# Convert coordinates from TEME to ITRF The TEME (True Equator, Mean Equinox) frame of reference is an Earth-centered inertial coordinate frame, 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 coordinates and velocities calculated with the SGP4 and SDP4 models are in the TEME frame of reference. This function converts positions and velocities in TEME to the ITRF (International Terrestrial Reference Frame), which is an ECEF (Earth Centered, Earth Fixed) frame of reference. In the ITRF, the origin is also placed at the center of mass of Earth, but the frame rotates with respect to the stars to remain fixed with respect to the Earth surface as it rotates. The Z-axis extends along the true North as defined by the IERS reference pole, and the X-axis extends towards the intersection between the equator and the Greenwich meridian at any time. This function requires the `asteRiskData` package, which can be installed by running `install.packages('asteRiskData',repos='https://rafael-ayala.github.io/drat/')` ```r TEMEtoITRF(position_TEME, velocity_TEME, dateTime) ``` ## 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 ITRF coordinates will be performed. It is important to provide an accurate value, since the point over the surface of Earth to which a set of TEME coordinates refers varies with time due to the motion of Earth. ## Returns A list with two elements representing the position and velocity of the satellite in the ITRF (International Terrestrial Reference Frame) 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 ITRF frame, previously # multiplying by 1000 to convert the km output of sgdp4 to m state_1day_ITRF <- TEMEtoITRF(state_1day_TEME$position*1000, state_1day_TEME$velocity*1000, "2006-06-27 00:58:29.34") } ```

TEMEtoITRF function