ECItoKOE: Calculate ECI coordinates from Keplerian orbital elements

In asteRisk: Computation of Satellite Position

Calculate ECI coordinates from Keplerian orbital elements

Description

Keplerian orbital elements are a set of six parameters used to described the orbits of celestial objects, including satellites. While satellites do not follow a perfectly Keplerian orbit, their state at any point can be defined by the orbital parameters that they would have if they were located at the same position with the same velocity following a perfectly Keplerian orbit (i.e., if perturbations were absent). These are called osculating orbital elements.

Keplerian orbital elements can be unequivocally determined from a satellite if its position and velocity are known. This function calculates orbital elements from the position and velocity of a satellite in an ECI (Earth-centered inertial) frame of reference. The elements (such as the equatorial plane) with respect to which the resulting orbital elements will be defined are the same as those used for the ECI frame of reference. The function calculates the six standard orbital elements, plus some alternative elements useful for the characterization of special orbits, such as circular ones or orbits with no inclination.

Usage

ECItoKOE(position_ECI, velocity_ECI)

Arguments

position_ECI	Vector with the X, Y and Z components of the position of an object in an ECI frame, in m.
velocity_ECI	Vector with the X, Y and Z components of the velocity of an object in an ECI frame, in m/s.

Value

A list with the following standard and alternative orbital elements:

semiMajorAxis	Semi-major axis of orbital ellipse in meters.
eccentricity	Numerical eccentricity of the orbit. Eccentricity measures how much the orbit deviates from being circular.
inclination	Inclination of the orbital plane in radians. Inclination is the angle between the orbital plane and the equator.
meanAnomaly	Mean anomaly of the orbit in radians. Mean anomaly indicates where the satellite is along its orbital path, and is defined as the angle between the direction of the perigee and the hypothetical point where the object would be if it was moving in a circular orbit with the same period as its true orbit after the same amount of time since it last crossed the perigee had ellapsed.
argumentPerigee	Argument of perigee in radians. This is the angle between the direction of the ascending node and the direction of the perigee (the point of the orbit at which the object is closest to the Earth).
longitudeAscendingNode	Longitude of the ascending node (also called right ascension of the ascending node) in radians. This is the angle between the direction of the ascending node (the point where thesatellite crosses the equatorial plane moving north) and the direction of the First Point of Aries (which indicates the location of the vernal equinox).
trueAnomaly	True anomaly of the orbit in radians. Unlike mean anomaly, true anomaly is the angle between the direction of the perigee and the actual position of the satellite.
argumentLatitude	Argument of latitude of the orbit in radians. Defined as the angle between the equator and the position of the satellite. It is useful to define the position of satellites in circular orbits, where the argument of perigee and true anomaly are not well defined.
longitudePerigee	Longitude of perigee of the orbit in radians. Defined as the angle between the vernal equinox and the perigee. It is useful for cases of orbits with 0 inclination, where the longitude of the ascending node and the argument of perigee are not well defined.
trueLongitude	Longitude of perigee of the orbit in radians. Defined as the angle between the vernal equinox and the position of the satellite. It is useful for cases of circular orbits with 0 inclination, where the longitude of the ascending node, the argument of perigee and true anomaly are not well defined.

References

https://www.gsc-europa.eu/system-service-status/orbital-and-technical-parameters https://celestrak.org/columns/v02n01/ https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/cami/library/online_libraries/aerospace_medicine/tutorial/media/iii.4.1.4_describing_orbits.pdf

Examples

# The following were the position and velocity of satellite MOLNIYA 1-83 
# the 25th of June, 2006 at 00:33:43 UTC in the GCRF frame (in m and m/s).

position_GCRF <- c(-14471729.582, -4677558.558, 9369.461)
velocity_GCRF <- c(-3251.691, -3276.008, 4009.228)

# Let's calculate the orbital elements of the satellite at that time

orbital_elements <- ECItoKOE(position_GCRF, velocity_GCRF)

asteRisk documentation built on Jan. 14, 2023, 5:07 p.m.