[fitsbits] Re: Q: Determining coordinates

[Thomas Schmidt]

Stupendous Man wrote:

[snip]
>   Voila.  An analog solution.  I suspect that this will be much
> quicker and easier than a digital solution.


Here is another analog solution:

Take the stars with known coordinates and draw a straight line from
each of those to each other (if you have many stars, you may omit 
some of these lines).

Now suppose you have one star at RA = 14.6° and one at RA = 15.1°.
Then you know that there is one point on the line joining them
with RA = 15.0°. This point is at a distance of 0.4/0.5 of the 
total distance from the former star and 0.1/0.5 of the total distance
from the latter star. Mark that point.

Now look for a different pair of stars with RAs below and above 15°.
Compute the location of the point with RA = 15° on the line joining
these and mark it, too.

The coordinate line of constant RA = 15° must pass through these
two points, so you can already draw it if your RA/Dec grid is
sufficiently rectangular. If it is not, you can approximate the
curved coordinate lines the better the more combinations of stars
you can use.

Of course, you can thus determine coordinate lines with any arbitrary
RA (e.g. 16.74°, if you know that the object whose coordinates you
want to measure is close to this RA; or a grid line for every 0.1° etc).

The declination grid is done the same way.

The accuracy achievable with this method depends on your patience,
the number and distribution of available stars and the deviation of 
your projection from rectangular. It should suffice for a quick-and-dirty 
analysis of your picture.

(But many thanks to Bill Owen for his description of the mathematical
method. I happen to have an application where it will be very
useful...)

Bye,
  Thomas

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  Thomas Schmidt                  e-mail:     schmidt at hoki.ibp.fhg.de