Sky and Telescope - September 2018 - 39

to slowly turn the polar axis through an angle of at least 30°,
and wait a few more seconds after you stop turning the axis
before closing the shutter. It's also possible to use two static
exposures made before and after you turn the polar axis, but
you must be careful if you touch the camera not to disturb its
position between the exposures.
The spreadsheet was developed in Open Office and converted
to Excel format. An overview of the mathematics is given in the
instructions that you download with the spreadsheet.
Two stars would be sufficient for the calculation of the
center of rotation in the star-trail image and its deviation
from the celestial pole. But with three stars the accuracy
improves. Moreover, three stars offer a way to check the
input data, since the angles of a triangle formed by the stars
in the image should be similar to those of the triangle in
the sky. If there was an error in the identification of a star
or a faulty coordinate entered in the spreadsheet, the angles
would not match.

Practical Experience
From where we live in the Northern Hemisphere (Germany),
my colleagues and I have successfully aligned multiple telescope mounts to the celestial pole with this method. Analysis
shows the method to be accurate to about 0.01°.
An important precondition for good results is the rigidity
of the camera support and the stability of the mount itself.
In one case we had two cameras on the telescope at the same
time. One camera was mounted on a small ball head, and its
results differed significantly from those of the other camera

mounted on a solid wooden support. I'd rather trust the latter. Stability of the lens is another critical point. The focusing
mechanism should have no play, and a lens with a fi xed focal
length may be better than a zoom lens.
When all precautions have been taken to make a good
image and an exact evaluation, it is highly desirable to make
the necessary adjustment to the altitude and azimuth of the
mount's polar axis with the same degree of accuracy. But this
is not always easily done. A heavy mounting may have jerky
movements, and it may be difficult to hit the target exactly.
Or the alignment can change in unexpected directions when
the mount's screws are tightened.
If the mounting has no calibration marks on its adjustment screws for the altitude and azimuth, the spreadsheet
can give some support by conversion of the necessary corrections to the number of turns of the screws. But you may want
to monitor the corrections by watching a star in a calibrated
reticle eyepiece. In any case, you can make a new star-trail
image after the corrections to verify the result.
So far we have had no opportunity to use this method in
the Southern Hemisphere, but it should be applicable there
too. I welcome feedback from other users, especially those in
the Southern Hemisphere.

¢ JÜRGEN KAHLHÖFER is retired from a career as a medical
physicist in radiotherapy and nuclear medicine. He is currently
a board member of the observatory of the adult education center in Neumünster, Germany, and can be reached at juergen.
kahlhoefer@web.de.

DENNIS DI CICCO

q Digital photography has made it easier than ever to create a classic fixed-camera image showing stars circling the celestial pole, as in this example
made during the 2011 annual Stellafane convention in Springfield, Vermont. A similar image made by rotating the camera on an equatorial mount's
polar axis serves as the data source for the author's polar-alignment spreadsheet.

sk yandtelescope.com * S E P TE M B E R 2 018

39


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Table of Contents for the Digital Edition of Sky and Telescope - September 2018

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Sky and Telescope - September 2018 - Cover1
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Sky and Telescope - September 2018 - 1
Sky and Telescope - September 2018 - Contents
Sky and Telescope - September 2018 - 3
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