Wednesday, November 07, 2007

The vastly overdue Shane reflector post

Back around the dawn of time I blogged about my visit to the Lick Observatory, and concluded by saying that a post on the 3-meter Shane reflector was "up next". Here it is. In my defence, I am following in the footsteps of a master here.

There's more, by the way, but it's not done, and if I wait for it this will never get blogged. You've heard the saying, "The perfect is the enemy of the good"? In my world, the adequate is the enemy of the incomplete and horribly delayed.

On to the scope.

The Mirror

For a while, this telescope was the second-largest in the world, behind the 200-inch (5-meter) Hale reflector at Mt. Palomar. And in fact this telescope came into existence as a by-product of the Hale telescope. No one had ever made a 200 inch mirror before, so they practiced with a series of test blanks to make sure they could cast that much Pyrex at once. The largest test blank was 3 meters in diameter, and it turned out fine, so they proceeded with the 5-m beast. The 3 meter blank went into a warehouse. It had never been intended to become a working mirror, it was just a prototype. But some UC astronomers got in touch with the folks at Cal Tech, who sold it to UC for something like $50,000, which was basically giving it away.

Like the 5 meter Hale mirror, the 3 meter test blank has a honeycombed back surface to reduce the mass of the mirror. From the reverse it looks like a waffle, with big spaces going deep into the glass. So deep, in fact, that when the blank was ground into a mirror, it could not be figured into a sharp curve or the center of the mirror would have been too thin. Most big observatory telescopes are fatties with short focal ratios (at least at the Newtonian focus; more on this in a later post). The Shane reflector has such long lines because the curvature of the mirror is so shallow; light rays coming off the primary mirror do not converge as sharply as they would if the mirror formed a deeper bowl. And a long telescope needs a big dome, so the Shane dome is huge. In contrast, the Automated Planet Finder will be a 2.4 meter telescope and it is going in a dome with less than half the diameter of the Shane dome.

Celestial Motion and Telescope Mounts

There is another reason why the Shane dome is huge. It's because of the telescope's mount. The rotation of the Earth means that from a fixed observing spot, everything in the sky appears to rotate. The only exceptions are the celestial poles; the north celestial pole is marked by Polaris, the North Star. It is the point of light around which all the stars are seen to whirl in long-exposure photographs like the one shown here (image swiped from here).

This constant motion of celestial objects is a real pain in the butt if you want to look at something at high magnification for more than a few seconds. You need some way to keep the telescope pointed at the same spot in the sky even though the Earth is rotating underneath it.

The simplest kind of telescope mount is the alt-azimuth mount. Think of how cannons are mounted in turrets. You have to be able to slew the barrel from side to side and raise it up and down. That's an alt-az mount. The problem is that celestial objects describe complex paths through the sky. Think about the southernmost stars you can see. They rise in the south-southeast, describe a very shallow arc across the sky, and set in the south-southwest. To track one requires constant adjustments in both altitude and azimuth; in fact, not just constant adjustments, but constantly varying adjustments. A clock drive won't cut it.

Now we have computers that can calculate these constantly varying adjustments and control the motors needed to track celestial objects using an alt-az mount. So a short, fat telescope like the APF can have a simple alt-az mount and sit in a very small dome (comparatively). But this level of computer control is a comparatively recent development in the history of astronomy; it was not available when the Shane reflector was built.

The other type of common telescope mount is the equatorial mount. Like an alt-az mount, an equatorial mount has two axles. The first axle is aligned with the Earth's axis of rotation (for backyard astronomers, it points toward Polaris). Slewing the telescope around this axis moves it in the equivalent of longitude (called right ascension in astronomy). The second axis is at right angles to the first, and moves the telescope in the equivalent of latitude (called declination).

Any sufficiently distant object in the sky has fixed coordinates for right ascension and declination. These are the fixed stars, and it is not hard to see why the ancients thought they were attached to the inside of a giant hollow sphere. Once a telescope on an equatorial mount is lined up on its target, it needs no further adjustment in declination (or latitude), and it can be adjusted in right ascension (or longitude) at a fixed rate--the rate at which the Earth rotates.

Compare this to the alt-az system, in which even the fixed stars have constantly varying coordinates in both axes, and keeping a 'scope on target requires adjusting its movement around both axes at constantly varying rates. The alt-az system does have one major advantage over the equatorial system, which is that it can be mechanically much simpler (assuming you have the computer power to keep it tracking); basically the telescope is on a simple turret or cannon-style mount.

If you need a better way to visualize this, most planetarium programs will project alt-az and equatorial grids on the sky (including Stellarium, which is free and a cinch to use). Speed up the time lapse and see what happens. The alt-az grid stays fixed and the stars move across it. The equatorial grid moves with the stars; the gridlines themselves rise and set as the whole grid rotates around Polaris (from our fixed viewpoint).

The Mount

The Shane reflector was one of the last big observatory telescopes to be completed before computer-controlled alt-az mounts became practical. Consequently, it is on one huge-ass equatorial mount. A giant metal fork holds the telescope; the whole assembly weighs 145 tons. The handle of the fork is the polar axis, aligned on the north celestial pole. The tines of the fork hold the telescope in the declination axis bearings. The whole thing is so well balanced that the right ascension drive motor, which turns the whole 145-ton rig, is a 1/25 horsepower electric motor that can sit in the palm of your hand.

A Word on Aperture

There is a saying in astronomy: Aperture Rules. Department store telescopes are often sold on (wildly inflated) claims about magnification, and when people see a telescope often the first thing they want to know is what magnification it yields. The answer for any telescope is, "Whatever you want, depending on what eyepiece (or optical instrument) is fitted." You can point a little department store scope at Jupiter and crank the magnification up to 1000x if you like, but beyond about 30-50 power the image will be too dim, too shaky, or just impossible to bring into focus because of poor optics.

Fact is, you can see a LOT at very low magnification. A pair of 7x35 binoculars only magnifies at 7x, but it will show you the Galilean moons of Jupiter, the Andromeda galaxy, the Orion Nebula, the Double Cluster in Perseus, and literally hundreds or thousands of other celestial objects. Binoculars often beat very small telescopes because they don't try to overmagnify; instead, they are built to optimize another variable: aperture.

When your eyes are fully dark-adapted, your pupils are about 7mm (+-1mm) in diameter. Now, I'm sure you've seen a zillion cut-away views of what eyes look like inside, so you know that your lens is bigger than your pupil and your retina is larger still. When you are looking at stuff up close, converging light rays can fit through your pupil and diverge on the other side to strike your much larger retina. But when you look at something far off, the light rays coming from it are parallel with each other and perpendicular to your pupil, so the size of the pupil aperture puts a very firm limit on how much light your eye can gather. The amount of light gathered is proportional to the area of the aperture; for a pupil with a diameter of 7mm, the aperture area is (pi)(r)^2 or just over 38 square mm.

The optical train of a binocular or telescope is effectively a funnel for light, gathering it over a large area and condensing it to pass through your relatively small pupils. Back to the 7x35 binoculars. Each primary lens is 35mm in diameter--five times the size of your pupil in linear dimensions, and 25 times larger in area (961.5 square mm). So you can gather 25 times as much light with binoculars as you can with the naked eye. A pair of 7x50s will be even better, with the aperture of each lens being just over seven times that of your eye in linear dimensions, and 49 times larger in area (1962.5 square mm). So although they are only 43% larger than the 7x35s in linear terms, the 7x50s actually gather just over twice as much light.

A good beginner's telescope (i.e., not a department store cheapie) will offer three to six inches (76-152 mm) of aperture. A three inch scope gathers 118 times as much light as one of your eyes. A six inch scope gathers 471 times as much as your eye, and four times as much as the three inch scope. Objects that are nearly invisible to the naked eye and dim blurs through binoculars can look awful purty when viewed through a six inch scope.

Now it is easy to see why the history of observatory telescopes has been one long quest for more aperture. At 3 meters in diameter, the Shane reflector has a mirror area of just over 7 million square mm, or 186,000 times the area of one of your dark-adapted pupils. The twin Keck telescopes on Mauna Kea (shown above) have mirrors 10.2 meters in diameter. Each telescope has a mirror area of 326 square meters, or 326 million square mm--almost 50 times more light-gathering area than the Shane reflector, and almost ten million times the light gathering power of the naked human eye.


What's "up next"? There is an unfinished section on the different foci of the Shane reflector, and all of this is just buildup to blogging about the Lick refractor, the one I put my eyeball next to back in September. All of this is subject to whatever delays come in because of teaching, doing enough writing to mollify my coauthors, feeding the monkey over at SV-POW, unanticipated manias, my general unreliability, and the erratic changes in topic and post rate that I deliberately cultivate here at ADV. Still...

Stay tuned, true believers.

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Blogger Mike Taylor said...

... doing enough writing to mollify my coauthors

When did that start happening? Did I blink?


1:22 PM  
Blogger Dr. Vector said...

It probably happened when you were recycling the same image you've used before on SV-POW!, slackass.

6:00 PM  

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