9 Astrometry of observations and coordinates

9.1 Description of observations

Documented positions are described by their location, reference frame, and date. Thus, the locations can be topocentric, geocentric, selenocentric, barycentric, or satellitocentric. The reference frames can be ICRF, true position, which is the equator of date referred to the CIP, or mean position, which is the equator of date referred to the CIP for some convenient epoch (used primarily for artificial satellites). The time scales for observations are those appropriate for the location and reference frame. Thus, topocentric and satellitocentric observations would be on UTC or better on TT, which has no discontinuities ( $\rm TT=TAI + 32.184$ s). Geocentric observations would be on TCG, and barycentric observations on TCB. Sometimes TT will be retained as a convenience.

There are geometric observations that involve time delay measurements, such as are made by radar and laser measurements between the actual positions of two different bodies. Individual measurements are independent of the reference frame, but the series of observations become dependent on the motions of the bodies and, thus, on the reference frame and kinematics of the system.

9.2 Types of observations

Let us describe what corrections are to be made for different types of observations.

1.

Narrow angle (topocentric observed positions): the observations of small fields of view with images at one exposure, are made by CCDs, either in stare mode or time delay integration, or by photographic plates and recorded in TT. These astrometric observations are made of program objects with respect to reference stars, whose positions are available from positional catalogs on the ICRF. So the resulting program object positions will be on the ICRF. The reference star positions must be corrected for their proper motions between the reference catalog epoch and the observational time with the correct time difference. It is also advisable to correct the reference stars for predicted refraction (including color effects), gravitational deflection, parallax, and differential aberration. Thus, the astrometry is done in observational coordinates and the plate constants will be partially free of the differential effects so that the magnitude of the unknown parameters will be smaller.

2.

Wide angle observations (topocentric observed positions): observations made independent of reference stars by means of interferometers, transit circles, and telescopes with positional readouts are topocentric apparent positions at a TT time. They require correction for instrumental parameters, refraction, diurnal aberration, Earth orientation, light bending, telescope location, and time correction (TCG-TT) to achieve a geocentric true position. Correction must then be made for precession-nutation, geodesic precession if not included in the latter, aberration, proper motion, radial velocity, parallax, and time difference (TCB-TCG) to reach barycentric ICRF positions. In practice, it is preferred to use the position and velocity of the observer with respect to the solar system barycenter and reduce the observation in one step, avoiding the use of the geocentric position.

3.

Radar and laser observations (time delay measurements): these are time delay measurements of geometric distances of bodies at specific times. The positions of the transmitting, reflecting, and receiving bodies are the actual geometric positions at specific times, which differ according to the transmission time between the bodies. Thus, an iterative solution is appropriate to determine the times and locations, and relativistic effects must be taken into account. For ephemeris determination the calculated ephemeris positions could best be fit to the observations to determine corrections to the computed positions. Alternatively, initial positions are topocentric in UTC and must be corrected to geocentric on TCG, based on Earth orientation parameters. Reductions should then be made to barycentric positions on TCB.

4.

Solar System observations: solar system observations can be of various types, such as radar, laser, and optical, narrow, or wide, angle observations. Depending on the type, reference should be made to the appropriate sections above. Correction for the motion of the solar system body may be an additional correction to the above descriptions.

5.

Pulsar timing: pulsar timings are topocentric, geometric measurements made on the observatory clock. Pulsar timings require the most accurate and careful relativistic reduction procedures, including correcting carefully for the time differences of the local clock and whatever atomic time scale is used for analysis. Reduction for the physics of the source and the actual geometry of the solar system and the Earth orientation must be made to reach the barycentric position on the ICRF and TCB.

6.

VLBI observations: Very Long Baseline Interferometer (VLBI) observations, made at radio frequencies, are similar to optical interferometer observations and are topocentric apparent positions at a TT time. They are an angular measurement with respect to the interferometer baseline and the true equator of date. They require correction for diurnal aberration, atmospheric effects, instrument locations, Earth orientation, and time correction (TCG-TT) to achieve geocentric positions. Then, they can be transformed to geocentric GCRF or barycentric ICRF positions by means of precession-nutation, geodesic precession, aberration, and time difference (TCB-TCG). In practice, since the VLBI observations of radio sources define the ICRF, the observations are used to solve for the corrections to precession-nutation, polar motion, Earth rotation, geodetic effects, and astronomical constants.

7.

Observations of artificial satellites: observations of artificial satellites can be made by various techniques. These include radar and laser observations of category (3) above. Also, astrometric observations of (1) and (2) above may be made. The computed artificial satellite ephemerides should be transformed to the observational positions for the determination of observed minus computed positions for orbital parameter improvements, and the time argument should be TCG. The reference frame, here, is a dynamically non-rotating reference system. Hence, geodesic precession must not be applied in the reduction of data, but the complementary terms due to accelerations must be included in the equations.

9.3 Reduction steps

This section presents the reduction procedure going from the raw observation to the position on the ICRF system. While a number of possibilities are proposed, it is generally advisable to reduce observations directly to ICRF positions. Standardized software for reduction procedures is being developed by the IAU Working Group SOFA (chaired by Patrick Wallace, ptw@star.rl.ac.uk), the IMCCE at the Paris Observatory, and the USNO.

1.

Raw observation: this is the observation as it is actually made with the recorded time in UTC. This should not be distributed or published as the observer is best able to make the appropriate corrections.

2.

Local place: this is the observation corrected for refraction and instrument parameters and recorded in UTC. This is also not of use except to the observer.

3.

Topocentric apparent place: this is the local place corrected for diurnal aberration and the time difference TT-UTC. It is on ITRF and TT.

4.

Geocentric apparent place: this is the topocentric apparent place corrected for polar motion, irregularities of UT1 (via Stellar Angle), diurnal parallax and light bending. It is on the CEO and true equator and can be either on TT or TCG. Accurate Earth Orientation Parameters are available from the IERS.

5.

Barycentric catalog position: the correction from geocentric apparent place to the barycentric ICRF involves precession-nutation including geodesic precession-nutation, stellar parallax (if known), stellar aberration, light deflection and light time. The positions are in ICRF and time can be TT or TCB. Right ascensions and declinations are equivalent to the old positions with respect to the mean equinox an the mean equator for the epoch J2000.0. Only the epoch of observation of moving objects and stars must be specified. There are no apparent positions in the fixed frame and the use of the word "mean'' is no longer necessary. The standard model of precession-nutation IAU 2000A is accurate to 0.1 milliarcsec. More precise values are available weekly from the IERS.