OOPS. These were all in INCHES, not FEET!
D’oh!! and Duh!
every single number in that table was supposed to be divided by 12 because there are, duh, 12 inches in a foot.
I have some bad news for myself and friends on the star-testing front. It turns out that even though it’s quite conceivable to make a source of light appear as a point for all practical purposes, and not too far from the telescope, I was forgetting all about spherical aberration.
The problem is that we don’t design and fabricate our telescopes so that they can look at birds or neighbors or even distant trees. Instead, our goal is to focus on sources that are INFINITELY far away – hundreds of thousands of miles or kilometers away at the very closest (i.e., the Moon and some comets). Our mirrors are designed to be paraboloids, which reflect light perfectly and to a point IF and ONLY IF the rays of light that hit the mirror are perfectly parallel to each other and to the axis of the mirror. But if the object being viewed is closer, you get a distortion that is known as Spherical Aberration. If you have objects that are, say, 8 feet away, the surface you want is a sphere with a radius of 8 feet, NOT a paraboloid. If you test a mirror at distance of merely, say, 40 feet, like I was planning to do, then your results will be all bogus: if the telescope passes the star test at that distance, then it definitely will NOT work on the stars.
Which means that all of my rejoicing over having been able to make small holes is pretty much worthless. The source has to be much, much farther away than I thought. How do I know? I finally got a chance to re-read a section of Harold Suiter’s famous book Star Testing Astronomical Telescopes (2nd edition) and on page 2 he has a table that shows how much you have to multiply the focal length of the telescope to avoid spherical aberration.
He does not give these distances in actual feet or meters, so I thought I would calculate those distancers. It’s not pretty.
So, for example, if you have an 8 – inch diameter telescope mirror, which you made to be f/5 (ie with a focal length of 40 inches, pretty typical with us), then you need for your point source to be 880 feet away from your scope,. In metric units, that would be a 20 cm diameter and a distance of 268 meters.
I do not have any idea how we are going to be able to arrange to hang a light source of any type at these distances. Notice that an 18 inch, f/5 telescope (46 cm) needs to have its point source be over 4400 feet away (1344 meters)!!!!
Thereare a couple of somewhat-distant radio towers visible from the parking lot of the Chevy Chase Community Center, but how on earth would we ever get permission to hang a tiny christmas tree ornament on one of them?