The Equatorial Imitation Game by Mel Bartels

Why does a telescope need to track?

Because the Earth rotates once every day, the stars at night appear to move across the sky in arcs. The telescope needs to follow the stars. We call this sidereal tracking or equatorial motion.

Equatorial mounts were invented to easily track the stars by rotating a polar axis at a slow constant rate (atmospheric refraction causes the tracking rate to slow ever so slightly near the horizons).

But the tipped polar axis in an equatorial mount adds bulk to the telescope and the popular German equatorial design requires counterweights, making transport and setup in the dark oftentimes a real chore.

Consequently much thought and innovation has gone into alternatives that imitate equatorial motion.

The altazimuth mount is often a more transportable and stable design but suffers from continuously varying tracking rates and field rotation at the eyepiece or camera. The Dobsonian, depending on your point of view, is either free from the complications that come with tracking devices, or is handicapped because the object drifts out of the field of view too quickly at higher magnifications.

The Poncet Platform and the Equatorial Table

A significant advance occurred in the 1976 with the invention by Adrien Poncet of the tracking platform, originally called a Poncet Table, but now more often called an equatorial table. He reasoned that if the astronomer was willing to accept limiting sidereal tracking time to say an hour before having to start over, then a flat platform could be devised that imparts equatorial motion to any telescope placed on top. Subsequently the Poncet Table evolved into what we call equatorial platforms that better support heavy telescopes and track more accurately.

All tracking tables suffer from the restriction that they are custom built to specific latitudes. I’ve worked to overcome this restriction with my omni-latitude table. Continue reading...

Designers invariably think of equatorial tables in terms of limited equatorial motion. The English Yoke mounting becomes the Alan Gee design with a pivot point and cylindrical bearing sector. The Horseshoe equatorial mount (think Palomar 200 inch telescope) becomes the modern equatorial table with dual cylindrical bearing surfaces.

But can a table that imitates equatorial motion such that it supports a telescope aimed in any desired direction be built from different motions, different placement of axes? Let’s investigate.

The Bartels Turret Table

Can an equatorial platform be devised using the well understood altazimuth Dobsonian design where the primary axis, aimed straight upward, spins like a platter and the secondary axis pivots at right angles much like a crane going up and down? We should only need a snippet of limited motion in both directions, potentially an easy to build design. We know conceptually that a three axis mount can perfectly imitate sidereal tracking motion and that the three axes can be arbitrarily aimed anywhere and in any order of preference. Is there a solution where a limited tracking time and a vertically oriented axis can be found such that the third axis can be foregone such that motion in only two axes is necessary? It is said that constraints help problem solving. I’m about to find out if that is true here.

I’ll use Sketchup, a free CAD program, to help picture the platform as it goes through its three dimensional motions. I’ll snapshot the platform as it begins tracking, and then take a second snapshot after one hour of sidereal tracking motion. I’ll then experiment with moving the snapshots around in order to find two axes of limited motion, one axis aimed upward and the other aimed sideways, just like a Dobsonian telescope.

Any flat table, as long as it pivots around the polar axis, will allow a telescope placed on top to be aimed anywhere in the sky and continue to track equatorially.

Here's the flat table oriented flat to the ground for a latitude of 45 degrees.

Now I'll rotate it through a half hour of sidereal tracking each way, snapshoting it. The three snapshots like this.

As long as their orientation is not changed, we are free to reposition the tables as desired, so I’ll place them so that a common point in their centers that represents a vertical axis of rotation. The tables intersect like this.

Here are the three tables from their south end: the first set the starting orientation, the second set a half hour into the tracking (the table is flat to the ground) and the final set an hour into the tracking, showing equal and opposite tip to the starting orientation.

The azimuth axis rotates +- 5 degrees as does the altitude axis. There is a slight tip to the azimuth axis of 0.6 degrees over the hour of tracking. That means a +- error in the eyepiece of 1/3 degree. For this to be an issue, the table will have to be polar aligned to 1/3 degree accuracy.

For latitudes closer to the pole the azimuth rotates more and the altitude roates less; the reverse occurs for shallower latitudes.

For a half hour of tracking, these numbers are halved.

The drive rates should vary by +- 2% causing a fraction of a degree positional error, but can be ignored for visual high magnification use.

The pluses of this design is that simple Dobsonian styled bearings can be used. The disadvantage is that the scope will tip a bit off-balance. The top plate will need springs to counteract the tendency to tipping.

There are other placments of the axes that can be studied also, but they are similar in nature.

So there's the result of my deisgn process. Onto other ideas, looking for constraints that lead to good solutions.