sgdp4 {asteRisk}

Propagate an orbital state vector with the SGP4/SDP4 model

Description

Given an orbital state vector of a satellite, applies the SGP4 or SDP4 model to propagate its orbit to the desired time point, as appropriate depending on the orbital period. The model will be automatically chosen depending on the orbital period. For objects in deep space (with orbital periods larger than 225 minutes, equivalent to altitudes higher than 5877.5 km) the SDP4 model will be applied. For objects near Earth (orbital periods shorter than 225 minutes, or altitudes lower than 5877.5 km) the SGP4 model will be used. It is not recommended to apply SGP4 to objects in deep space or SDP4 to objects near Earth, but this can be forced by calling directly the sgp4 and sdp4 functions.

Usage

sgdp4(n0, e0, i0, M0, omega0, OMEGA0, Bstar, initialDateTime=NULL, targetTime,
      keplerAccuracy=10e-12, maxKeplerIterations=10)

Arguments

n0

Mean motion of the satellite at epoch in radians/min.

e0

Mean eccentricity of the orbit of the satellite at epoch. Eccentricity ranges from 0 (perfectly circular orbit) to 1 (parabolic trajectory).

i0

Mean orbital inclination of the satellite at epoch in radians.

M0

Mean anomaly of the satellite at epoch.

omega0

Mean argument of perigee of the satellite at epoch.

OMEGA0

Mean longitude of the ascending node of the satellite at epoch. Also known as right ascension of the ascending node.

Bstar

Drag coefficient of the satellite in units of (earth radii)^-1^. Bstar is an adjusted value of the ballistic coefficient of the satellite, and it indicates how susceptible it is to atmospheric drag.

initialDateTime

Date-time string in UTC indicating the time corresponding to the known state vector of the satellite. It must be provided for objects in deep space, and also for objects near Earth if targetTime is provided as a date-time string.

targetTime

Time at which the position and velocity of the satellite should be calculated. It can be provided in two different ways: either as a number corresponding to the time in minutes counting from epoch at which the orbit should be propagated, or as a date-time string in UTC, in which case the date-time string for epoch must be provided through initialDateTime.

keplerAccuracy

Accuracy to consider Kepler´s equation solved. If two consecutive solutions differ by a value lower than this accuracy, integration is considered to have converged.

maxKeplerIterations

Maximum number of iterations after which fixed-point integration of Kepler's equation will stop, even if convergence according to the accuracy criterion has not been reached.

Value

A list with three elements. The first two elements represent the position and velocity of the satellite at the target time, in the TEME (True Equator, Mean Equinox) frame of reference. Position values are in km, and velocity values are in km/s. Each of these two elements contains three values, corresponding to the X, Y and Z components of position and velocity in this order. The third element indicates the algorithm used to propagate the orbit (sgp4 or sdp4).

References

https://celestrak.org/NORAD/documentation/spacetrk.pdf http://www.celestrak.org/publications/aiaa/2006-6753/AIAA-2006-6753.pdf

Examples

# 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"

# Calculation of the orbital period

2*pi/n0

# The period is higher than 225 min, and therefore the SDP4 model should be
# applied. Let´s calculatethe position and velocity of the satellite 12 hours
# after epoch.

italsat_12h <- sgdp4(n0=n0, e0=e0, i0=i0, M0=M0, omega0=omega0, OMEGA0=OMEGA0,
                     Bstar=Bstar, initialDateTime=epochDateTime, targetTime=0)
italsat_12h$algorithm

# The SDP4 model was correctly chosen.