Subsections

• Space motion and FK4 to FK5 conversion
• Disabling co-ordinate corrections

Co-ordinate systems and transformations

The flow of transformations from input co-ordinates to servo demands, and vice versa, is shown in Figure 1 (after that of Sun/67). Co-ordinates which are accessible to the observer (either as inputs to the system, or as reported in the Antenna FITS file) have bold labels. Starting at the top, and working down, the possibilities are as follows:

Figure 1: Relationship Between GBT co-ordinate systems (after Sun/67, Figure 1.)

GALATIC

IAU 1958 galactic co-ordinates as described by Blaauw et al., 1960, Mon.Not.R.astr.Soc., 121, 123. These can be converted to mean FK5 J2000 by a simple transformation, e.g. as provided by SLA_GALEQ.

JMEAN

Equatorial co-ordinates with respect to the mean equator and equinox of a specified Julian epoch, in the FK5 system. These are related to mean FK5 2000 co-ordinates by allowing for luni-solar precession, as implemented for example by SLA_PRECES.

B1950

Equatorial co-ordinates with respect to the mean equator and equinox of B1950, in the FK4 system. The rigourous transformation of FK4 B1950 co-ordinates to FK5 J2000 is a complex process, the GBT implementation is discussed in more detail in Section 2.1 below.

J2000

These are mean equatorial co-ordinates with respect to the mean equator and equinox of J2000, in the FK5 system. Strictly speaking, these are barycentric positions, a correction for annual parallax is required to convert to geocentric mean place. This correction is $<$ tex2html_wrap_inline$1 ^' '$, and is relevant only for the nearest stars; in the GBT implementation parallax is currently always assued to be zero, and so the J2000 co-ordinates are effectively treated as geocentric.

GAPPT

Geocentric apparent co-ordinates referred to the true equator and equinox of the start of the observation. Conversion from J2000 to GAPPT requires allowing for light deflection, annual (stellar) aberration and the combined effects of precession/nutation from J2000.0 to the date of observation.

HADEC

apparent $[ h,\delta ]$  calculated from geocentric apparent $[ \alpha,\delta ]$  by allowing for earth rotation via the local apparent sideal time for the start of the observation. This input system is unlikely to be heavily used (if at all?)

Apparent $[ h,\delta ]$  is converted to topocentric $[ h,\delta ]$  on the way to topocentric $[ Az,El ]$  by correcting for the effects of dirunal aberration.

AZEL

Topocentric azimuth and elevation. A horizontal co-ordinate system in which azimuth runs from $0^{\circ} \hspace{-0.37em}.\hspace{0.02em}0$ - $360^{\circ} \hspace{-0.37em}.\hspace{0.02em}0$, with North at $0^{\circ} \hspace{-0.37em}.\hspace{0.02em}0$, and East at $90^{\circ} \hspace{-0.37em}.\hspace{0.02em}0$ degrees. Again this co-ordinate system is unlikely to be used apart from for engineering purposes.

The conversion from topocentric $[ h,\delta ]$  to $[ Az,El ]$  requires the geodetic latitude of the antenna, corrected for polar motion.

MOUNT

Mount $[ Az,El ]$  generated from topocentric $[ Az,El ]$  via the refraction correction and application of the pointing model. The details of this process are described elsewhere. The observer is not offered mount $[ Az,El ]$  as in input co-ordinate system (the CableWrap mode is available to engineers). Indicated mount $[ Az,El ]$  values are stored in the Antenna FITS files but these should not normally used by the observer.

In addition to the above, two other input mechanisms not shown on Figure 1 are available:

USER

A co-ordinate system in which the user specifies the location of a spherical co-ordinate system pole and prime meridian in J2000 co-ordinates, and optionally the first and second derivates of these locations.

SOLAR SYSTEM

Finally, the user may specify a named solar system object, and GO will automatically calculate the appropriate pole and prime meridian values and rates to centre the co-ordinate system on the (moving) solar-system object.

These will be described in more detail at a later date.

Space motion and FK4 to FK5 conversion

Space motion refers to the movement of a stellar object with respect to the fixed background. It is traditionally divided into proper motion, given as components in right ascension and declination, and radial velocity, which occurs along the line of sight.

For the vast majority of objects, the effects of proper motion are small ($<$ tex2html_wrap_inline$1 ^' '$ per year), and are not usually known. The GBT has made the decision not to support these corrections. Therefore, in the (rare) case where the observer feels it important to allow for them (or for annual parallax) they should perform all of the initial co-ordinate transformations themselves, and provide adjusted input co-ordinates as true geocentric apparent co-ordinates.

Since FK4 is a non-inertial reference frame, objects (such as quasars and radio galaxies) will have a non-zero fictitious proper motion of about $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ per century. The correct conversion from FK4 to FK5 therefore requires knowledge of the epoch of observation used to derive the position. In addition, star positions in the FK4 system are part-corrected for annual aberation, and embody the so-called E-terms of aberration (see Sun/67 for an excellent discussion of these effects).

The GBT conversion from FK4 B1950 to FK5 J2000 assumes inertially zero proper motion, and zero parallax and radial velocity, as performed by SLA_FK45Z, and assumes an epoch of the original observation of B1950. This conversion will therefore take care of the effects of 50 years of precession, which is the bulk of the change, but may have residual errors at the tex2html_wrap_inline$1 ^' '$ level. Again, those who require the utmost precision should supply correct J2000 or GAPPT values.

Disabling co-ordinate corrections

The Antenna Manager has four type of corrections which may be enabled or disabled: polar motion, diurnal aberration, refraction and the pointing model. For all normal observations, all of these should be enabled. The state of these corrections is not recorded in the GO FITS file; however this information is recorded in the antenna FITS file, and will be used in the process of calculating derived telescope positions from encoder co-ordinates and vice versa.

If any of these co-ordinate corrections have been disabled, the celestial co-ordinate values recorded in the antenna FITS file will not in general be correct.