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Missile Defense

Technology has always found its greatest consumer in a nation's war and defense efforts. Since the last attempts at a "Star Wars" defense system, has technology changed considerably enough to make the latest Missile Defense initiatives more successful? Can such an application of science be successful? Is a militarized space inevitable, necessary or impossible?

Read Debates, a new Web-only feature culled from Readers' Opinions, published every Thursday.

gisterme - 03:06pm Feb 8, 2002 EST (#11360 of 11364)

rshow55 2/7/02 3:41pm

"...If Chaisson's 1 arc second number is the right one to use for the illumination -- there is no reference available, with respect to the missile, better than 1 arc second -- which would spread a line source to a 30" beam in 100 miles -- not nearly good enough. Nor is there light enough on the return, for long enough -- any light from the illumination onto the missile will be attenuated, on the way back, more than ten million fold..."

I haven't read Chaisson's book, Robert; but I think you may be misapplying the 1-arc second resolution figure. Your implication is that an arc second is not good enough resolution to track an ICBM through 100 miles of atmosphere. Could that be so? Let's check. Hmmm...how large an angle is an arc-second?

http://whatis.techtarget.com/definition/0,,sid9_gci524077,00.html

"The second is sometimes specified as a unit of angular measure, especially in astronomy and global positioning. In these contexts, it is also known as an arc second or a second of arc, and is equal to exactly 1/3600 of an angular degree or 1/1,296,000 of a circle. Sixty arc seconds comprise an arc minute; 60 arc minutes comprise an angular degree. One arc second of latitude at the earth's surface corresponds to a north-south distance of only about 31 m."

So an arc second is one thirty-six hundredth of one degree of arc. You knew that didn't, you Robert? Just making sure that everybody else knows what an arc second is too.

So how small of an angle is that really? Let's suppose we have a piece of plywood that's 1 meter square. Presuming that it's flat side is kept facing the observer, how far away would that piece of plywood have to be taken for the visual angle it subtends to equal 1 arc second? Let's see. Using a right trangle forumla, (because you claim to understand that, Robert), with half the diameter of the square equaling the opposite side of the right triangle(O)and the angle being half the total angle (V), the distance to the square would be the length of the adjacent side of the trangle (A). That distance is given by:

A = O / TAN(1/2 V)

So for V = 1 degree, the square would be

A = .5M/TAN(.5 degrees) = 57.3 meters away

for V = .01 degrees

A = .5M/TAN(.005 degress) = 5,730 meters away.

You can see that the relationship of distance to angle subtended is linear.

For one arc second the distance would be 36 times that or 206,280 meters. That's 206.3 kilometers. That's about 128 miles. That's roughly the distance from Los Angeles to San Diego. For a telescope with an order of magnitude better resolution, 0.1 arc seconds, as your reference indicates the HST has, the 1 M square would just be visible at about 1,280 miles. That's about the distance from Los Angeles to Seattle.

So given a flat earth, a 1-meter square piece of plywood in Seattle, viewed flat-on from Los Angeles would subtend a visual angle of 0.1 arc second. That's a really tiny angle...About 0.48 microradians.

So what can cameras on the HST really resolve?

http://www.geocities.com/CapeCanaveral/Hangar/5421/hubble.html

HST Faint Object Camera...

"...The FOC offers three different focal ratios: f/48, f/96, and f/288 on a standard television picture format. The f/48 image measures 22 X 22 arc-seconds and yields resolution (pixel size) of 0.043 arc-seconds. The f/96 mode provides an image of 11 X 11 arc-seconds on each side and a resolution of 0.022 arc-seconds. The f/288 field of view is 3.6 X 3.6 arc- seconds square, with resolution down to 0.0072 arc-seconds."

The 1M square piece of plywood would subtend an optical angle of 0.0072 arc seconds at a distance of 17,777 miles. 0.0072 arc seconds is an angle of 34.5 nanoradians.

(continued)

gisterme - 03:10pm Feb 8, 2002 EST (#11361 of 11364)

continued...

Now that everybody's on the same page about how tiny an angle an arc second is, Robert, let's consider your application of this 1 arc second atmospheric spreading thing. Here's what you've said:

"...If Chaisson's 1 arc second number is the right one to use for the illumination --..."

It isn't right for the illumination, Robert, it's right for the resolution of the return detector. The outgoing reference beam wants to illuminate the entire ICBM...makes it much easier to see...like an airplane caught in a searchlight...

"...there is no reference available, with respect to the missile, better than 1 arc second..."

Wrong answer and another wild conclusion not based on the reference you gave. What Caison's reference means is that using 1995 a ground-based telescope, looking through the thickest part of the atmosphere, without adaptive optics, you'd just be able to make out the 1 m square at a distance of 128 miles above the telescope. The 1995 reference you posted says that the HST gives a full order of magnitude better performance than that. The reference link included above says the Faint Object Camera has a resolution of 0.0072 arc seconds. That's 1/138 arc second! So things have changed a bit since 1995.

Anyway, using the equation above, a 20 meter tall x 3m wide ICBM at a distance of 120 miles would subtend an optical angle of about 20 arc seconds along its length, and 3 arc seconds diameter-wise. Well within the resolving power of even a 1995 non-AO telescope. Even with only 1 arc second resolution "seeing" a brightly illuminated 20x3 arc second target would be quite doable. With the order of magnitude improvement in performace offered by present day adaptive optics over the 1995 telescope, and the removal of six or seven miles of the thickest part of the atmosphere it should be a peice of cake even at 10 times the distance.

Those are not feelings, Robert, those are proper applications of your own reference that you apparently don't know how to do. You're reference proves that what you say is impossible, is actually quite doable using existing technology. Sorry to rain on your parade. And you're right about one thing...there are no classified numbers involved there and the reference material would be almost universally accepted.

rshow55 - 03:10pm Feb 8, 2002 EST (#11362 of 11364)

I'm paying attention . . .

gisterme - 03:12pm Feb 8, 2002 EST (#11363 of 11364)

That's fixed. Sorry for the screwup.

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