Name

Reference Frames and time scales Presentation of Reference Frames and time scales used in CelestLab

Reference frames used in CelestLab

Several Reference Frames are used in CelestLab. Inertial Reference Frames are used in the definition of the orbits (integration of the equation of motion) whereas Terestrial Reference Frames are convenient for the access analysis (location of ground stations for visibilty analysis for example).

Terrestrial Reference Frame (ITRF)

Origin: G, the Earth center of mass co-rotating with the Earth in its diurnal motion.

• Z-axis : Pole IRP (IERS Reference pole)  Equatorial plan: Perpendicular to Z

• X-axis: IRM (IERS Reference Meridian) = Greenwich meridian

• Y completes the trihedron

Figure 1. ITRF International Terrestrial Reference Frame

ITRF International Terrestrial Reference Frame

Inertial Geocentric Reference Frame: J2000 Reference Frame

This Reference frame called J2000 in CelestLab follows the definition of the International Celestial Reference Frame (ICRF) in the IERS 1996 conventions.. It is a standard inertial Earth centred, equatorial, mean of epoch Reference system. This is an inertial Reference frame defined as follow:

• The Reference epoch is January 1st, 2000 at 12h00 (BDT time scale)

• The origin 0 is the Earth centre of mass

• Z2000 points along the mean Earth rotational axis at epoch oriented towards the North pole

• (X2000, Y2000) lies in the mean equatorial plane of epoch

• X2000 axis points toward the mean vernal equinox of Reference epoch.

• Y2000 axis completes the right handed co-ordinate system

Figure 2. Earth Mean Equator and Mean Equinox of Epoch J2000

Earth Mean Equator and Mean Equinox of Epoch J2000

In CelestLab, the transformation from ITRF to ICRF (J2000 in CelestLab) is achieved through a succesion of rotations:

  • Polar motion : PI(xp,yp) - no model, data available on iers web site

  • Sideral time : (theta) IERS 1996

  • Nutation : (N) Wahr IAU 1980

  • Precession : (P) Lieske 1996

Figure 3. Rotation Terrestrial to Celestial

Rotation Terrestrial to Celestial

G50 Veis

The advantage of this "quasi-inertial" Reference Frame is to allow the transformation from a Terrestrial Reference Frame (RF) to a Celestial Reference Frame by a single rotation around Z-axis (Sidereal time of Veis). This Reference Frame may may be very useful for analysis that require a large number of transformations from Terrestrial RF to Celestial RF (or vice versa) because there is only one rotation per transformation.

The G50 Veis is defined as follows:

• The axis of the Earth Centre-North pole is considered inertial

• The X-axis is the projection of the mean vernal direction on to the true equator at a given epoch: 01/01/1950 at 0h00. This construction minimizes the error on orbital parameters due to non-inertiality

• The Y-axis is defined in order to obtain a direct trihedron

Figure 4. G50 (Veis) Reference Frame

G50 (Veis) Reference Frame

Time scales and julian days used in CelestLab

The Universal time Co-ordinated (UTC), is deduced from the International Atomic Time (TAI), so as not lose entirely the relation between time and Earth ‘s orientation (UT1). Since January 1 1972, the UTC and TAI differ by an integer number of seconds, and adjustments are made whenever UTC deviates by more than  0.9 second from UT1.

TAI-UTC=n seconds (n integer 0)

|UT1-UTC| <0.9 seconds

The quantity UT1-UTC is available on the IERS web site.

Thus the difference between UTC and TAI is constant over a given period. The “Temps Atomic International” TAI is the continuous time scale produced by the Bureau International de l’Heure in Paris. It is a time scale based on the readings of approximately 150 atomic clocks. The Ephemeris Time scale (ET) is a time scale based on the Earth revolution around the Sun. Defined with:

ET=TAI+32.184 s

For most applications in CelestLab the time scale is UTC. For the computation of the sidereal time the time argument is in UT1 time scale. For change of Reference Frame the user may, for accurate computation, give in optionnal argument the quantity UT1-UTC.

Julian days

Julian days are the most commonly used unit of time used in CelestLab.

The Julian date (JD) is the interval of time in days and fractions of a day since a reference date:

January 1, 4713 BC Greenwich noon for julian days (jd)

January 1, 1950 at 0 hour for CNES julian days (cjd)

November 17, 1858, Wednesday at 0 hour (Modified Julian date =Julian date - 2400000.5) Modified Julian days (mjd)