Pick a double star - any double star . . .

A simple challenge:

Choose a reasonably close double star. Look at the pair in your scope with an eyepiece of fixed focal length that splits the pair cleanly, but not widely. That is, you should see black sky between them - at least as much black sky as the image of the brightest star occupies.

Now do this – estimate how many of them could fit across the diameter – or radius – of your field of view. Just mentally stack them side-by-side and give it your best guess.

Then do the math. I’m curious to see if what happened to me, happens to others. Even if you know what to expect.

(Yes - I know this doesn't look double. That's explained later. )

So I put a 20mm Plossl in the 8-inch LX90 , examined Izar once more, and mentally marched the pair in even steps from the center of the field of view to the edge. A lot more seemed to fit than I first thought. My first guess was maybe 10 or 12 could fit across the field. I knew that couldn’t be right, so I tripled it. I decided 30-40 would be a more realistic estimate. Then I did the math.

Let’s call the separation three seconds of arc. The stars themselves, in an 8-inch scope, produce an image that is about one second of arc in diameter. (Yes, they are really point sources – but they don’t appear that way to us and the bigger the telescope, the smaller they appear – but they do take up space.) So this whole combination of two stars and the gap between them represents about five seconds of arc. We’ll throw in another second as a fudge factor for modest seeing conditions. So the whole package is six seconds of arc.

Now that’s hard to believe? Why? Because the 20mm Plossl on the 200mm F10 scope should yield a field of about 30 MINUTES of arc, or half a degree. So if this pair of stars was taking up just six seconds (or less) in the center of my field, that means I could fit 10 such pairs in every minute of arc, or 300 of these pairs across the full 30-minute field! Is this image of these two charming stars really that small?

I think part of my problem is I failed to appreciate the huge difference between degrees, minutes, and seconds. For my own enlightenment as I pondered this after my observing session, I built a simple scale model. I made a dot on a piece of paper about 1 mm in diameter. That’s small – one= twenty-fifth of an inch. But call that a second of arc. Then I drew a circle 60 mm in diameter – more than two inches. That’s a minute of arc. And a degree? That’s 60x60, or 3,600 mm which is about 12 feet! Obviously my paper was way too small ;-) Please feel free to check my math and tell me I have this all wrong – but what I get is a dot for a second, a 2.25-inch circle for a minute, and twelve feet for a degree. )

So using this scale, my fov of my 20mm eyepiece was about 6-feet in diameter. And my double was occupying about one-quarter of an inch. That would mean you could fit 48 of them in a foot and close to 300 in 6-feet.

Now among other things this does give a hint about the difficulty of representing a double on sky software or a chart. You can see in the image above how Starry Nights depicts the situation. Izar is shown as a dot about 10 pixels in diameter in a field of view that's about 550 pixels in diameter – so you could fit maybe 55 of these dots across the simulated field, not 300. You can actually play around with this representation in the preferences, making star images larger or smaller. Trouble is, when you get them down to something close to their real size they become very difficult to see! And as you undoubtedly noticed, at this scale Starry Nights does not show Izar as a double. You have to keep zooming in before it does that - but the eyepiece at this scale it was show as a double, albeit a delicate one, quite nice.

And I think that tells us something about brightness and our eyes and how we see a star. The only place I've seen this described is in an old, worn book I have called "All About Telescopes" that I got from Edmund Scientific back in the Sixties. (I found out it's still available – in a revised edition – and as my copy is pretty ratty, I ordered a new one. )

It says that a star has an angular diameter of about 1/20th of a second of arc – which means we shouldn't see it at allin any Earth-bound telescope. Except . . .

The light-receiving cones and rods in your eyes are actuated by any light beam, even though the beam itself may be so small as to light only a small portion of one cone. Hence, one star can "trigger" a light cone and the brain gets the same impression as if the cone were fully illuminated. But the telescope has to magnify a star 13X per inch of objective to fully illuminate one cone. Hence, even at the top magnification of 50X per inch, stars are magnified only about four times the naked eye view."

Fascinating! I don’t know if that is accurate science today – or even if it was accurate when it was published, but it makes sense to me. So at 100 power the stars were illuminating just one cone? And what exactly does that imply? I'd love to hear from anyone who can shed some more light on all this. (No pun intended.)

So why was my eye telling me that this pair seemed to be much bigger? The simple answer for me is brightness. We simply are fooled by something bright in the middle of our field of view. Afterall, how many people would guess that you could fit 11 full moons between the Pointer Stars of the Big Dipper? Most amateurs know that. They know that the moon is so small – and the sun – that it actually can be easily covered by the tip your little finger held at arms length. But it doesn’t look anything like that small because of its brightness. Same with the sun.

Being armed with this knowledge – and having just a few moments in which I could leave the sleeping puppies alone – I dashed out and tried a quick experiment. I hauled out a six-inch F8 DOB and looked at Mizar (not Izar, but the familiar double in the handle of the Dipper.)

Without checking the data on Mizar first I put in the 20mm Plossl and estimated the number of Mizar-Alcor pairs I could fit in the field by moving the pair across the field several times. My conclusion – close to four. And that’s what the math shows – four. That is, a 20mm Plossl in a scope of 1200 mm focal length yields a power of 60. The power into the 50-degree apparent field of the Plossl give a true field of view of about 50 minutes – 50/60. The separation between Mizar and Alcor is just about 12 minutes so you should be able to fit a tad more than 4 of these pairs across the widest part of the scope’s field of view. I would call my estimate well within the margin of error ;-)

Here's how Starry Nights represents this pair and fov:

BUT . . . when I looked at Mizar alone with it’s closer companion just 14-seconds away (not visible in the Starry Night image) , I had a devil of a time making an estimate. Being forewarned I would guess somewhere around 40 or 50. But do the math and it comes out closer to 200!

So what’s the lesson here? Well, if something comes close to filling the field – so that no more than say five-to-10 can fit, you may be able to estimate pretty closely. But when you’re dealing with something much smaller – well, it’s much smaller than you are probably going to think and guess. And I suspect that’s especially true if it’s also bright.

Come to think of it, one of the surprising images many have seen lately is of Saturn's rings being occulted by the moon. What is surprising here is how tiny Saturn is when seen next to the moon - much smaller than we might think, having seen Saturn in all its glory at the center of our field of view with no moon nearby. (To see that image go to the Astronomy Picture of the Day Web site.)

I know this isn’t earth-shattering knowledge – but it’s the sort of thing I find important. It worries me that the telescope tends to become another black box that we accept to readily. I’m continuously striving to understand the reality of what I see. So, for example, I know that pair of lovely pinpricks of light that we call “Izar” are really raging nuclear fires far larger than anything we can generate or imagine. Yes, they fit nicely into my eyepiece, but the truth is I’m seeing a pair of stars, either of which could swallow a million or more Earths.

Part of starting to grasp that reality is to understand how we can be fooled by brightness into thinking the image we are seeing is larger than it is.

Bottom line – anything that allows us to get a bit closer to the truth behind the information reaching our eyes is worth pursuing.

As always – I would love to here your comments and experiences in this regard and would be happy to post them here as part of this file.

Comments? Please send to gstone@umassd.edu