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May 19, 2004

Space Fleet - Observing

In terms of object detection in the inner solar system, optical and infrared are probably unmatched. Objects near earth's orbit are lit up by the sun, and observable at extreme range. Apollo capsules were observed orbiting the moon using earth-based optical telescopes, and astronomers think they've recently found the upper stage of Apollo 12, lost since 1971. Amazingly, they spotted it from the ground when it was twice as far away as the moon. At first they weren't sure what it was, so they looked at its spectrum, which matched very old titanium dioxide paint, calculated its rotation rate, which ruled out an asteroid, and calculated its trajectory into the past and future. All this was done through the thick haze of the earth's atmosphere, where telescope resolution is generally limited to what a 10 inch space based telescope can deliver. When you're observing things that will be much smaller than any future long duration warship, and observing them from down here under our blanket of atmosphere, and picking them up at twice the earth moon distance, you can bet that moving ships into close range while staying unobserved will prove difficult, if not impossible.

I See You, You See Me

So the first space fleet game we play is a simple one. Can you observe your observer? My example scope is one with a 1-meter aperture (diameter) with a resolution, out in space instead of on earth, of 0.671 micro-radians or 0.138 arc-seconds. For you riflemen out there, that angle is 434 times finer than 1 MOA (minute of angle). Very roughly, this telescope could resolve individual features 1-meter across at a distance of 1,500 kilometers or about 900 miles. However, you don't need to resolve the target in order to observe the target, and stars themselves are much too far away for most telescopes to even come close to actually resolving. All they have to do is detect the light from the star, not turn it into an extended image.

For example, the Hubble Space Telescope, when lit by the sun and making a pass about 1000 km away from the observer, appears as a bright as a third magnitude star. You can step outside at night and watch it shoot across the sky as long as you know where and when to look, and for help on seeing orbiting satellites try here. Yet the limiting magnitude the HST can itself detect is about 21 (Magnitudes are on a log scale, and bigger numbers mean fainter objects. The naked eye can see stars of 6th or 7th magnitude). A little math says that in an orbit near Earth's own a Hubble Telescope could detect another Hubble that was about 4 million kilometers away. That's about 2.6% of the distance from the Earth to the Sun, or over 10 times the distance from the Earth to the Moon. And the Hubble far smaller than any conceivable manned craft that we'd care to call a warship instead of a capsule, so warships could be detected while still very, very far away.

If you doubled the diameter of the Hubble then it would have four times the light grasp, and could detect a regular sized Hubble twice as far away, due to the inverse square law of apparent brightness and distance. But then the larger Hubble is reflecting four times more light, and the regular Hubble could see its larger cousin, too. A smaller scope would escape detection by the larger Hubble, but in return couldn't see the Hubble either. The basic thing driving this affect is that bigger scopes appear brighter when lit by the sun. For a rough idea on the scope-to-scope observation distance try multiplying the apertures of the two scopes, in inches, by 450, to get how many kilometers of separation before they'd probably see each other with modern CCD detectors.

That number is very crude, based on what the Hubble can see, how bright it is, and also what size CCD equipped scope it takes to see Pluto. However, it's also a function of how bright the target is, and Pluto, for example, barely receives any sunlight, getting just 1/1600th as much sunlight as earth. So the range at which your scopes can see things decreases with the square of the distance from the sun. My figure of 450 times the two telescope's apertures is a rough estimate for near earth. But keep in mind that even two common 8 inch telescopes could easily see each other from a distance that's over twice the diameter of the earth, and with just a 24" scope you've got high orbit covered, able to detect any object bigger than Sputnik out to 20 times the diameter of the earth.

For example my roughly 200-inch Super Hubble is able to detect and be detected at roughly 8 million kilometers, which is 627 times larger than the Earth's diameter of 12,756 km. For comparison, if the earth was shrunk to the diameter of a basketball, 9.5 inches, our zone of detection for Hubble sized objects would extend for 500 feet around it in all directions, which is one city block.

But I'd also like to note that detectability does not equal detection, and there's a big difference between getting hourly updates on the position of a known target versus picking one up cold. Telescopes magnify very well, but they tend to have a very small field of view. If a long-range target changes position in between observations then it's no longer exactly where it was, but where it might be is still confined to a very small region of space, and the detecting scope can start a narrow search sweep to reacquire it. To truly present itself as a cold target, thus slipping in closer prior to reacquisition, the target would need to move beyond detection range, which might be difficult since such a maneuver would likely draw the attention of scopes that are very much larger than ones detailed to keep tabs on it.

On the topic of picking up entirely new targets, suppose we used a wide-field IR (WFIR) telescope, such as a space-based counterpart to the ground-based 8-meter telescope the Canadians are pursuing. It has a field of view of 0.7 degrees by 0.7 degrees, and could image the entire dome of the sky in around 84,000 observations. If it used one observation per second it would take it about 24 hours to complete a sweep. Of course, build 24 of them and your sweeping the entire sky every hour. With its 314-inch aperture it could also pick up objects pretty far away, the Hubble at 13 million kilometers for instance, though this might take more than one-second observation times.

Now a couple caveats on this whole game. The first is that if you're further from the sun than the target you'd like to detect, you're probably front lit to it while the target's side that's facing you is mostly shadow. So the object nearer the sun has an observational advantage. This applies in the IR as well, as the shaded side of a ship tends to be very cold. The second is that a telescope looking directly at you probably presents the hardest target to detect, since your looking at the end of a shaded cylinder. So it's easier to see the scopes that aren't specifically looking at you. In an environment of warships, weapons, and telescope sensors, working at maximum detection ranges, the sensor that's keeping tabs on you will likely be the one of the last ones that you can in turn detect.

May 19, 2004 in Science | Permalink


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With any EM detector, there will be tradeoffs - telescopes are an extreme case - between what, not knowing the exact technical terms, I'll call

field of view (anglar size of area scanned)
sensitivity (ability to pick up faint objects)
resolution (ability to distinguish exact shapes)
color (ability to distinguish exact wavelengths)
speed (number of updates per second)

Telescopes maximize sensitivity and resolution at the expensive of tiny field-of-view and long exposures.

Human eyes are actually two or three systems sharing the same optics, all with pretty good speed; one optimized for wide field-of-view(periphial vision), one with high sensitivity and moderate resolution (black-and-white night vision), and one with good color, resolution and speed but a small field-of-view and poor sensitivity (your normal, daytime, frontal vision).

It seems there would be multiple sensors, sometimes sharing the same optic/antenni (a whole other set of tradeoffs) - some designed for picking up faint, distant objects; some for identifying exact velocities of fast-moving nearby objects; and possibly others.

Sweeping is just a kludge for making a small-field-of-view into a wide one at the expense of speed - not that there's anything wrong with that...

Posted by: mike earl at May 20, 2004 2:06:27 PM

Three issues you should consider:

1) Albedo - Passive detection ranges based on reflected energy depend quite strongly on the reflectivity (albedo) of the object in the frequency you are scanning. More simply, dark things are hard to see.

Your example of the Apollo 12 upper stage is white (that is highly reflective in all or most frequencies of visual light). There is no reason to assume that military spacecraft would choose colors (broadly construed, variable reflectivity at different radio frequencies could give a 'color' to radar returns) easy to detect at long ranges.

2) Geometry - One of the principles of stealth is to reduce the angle from which you can get a strong reflection by choosing the shape of the craft carefully. The first thing to avoid is a corner reflector (three mutually perpendicular planes that meet in a corner), which will strongly reflect any signal from an appropriate angle directly back on itself. The second thing to avoid is smooth curves, some part of which is always perpendicular to an observer (a sphere, for instance). That same Apollo 12 upper stage, while not spherical, is cylindrical, thus there is a wide area from which a surface reflecting any incoming radiation is visible.

Other shapes reflect much less in arbitrary directions. For example, a tetrahedron (four-sided solid) will reflect a single incoming signal strongly in at most three directions. Since the restrictions on the shape of a vacuum craft are much less serious than those on shapes moving in an atmosphere, you can get away with some pretty odd stuff.

3) Passive vs. Active Detection - Your analysis assumes only the use of passive detection, specifically the reflection of solar radiation. Since it's easier to detect an emitter than it is to detect the reflection from an emitter, it is reasonable to assume that a spaceship that is hiding would use passive detection.

On the other hand, if you have a base whose location cannot be hidden, say an occupied planet, you can freely emit in the knowledge that you aren't giving any new information to an enemy. This allows a stationary and known defender much broader options for detection technology than those available to anyone trying to sneak up on him. By analogy, sneak thieves don't get to use 2 million candlepower flashlights, but guards do.

Note that there are few restrictions on the frequency of the light used by the 'flashlights' in space combat: radio (radar), visible light, x-ray, microwave, whatever. Furthermore, there isn't anything requiring you to use only a single frequency or a single 'flashlight' in a given frequency.

With tight clock synchronization, you don't even have to put your receiver next to your emitter. You can shine the light from earth and detect the reflections on a spaceship anywhere nearby. With multiple emitters, you can synthesize the information obtained in some interesting ways.

Posted by: Doug Sundseth at May 20, 2004 7:24:18 PM

Good points, Doug.

I think the problem with going to a black ship might be that it will absorb more heat, so it might dim in the optical band but brighten in the IR. You could use cryogenics to keep the black side cool, however, and instead radiate in a direction not visible to your opponent. But part of my thought was that small telescopes are so light and rather difficult to detect that there probably won't be any such direction available.

And as another example, if you stick a small amateur sized telescope in a crach on a tiny asteroid or moon, there's no way anyone will find it. Talk about searching for hidden WMD!

The same problem makes geometric solutions difficult, since I assume that all sensors form a net with tightly directed laser communications to some known receivers, such as space stations or planets. Since you don't know where your observers are geometric shaping still doesn't tell you which ways your surface must never face, and once you've flashed one the rest take a very critical look at you, possibly using active sensors and such. So you might achieve some level of stealth, but once you've been seen you'll continue to get pinged. They also might keep looking for star occulations, and the number of possiblities to detect these goes up rapidly with the number and spread of the observers.

I think passive detection will play a role in spotting incoming stealthy projectiles, where you need a targeting solution immediately, and it might be handier for picking up smaller objects, but I figure the large objects will already be watched passively, just because it's a more power-efficient method of observation.

Posted by: George Turner at May 20, 2004 8:25:28 PM

Gravity wave detectors might be possible. They would be incredably hard to stealth against; unfortunately, they'ld also likely be huge, stationary, and fragile. (I'm also not clear you could really get enough resolution for them to be useful for detecting ships, though from what little I understand you might have a chance to pick up massive, rapidly accelerating ones.)

Posted by: Mike Earl at May 20, 2004 8:41:57 PM

Another possibility, perhaps, would be Electromagnetic detection? I know they use something similar in Submarines, but as far as I know——and please correct me if I'm wrong——such detection is aided by the Earth's omnipresent magnetic field.

However, I'm sure that you could either a) find disruptions in already-present magnetic fields or b) somehow "create" almost a magnetic mine-field, of sorts... Anything massive and metallic would slightly disrupt said fields and thus prone to detection. I'm not well versed in the area, but the thought has occured to me.

Posted by: David Wyly at Feb 9, 2005 12:17:02 PM