From: "Mel Bartels" 
To: 
Cc: 
Reply-To: "Mel Bartels" 


Alt-Alt or El-El telescopes (abbreviations for Altitude-Altitude or
Elevation-Elevation) look like yoke mounts laid flat.  The yoke is
horizontal.  Typically the polar axis of the yoke points towards a pole, as
that area is usually deemed less important and thus left inaccessible,
unless the mount is made more complicated by an offset-yoke design or
horseshoes at each end ala a mirrored-Palomar 200 inch.  By moving the
scope in the primary axis, the scope rises in elevation.  By moving the
scope in the secondary axis, the scope also rises in elevation, but at a 90
degree angle to the primary axis.  Since movement in both axes raises the
scope in elevation, the name is appropriately given.

For people in the mid-latitudes, field rotation can be obtained by looking
at the field rotation of a standard altazimuth (Dobsonian styled) mount
near the polar horizon.  That is, an Alt-Alt telescope is essentially a
Dobsonian that is tipped over at 90 degree angle to point to pole.  The
Alt-Alt's field rotation at the sky's zenith is the same as the field
rotation of a Dobsonian aimed at the polar horizon.  A typical rate would
be 0.18 degree per minute of time.  So if aimed at the sky's zenith, a
digital imager can go for several minutes before rotation shows in the
corners of the digital frame.  A traditional Dobsonian might have say 6
times more image rotation when aimed within 10 degrees of the sky's zenith,
and will have to cut the exposure that much shorter.

Consequently, often the imager will keep exposures to a couple of minutes
and avoid the zenith when using an altazimuth scope, or, add a field
rotator unit at the focuser.  This field rotator unit can also be a
mechanism that rotates the entire tube assembly, instead of rotating the
focuser.  Some consider this no more difficult to make than the
focuser/derotator.  And, it is possible to move this third axis of motion,
added to eliminate field rotation, to elsewhere in the mount.  More on this
in a bit.

The primary axis of an Alt-Alt telescope need not be aimed at a pole.  It
can be aimed anywhere, depending on what you wish to optimize.  Imagine a
star or a satellite moving in a short arc across the sky.  It is possible
to orient the Alt-Alt in such a manner as to minimize overall motion of the
two axes, or to minimize the highest speed of the two axes.

As long as we are moving the Alt-Alt's primary axis in a circle and aiming
it at different horizon points, why not turn it into a full fledged axis
and motorize it?  We have what is called a 3-axis mount, or what I will
call an Alt-Alt-Az mount.  By suitable orientation, any object (ie, a
satellite) scribing a great circle can be tracked with motion in a single
axis.

By tracking in the third additional azimuth axis, the field rotation that
occurs while tracking a celestial object can be stopped completely.

For instance, consider the following scenarios (I wrote out an algorithm in
Java last night and tonight to do the 3-axis initializations and tracking
numbers - that's where the data comes from).  All these use my northern
latitude of 44 degrees.

Primary axis aimed at northern pole, object at zenith: to null field
rotation over a 1 minute exposure, the axes must move the following
amounts: alt-primary      0.1798 degrees
alt-secondary -0.0012 degrees
azimuth            0.1737 degrees

That's pretty nice - easy small amounts of motion in all three axes to
track a celestial object with no field rotation. Primary axis aimed at
northern pole, object in the east: to null field rotation over a 1 minute
exposure, the axes must move the following amounts: alt-primary      0.2699
degrees
alt-secondary  0.1799 degrees
azimuth            0.1737 degrees

Hmm, what's this - the azimuth rate seems suspiciously similar.  Let's try
it again for an object to the south. alt-primary      0.1797 degrees
alt-secondary  0.0000 degrees
azimuth            0.1737 degrees

Ok, too much for coincidence, and, if you think about this 0.1737 number,
and think about the distance tracked in equatorial coordinates over 1
minute of time, which is 0.25 degrees, this 0.1737 is the sine of the site
latitude times the tracking time!  No matter where you are aimed in the
sky, with the primary axis aimed at the polar horizon, the tracking rate in
the azimuth axis is constant.

Let's try this same game but with the primary axis aimed say at 90 degrees
azimuth, towards the east instead of the north. At the pole:
alt-primary      0.0000 degrees
alt-secondary  0.1798 degrees
azimuth            0.2357 degrees

Now aimed at object in the east:
alt-primary      0.0578 degrees
alt-secondary  0.1222 degrees
azimuth            0.2357 degrees

Ah, so the azimuth tracking rate is constant no matter where the scope is
aimed with the two Alt-Alt axes, and is about 1.36 times greater with the
azimuth axis aimed to the east - hmm, what relationship applies here
?

Remember where I mentioned that the field rotation compensation can be at
the focuser, or at the optical tube assembly?  Well, it can also be at the
azimuth axis of an Alt-Alt-Az scope.  We can generalize that any 3 axis
telescope can be made to track and null field rotation no matter its
orientation with respect to the sky.  The 3 axis scope can be an
altazimuth-field derotator, or, an Alt-Alt-Az mount.

I an imagining all sorts of interesting Alt-Alt-Az designs that could be
built by amateurs with ordinary skills and tools.  I have the software
routines - any takers ?

Mel Bartels

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