TEMEtoLATLON {asteRisk}

Convert coordinates from TEME to geodetic latitude, longitude and altitude

Description

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 position in TEME to geodetic latitude, longitude and altitude, which can be considered to be a non-inertial, Earth-centered frame of reference.

Usage

TEMEtoLATLON(position_TEME, dateTime, degreesOutput=TRUE)

Arguments

position_TEME

Vector with the X, Y and Z components of the position of an object in TEME frame, in m.

dateTime

Date-time string with the date and time in UTC corresponding to the provided position vector. This specifies the time for which the conversion from TEME to geodetic 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.

degreesOutput

Logical indicating if the output should be in sexagesimal degrees. If degreesOutput=FALSE, the output will be in radians.

Value

A vector with three elements, corresponding to the latitude and longitude in degrees (or radians if specified) and the altitude in m.

References

https://arc.aiaa.org/doi/10.2514/6.2006-6753

Examples

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 geodetic latitude, longitude
# and altitude, previously multiplying by 1000 to convert the km output of 
# sgdp4 to m

state_1day_geodetic <- TEMEtoLATLON(state_1day_TEME$position*1000, 
                                    "2006-06-27 00:58:29.34")
}