How Telescopes Really Work and What You Can See Through Them

For my birthday a few weeks ago (40!) I received an 8" dobsonian telescope from my wife and her family. Of course the weather here in Northern California suddenly took a turn for the worse immediately after I brought it home, but there have still been a few clear nights.

One of the frustrating things about astronomy is that what you can see with an amateur telescope from your back yard in a well lit city is quite different from what you can see from the wilderness with a telescope the size of a truck. Unfortunately, even a great book like The Backyard Astronomer's Guide is dominated by the latter type of picture (like that fantasic picture of the Andromeda galaxy on its cover). So I thought I'd tell it like it really is and give you an idea of what you can see from my location.

How Telescopes Work

Before that, I want to mention something about telescopes. My telescope is a Newtonian reflector and if you look at the pictures on Wikipedia you'll notice that the secondary mirror forms an obstruction that blocks some of the light entering the telescope. A frequently asked question is "why can't you see the obstruction through the scope"? In fact, if you put your hand in front of the aperture the effect on what you see, if the image is in focus, is negligible, just a little darkening. The explanation is very simple, but nobody seems to phrase it the same as me.

The idea is this: a lens, that's in focus, is a device that converts direction into position. Suppose the telescope is oriented along the x-axis. Think of a ray of light as having the equation y=mx+c. Think of m as the ray direction and c as its position. If that ray passes through a lens or mirror and is projected onto a screen, denote the position at which it arrives on the screen by f(m,c). It's clearly a function of m and c. The crucial point is that for a screen at precisely the focal length away from the lens or mirror, f(m,c) is independent of c. That's the raison d'être of a telescope. All rays with gradient m arrive at the same point. So we end up with a bright image because we can collect lots of rays coming from the same direction. But also, any information about the ray's position, ie. c, has been erased. Information about the shape of the obstruction is positional information contained in c. This has been erased, and hence you can't see the obstruction. In practice you really need to consider primary lens (or mirror), plus eyepiece, plus lens of the eye projecting onto the retina, but the principle is the same. For the more formally inclined, the erasure of c information corresponds to a zero in a transfer matrix.

In brief: a lens or mirror focussed on infinity is a position eraser.

And What You Can See Through Them

Andromeda Galaxy

My first two subjects were probably the same as every other amateur astronomer. I started with the Andromeda galaxy. Through binoculars it looks like a faint fuzzy blob. And here's the truth of how it looks through a telescope: it looks like a fuzzy blob, at least from a well lit city. I couldn't make out any kind of structure at all, let alone spiral arms. It didn't even look elliptical, just a circular blob with brightness falling off radially from the centre. I also saw one of its neighbours, M32 or M110. At first I thought that the fuzzy blob was the galaxy and that I needed more magnification to see detail. But now I think that I was seeing just the core of the Andromeda galaxy with the arms filling a wider area but remaining invisible because they're no brighter that the sky in my part of the world.

Orion Nebula

The Orion nebula, on the other hand, was stunning! In outline, it looked remarkably like the picture at wikipedia, but without the colour. When I switched to using a filter (a narrow bandpass Lumicon UHC filter) it became even clearer. Not only could I clearly see the shape of the nebula but I could also see structure all the way through the cloud. It looked even better after I'd been viewing it for a while, probably as my eyes became better adapted to the dark. This was the best thing I've seen through a telescope ever!

Almach

I'll mention the last thing I looked at: γ Andromedae, otherwise known as Almach. It's a binary star system that can't be resolved with the naked eye. I used a wide field of view lens and was disappointed to see that it still looked like a single star. But then I switched eyepieces and I saw it - a beautiful pair of stars, one brighter and yellowy orange and the other deep blue. You read about the colour of stars but it's often a disappointment. A single star on its own tends to look white with a hint of colour because the eye doesn't register colour well in such low light conditions. But when you see two contrasting stars so close together it makes a world of difference. The deep blue of the smaller star was unmistakable and the blue really was astonishingly blue. That must be quite a sight for the γ Andromedans. But I should add that the blue star is in fact a triple star system in its own right, so γ Andromedae is actually a quadruple star system. I was unable to resolve more stars than two (and you can only tell there are four by inference from spectrography, not direct viewing).

I also tried to find the Crab Nebula. I'm 99% sure that I was pointing at the right part of the sky and I did in fact see a faint smudge just at the limits of my perception. I had a jiggle the telescope around a bit just to be sure I wasn't imagining it, but sure enough, it appeared to be attached to the sky, not the scope or my eyes. But it certainly didn't look like the pictures.

Anyway, now you have a better idea of what you can see from a city.

Solar Astronomy

I mentioned recently that I'd been volunteering at the local observatory/science museum. You might think there wasn't much astronomy to be done during the day. It turns out you can view Venus. But during the day, if you're armed with the right filters you can also observe one of the most amazing and dynamic astronomical phenomena that are visible: the Sun.

Normally the sun looks like a bright disc of uniform colour. But view it through a hydrogen-α filter and it suddenly transforms into a bizarre alien object. And amazingly you don't need a billion dollar satellite to view the sun this way. A $500 telescope is good enough. Follow that link and you'll see pictures actually taken with that telescope (and subsequently image processed...). You can clearly see solar granulation, filaments, prominences and some of the structure around sunspots.

The problem with solar viewing is that the Sun pumps out vast quantities of energy fairly indiscriminately following a Planck distribution. This tends to overwhelm phenomena that emit at a specific wavelength. So you need an incredibly narrow band pass filter that only allows light at a given wavelength to be transmitted. In this case we were using a filter whose bandwidth was less than 0.1 nanometre to view emissions at 656.3nm caused by electrons dropping from the third to the second energy level in hydrogen atoms.

Making filters this good is itself is an amazing feat. What material could possibly have the correct properties to allow that degree of selectivity? As far as I can make out from the sales blurb, the filter on this telescope is in fact a Fabry-Pérot etalon. Essentially it's two highly reflective (but still slightly transmissive) parallel layers. Consider light travelling perpendicularly through such layers. It might travel straight through. Or it might bounce 2n times before continuing on its way. So the light we see is the sum of light that has bounced 0, 2, 4, 6, ... times. If all of these reflected rays are in phase they'll constructively interfere. Otherwise the infinite sum will be over widely varying phases resulting in destructive interference. So by choosing the correct spacing between the layers we can ensure that only one wavelength (and higher harmonics of it) will be transmitted. You can imagine the difficulty in getting the precise layer separation and that's why these filters can cost many thousands of dollars. And fabrication isn't the only problem - it also needs to be stable even though it has solar energy falling directly onto it.

Anyway, I'm so taken with this solar astronomy stuff I'm going to read this book. And I'll leave you with this link to some even more amazing pictures of the Sun.

(BTW In lieu of having a way to attach my camera to the solar telescope I borrowed the picture from here. Note that the comment is now out of date, the solar neutrino problem has since been solved.)

The Solar Corona Problem

It's all been a bit abstract a bit lately. So I thought I'd bring things down to Earth a bit. But only metaphorically speaking.

I've decided to volunteer some time at the Chabot Space and Science Center. I'll mainly be manning their 20" reflector pictured here:



Basically I'll be something like a tour guide for visitors, answering any questions they may have. Only during daylight hours for now. It's a good excuse to read up a little on astronomy and if I stick at it then one day I'll be qualified enough to work the telescope at night, and maybe even catch a few photos through it with my own camera.

Anyway, one of the visitors was asking about the temperature of the Sun. As any photographer can tell you, the surface of the Sun has at a temperature of 5800K. But observations during eclipses show that the corona has some pretty weird spectral emission lines that correspond to atoms at very high temperatures, of the order of a few million K. Strangely, this is a bit of a mystery. At first you might think what's the problem? There's a gigantic fusion reactor with something like 2×10³⁰kg of fuel burning right next to it. But the problem is this - how is that energy getting to the corona when the surface of the sun is at 5800K. As everyone knows, heat doesn't generally flow from a cooler region to a hotter one. To me this is much more interesting than the Solar neutrino problem. Neutrinos don't play a large part in anyone's lives and all of the evidence that there is even a problem rests on indirect evidence and theoretical work. But the solar corona problem is pretty immediate. You can literally see the temperature of the sun's surface and the anomalous high temperature emission lines require nothing more abstract than spectrography. When a visitor asked about this I had no answer so I decided to read up on the issue.

Turns out there are a few possible explanations, though none of the corresponding predicted physical proceses have been directly observed yet. My money is on Alfvén waves. These are essentially waves that form solutions to the combined Maxwell and Navier-Stokes equations. If you imagine wave travelling down a whip when it is cracked, all that enerfy gets to the end of the whip and gets concentrated in the tip resulting in it moving at supersonic speeds. Something similar may be happening with these waves. They proceed out from the sun but when they get to the corona there's nowhere for the energy to go except into heating it to incredible temperatures.

Anyway, next time someone asks about the corona I won't be telling them this. Most people don't want this much detail and even if they did, they have impatient kids with them. But it's good to have people prodding me to read up on interesting physics.