Colour terms in MK IV astrometry

[Andrew Bennett <andrew.bennett@ns.sympatico.ca>]

Back in the mists of time, somebody whose
post has long disappeared from my computer
suggested that colour terms might be significant
in the MK IV astrometry.

I have finally got round to testing this using
Tycho2 B-V as a surrogate colour. Results for
mean probable error in one coordinate in arc
seconds using (RA, DEC) = polynomial in X1, X2:

Order   No colour   3 colour terms
   1     4.206       4.162
   2     0.500       0.501
   3     0.142       0.140
   4     0.130       0.125
   5     0.127       0.120

The low order fit errors (order 1 and 2) are dominated
by the approximation involved in using the simple polynomial
in X1, X2 instead of the proper tangent plane solution.
According to my sums, this source of error is below 0.01
arc seconds for the 3rd order fit at the low declination
involved: the error increases rapidly with declination.

I conclude that the astrometry is adequate for our purposes
using the 3rd order fit and that the colour effects are small.

Andrew Bennett, Avondale Vineyard