#### Map Projections and Offsets.

In general, a “map projection” describes the relation between 2 spherical coordinates, longitude and latitude , 1 on the celestial sphere, and 2 Cartesian coordinates and , which in radio astronomy and the NCS we often call “position offsets”.

Up to now, , only the “radio” projection is supported, for which:

where and are the source coordinates specified with SOURCE. 2 Note that this is the same system of offsets as in “OBS” of the old control system.

If we want to observe several positions on the sky at or near the source position as specified with SOURCE, we often do this by requesting position offsets in the map projection. Also, the resulting data, e.g., images, are usually stored and displayed as a function of and .

For most observations, parameters and options of the observing mode are sufficient to specify the position offsets:

- for TRACK and VLBI and are fixed during the complete scan;
- for ONOFF and change from subscan to subscan;
- for OTFMAP and change continuously or “on-the-fly” (OTF) during the OTF subscans.

The PAKO commands for most Observing Modes expect fixed offsets (or start- and end-offsets for OTFMAP) as parameters. These can be either in the radio projection, specified with the option:
/SYSTEM projection
or in the true angle horizon system (see below), specified with the option:
/SYSTEM trueHorizon

NOTES. For POINTING, the OTF offsets are always in system trueHorizon, and are specified implicitly though the angular length of the subscans.