The Thousand-Mile Telescope

Next week I will go back to talking about my algorithm, but right now it's snowing when it should be springtime, it's colder outside at this time of the year than it has been ever before in my life, and I think it's time for me to come out of the closet and tell you what I really want.

I want a Thousand-Mile Telescope.

Does that sound like an awfully long focal length for a telescope?  After all, the CDK700 I am using right now is only 15 feet.  Well, however bad it sounds the truth is a lot worse.  What I want is a telescope a thousand miles in diameter.

OK, so the first questions we should ask are Why Do You Want a Thousand-Mile Telescope?  And after that, How Can We Make a Thousand-Mile Telescope?

One Million Dishes in One Hundred Arrays.

Actually, these two questions are related, and I need to answer a little bit of the second question first.  We are going to build a Thousand-Mile Telescope by first making a One-Mile Telescope, and then making 999,999 more just like it.  A million One-Mile telescopes add up to have the surface area of a single Thousand-Mile Telescope. 

But!  What can we do with a telescope that's made of many separate mirrors?  There are two ways of combining the dishes so that they become a single instrument.  The easy way is to simply add the images together.  (We will need 40-bit per channel color images.  Heh heh.)   But that only gives us the light-gathering power of the TMT.  Not the resolving power.  Can we get the resolving power?

Yes, but we'll have to work at it a little.  We need a 2D array of dishes a thousand miles in diameter, constructed such that it is possible to know the location of each one-mile dish relative to the others to an accuracy of about 1/4 of a wavelength of violet light, or about 4 millionths of an inch.

Now we can't possibly do that with all million dishes, so what we'll do is we'll make an array like this:

That's a circular array 1000 miles across, containing ten thousand dishes.  Well, close enough.  (And only a few are shown, to give you the idea.)  The dishes are arranged on aluminum trusses that can move them precisely and measure their positions.  This array, with a little bit of computing power, can simulate the resolving power of a TMT.

So we make 100 of these, and add all the images together.  Boom!  You have both the resolving power and the light gathering power of a true TMT.

What Can It See?

The resolving power of a telescope, in radians, is 1.22 * wavelength / diameter.  The wavelength we care about is the worst case (longest) wavelength of visible light, which is red, which is 25 millionths of an inch -- 2.5e-7 inches.  Our diameter is 1000 miles, which is 6.3e7 inches.  1.22 * 2.5e-7 / 6.3e7 == 0.48e-14 radians -- call it 5e-15 radians.

At a radius of 1 light year, 1 radian is .. um .. 1 light year -- about 6e12 miles.  Multiply that by my 5e-15 radians and you get 30e-3, or 3e-2 miles.   So it's about 1 mile at 30 light years,  5 miles at 150 ly, and so on.

With this telescope, here is what our planet would look like at 1000 light years:

The Earth from 1000 light years with the Thousand Mile Telescope

 



Now it wouldn't really be all lit up like that, because ... um ... the Sun would be in the way.  But whatever you could see of the planet would have that level of detail.

And here it is from 25,000 light years -- the distance to the galactic center.

The Earth at the distance of the galactic center, with the TMT.

With the Thousand Mile Telescope, you can see half the galaxy well enough to know whether you would like to live there.

And over a distance of a thousand light years -- a volume containing 10 million star systems -- you can see planets well enough to see this:

Lights in the Night

That's why I want my Thousand-Mile Telescope.