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<title>Munipack ‒ Periodic Error</title>
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<h1>Periodic Error Determination</h1>
<p class="abstract">
A short tutorial for determination
of the periodic error of a telescope mount.
</p>
<h2>Periodic Error</h2>
<p>
Periodic error of a telescope mount has its origin in gears of
the sidereal driver.
Common arrangement of gears of mount is the main
cogwheel of the mount which is driven by a smaller ones (worm).
The control force is carried from the main to the secondary
wheel via a single tooth or more worse via a small contacting area
on the tooth. As a consequence of the assembly, the driver
periodically accelerates and decelerates of the sidereal movement of
the telescope. The effect can be seen directly in small telescopes
(without any corrections) as slow periodic drifting of objects throughout
the field of view. Characteristic time periods are in order of minutes
and their angular amplitude about a few arcseconds.
</p>
<p>
The periodic
error can be suppressed by large gears, precise mechanics work on gears
or an electronic correction (PEC). Perhaps (!), the best way to eliminate ones is
use more than one driven worm or use of conical worms.
</p>
<h2>How To Determine The Periodic Error</h2>
<ol>
<li>Switch-off any electronic corrector.</li>
<li>Select a suitable star: a bright star near of the celestial equator
and meridian,
which will have peak intensities approximately half of full dynamic
range at a very short exposure (under second). The star
must be arranged near of the center of field of view to suppress
deviations due to non-complanar mount (rotated field) of CCD.
An alone star is preferred.
</li>
<li>
Grab a long time serie of frames. Use shortest exposures as possible
and also frequently as possible. Cover multiple expected periods.
</li>
<li>
Than process the acquired images:
<pre>
$ munipack find -th 10 -f 2 per_*.fits
$ munipack timeserie --extname FIND -c X,Y --coo-type RECT --stdout
> --tol=66 666,666 per_*.fits > per
</pre>
The find tool detects bright stars (10 times over background
noise and with FWHM about 2 pixels). The second command lists rectangular
coordinates (--coo-type RECT) from FIND table (--extname FIND)
of a selected object near of center (at pixel
in 666,666) at circular surrounding of radius 66 pixels (--tol=66)
(this is why we had used an alone bright star) to a standard output (--stdout).
Results are stored in 'per' file (and timeserie.fits) with the structure:
<pre>
Julian Date at mid X Y
2455945.24947 421.682 234.723
</pre>
</li>
</ol>
<p>
That's all. The output file can be used in a data analyzing tool
to visualize and analyze your mount.
</p>
<figure>
<img src="pererr.png" alt="pererr.png" title="Periodic error">
<figcaption>Periodic error of 0.6 m MonteBoo telescope (imperfect mount example)</figcaption>
</figure>
<p>
The above figure shows horizontal coordinate of star Menkar for ten
periods of mount on MonteBoo observatory. The periodic pattern is
result of the periodic error. The slow decreasing of the graph
shows difference between angular velocity of the telescope and Earth rotation.
</p>
<h2>Similar Tasks</h2>
<p>
The above example of determination of the periodical error describes
how to get a list of coordinates of
a star on frame. One can be generalized on any task
where coordinates of moving objects are required:
</p>
<ul>
<li>Telescope alignment </li>
<li>Tracking of fast moving objects: satellites, asteroids or comets</li>
</ul>
<h2>See Also</h2>
<p>
Manuals:
<a href="man_timeseries.html">Timeseries</a>,
<a href="man_aphot.html">Aperture Photometry</a>.
Tutorial:
<a href="lctut.html">Light Curve</a>
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