m/s. - `dateTime`: Date-time string with the date and time in UTC corresponding to the provided position and velocity vectors. This specifies the time for which the conversion from TEME to GCRF coordinates will be performed. It is required due to the change in the exact position of the rotation axis of Earth due to precesion, nutation and polar motion. Either `dateTime` or `ephemerisTime` must be provided. - `SPICEAlgorithm`: Logical indicating if the algorithm implemented in SPICE's ZZTEME routine should be used instead of the default algorithm. By default, `SPICEAlgorithm=FALSE`, and SPICE's algorithm is not applied. - `ephemerisTime`: Time in TDB seconds since J2000 for which the conversion from TEME to GCRF coordinates will be performed. This is also known as "ephemeris time" in SPICE. Either `dateTime` or `ephemerisTime` must be provided. ## Returns A list with two elements representing the position and velocity of the satellite in the ECEF (Earth Centered, Earth Fixed) frame of reference. Position values are in m, and velocity values are in m/s. Each of the two elements contains three values, corresponding to the X, Y and Z components of position and velocity in this order. ## References https://celestrak.org/columns/v04n03/#FAQ01 ## Examples ```r if(requireNamespace("asteRiskData", quietly = TRUE)) { # The following orbital parameters correspond to an object with NORAD catalogue # number 24208 (Italsat 2) the 26th of June, 2006 at 00:58:29.34 UTC. n0 <- 1.007781*((2*pi)/(1440)) # Multiplication by 2pi/1440 to convert to radians/min e0 <- 0.002664 # mean eccentricity at epoch i0 <- 3.8536*pi/180 # mean inclination at epoch in radians M0 <- 48.3*pi/180 # mean anomaly at epoch in radians omega0 <- 311.0977*pi/180 # mean argument of perigee at epoch in radians OMEGA0 <- 80.0121*pi/180 # mean longitude of ascending node at epoch in radians Bstar <- 1e-04 # drag coefficient epochDateTime <- "2006-06-26 00:58:29.34" # Let´s calculate the position and velocity of the satellite 1 day later state_1day_TEME <- sgdp4(n0=n0, e0=e0, i0=i0, M0=M0, omega0=omega0, OMEGA0=OMEGA0, Bstar=Bstar, initialDateTime=epochDateTime, targetTime=1440) # We can now convert the results in TEME frame to GCRF frame, previously # multiplying by 1000 to convert the km output of sgdp4 to m state_1day_GCRF <- TEMEtoGCRF(state_1day_TEME$position*1000, state_1day_TEME$velocity*1000, "2006-06-27 00:58:29.34") } ```

TEMEtoGCRF function