Built on Facts

In the Stealth in Space post earlier this week, we discussed the problem of detecting the thermal emission from a spacecraft. If the interior isn’t generating a lot of power, there’s not much thermal radiation being emitted, making it a tough job to detect.

But it was pointed out in the comments that the heat from the sun would itself warm the spacecraft exterior, increasing the thermal signature by potentially a large amount. Let’s verify this. If you take a perfectly absorbing sphere and set it in orbit around the sun (say, at the distance of the Earth), it’ll absorb all the light from the sun that intersects its cross-sectional area. But assuming it conducts heat well, it’ll be radiating equally in all directions – the area of emission will be the whole surface of the sphere. Thus at equilibrium, the power in from the sun equals the power out via radiant heat.

The power in is the power-per-area from the sun (about 1300 W/m^2 at the distance of the earth) time the area of cross-section, and the power out will be equal to the thermal-power-per-area given by the Stefan-Boltzmann law times the whole area:

Where Ac is the area of cross section, At is the total surface area, capital phi is the flux from the sun, and sigma is the Stefan-Boltzmann constant. For a uniform sphere, we can plug in the area:

Solve for T:

Notice the r’s have canceled; the final temperature is independent of the size of the sphere. With our numbers, the temperature is a toasty 275 K. Well, toasty with respect to space. You’d still want to wear a jacket.

But that’s a pretty hefty temperature if you want to stay stealthy. In the comments I suggested making the spacecraft out of reflective or transparent materials, both of which have potentially serious problems. It would probably be a better bet to just tweak our formula above by simply giving our spacecraft a convenient shape. If for instance we shaped our spaceship like a pencil and kept either the point or the eraser aimed at the sun, there would only be a small fraction of our total radiating area available to absorb sunlight. I’ll leave the equation-modification aside and quote some results: if there’s 100 times as much radiating area as there is absorbing area, the temperature is down to 123 K. If there’s 1000 times, it’s down to 69 K. Returns are diminishing (it scales as the inverse fourth power of the ratio), but still significant. That combined with some judicious reflectors and I think you can get the hull temperature pretty low.

Fig 1: Pencil-shaped spacecraft design, from 2001

The problems the sun’s heat poses are also strongly influenced by where you’re trying to be stealthy. Around Mercury there’s a lot more solar light to deal with. Around Saturn, much less. All other things being equal, your hull temperature scales with the inverse square root of your distance from the sun. At Saturn, for instance, our 100x area blackbody spacecraft would have a hull temp of a frigid 39 K.

So it’s something to think about if people ever come to blows over mining Ceres or something.

UPDATE: In the previous post, commenter Anthony brings up something well worth discussing here:

…if a ship is being hit by X watts of sunlight, it’s pretty much going to emit X watts worth of photons (unless it has somewhere to store the heat, and it usually only takes hours to days to overwhelm any practical heat sink), and tweaks to albedo and heat distribution across the surface just modify the spectrum and direction of the emissions.

Which is pretty important, lest we fall into the same trap I criticized in my previous post. In the end, total incoming = total outgoing. Lowering the temperature is good for reducing that part of the total emissions which are promiscuously broadcast in all directions. Hopefully you can catch most of the rest with a mirror and reflect it in a narrow, specific direction away from enemy sensors.

Comments

#1 amphiox
March 12, 2010

How much consideration are we giving to the possible types of detection technologies that these hypothetical space stealth systems will be required to beat?

If we’re only looking at passive observation capabilities on par with what modern human astronomy is capable of, but pitting it against as adversary presumably capable of launching an interstellar invasion, then that is hardly a fair contest.

If we instead posit a contest between approximate equals, assuming a technological level capable of launching an interstellar invasion fleet, what level of sensor sophistication might we expect?

How much of the sky would the defenders be able to monitor, and how quickly? What would the sensitivity limit in terms of ambient radiatio detection be likely to be for their telescopes, etc? What arrays of space based observation stations might they be expected to be able to control?

If we’re talking subluminal technologies only, for example, all approach paths will have to be orbits. If the defending civilization has reasonable knowledge of where an attack will likely originate from (they can observe the surrounding stars, after all), they can compute all the likely orbital trajectories that such attackers will have to traverse to enter their system, and focus their sensors primarily on those. Would they even be able to have a chance of, say detecting the enormous energy of the initial launch against the glare of the enemy’s home star? If they could then they would have years of forewarning to focus their defensive scans on the likely orbits of approach.

If the defending civilization has multiple observation posts scattered throughout their home system, and not just on one planet, then all strategies of concentrating and focusing your emissions in any particular direction will not work – once you’re deep in the enemy system, you can expect that there will be sensor arrays in all directions relative to you.

How will you deal with active detection systems, that might use lasers or radar directed towards you to look for echoes, or even arrays of stations scattered throughout the system sending constant EM transmissions to one another, such that if you intercept/occult any of these beams, you will be detected just by your shadow on the receiving end?

For a civilization at this level of technical sophistication, would access to alternate detection means not dependent of electromagnetic radiation be feasible? Could they, for example, have a satellite network in place capable of detecting you by the effects of the gravity of the mass of your ship(s)?
#2 Benjamin Franz
March 12, 2010

..if a ship is being hit by X watts of sunlight, it’s pretty much going to emit X watts worth of photons (unless it has somewhere to store the heat, and it usually only takes hours to days to overwhelm any practical heat sink), and tweaks to albedo and heat distribution across the surface just modify the spectrum and direction of the emissions.

He is forgetting that modifying the albedo changes the X being adsorbed. A 99% reflective surface exposed to 1500 watts/sq. meter is only absorbing 15 watts/sq meter. That will make a big difference in the equilibrium temperature.

And the shape and orientation of the surface can ensure that virtually all of the incident 1485 Watts/Sq. meter from the Sun that is not adsorbed will be reflected in a direction that ensures it isn’t detected.
#3 Anthony
March 12, 2010

The lower limit for a spike-type build is, as far as I can tell, a double-cone structure (one end pointing towards the sun, one away) with a length to width ratio equal to the ratio of the sun’s diameter to the distance to the sun. Anything longer than that will have side illumination, since the sun is not a point-like object. For a given base radius R, this works out to a length (at 1 AU) of ~430R, a cross-sectional area of pi*r^2, a volume of ~430*r^3, and a surface area of ~1,350r^2, for a surface temperature of about 85K.

A separate problem for this is that you won’t naturally stay aligned with the sun as you orbit, and in fact the forward cone means that light pressure will magnify any instability.

That’s actually interesting in the context of ‘how close can a ship get to the sun’; while the incoming flux is order -2 in range, the heat which must be dissipated per unit surface area is roughly order -3 in range, because as you get closer, the aspect ratio gets worse. Still, it looks like you could maintain living temperatures with only passive cooling as close as 0.21 AU from the sun.
#4 Anthony
March 12, 2010

Btw, I wasn’t forgetting reflection, I was classifying reflection as a form of emission. Which is probably misusing the term, but the basic point remains: X watts in, X watts out. If you’re reflecting, much of that power has an emissions spectrum similar to the sun, rather than a black-body emissions spectrum, but it’s still the same total energy.
#5 Benjamin Franz
March 12, 2010

I don’t care about the 1485 W/Sq. Meter NOT being absorbed because it isn’t going to be detected by my opponent.

Other possibilities include making your thermal emission asymmetric. You could put a refrigerated plate between you and the direction you wanted to be stealthed. You still radiate heat (more in fact) – just not in that direction.
#6 Carl Brannen
March 12, 2010

The point about reflection is that it’s only visible in certain directions. So stealth vehicles tend to have large flat surfaces. They’re very visible if you happen to be on the right line, but that’s a very small probability.
#7 Andre Vienne
March 12, 2010

Of course, with refrigeration, you’re still dealing with a lot of waste heat. Not only that, but depending on what you have powering the ship, you’re going to need radiators to bleed off that excess heat, or else it starts getting toasty inside.

How are you going to make the radiators invisible?
#8 Rick Pikul
March 12, 2010

OK, folks: Please go read the “Space War: Detection” page at Atomic Rockets.

http://www.projectrho.com/rocket/rocket3w.html

How hard it is to scan the sky, and pointing the radiation away from the people you are hiding from are both addressed.

Scanning the sky: A complete sweep with a single wide-angle telescope can be done in 4 hours, and this will generate about a terabyte of data. Scanning even once per 4 hours is more than often enough to find things to take a close look at long before they can do anything, and enough processing power can be had from Best Buy for a few grand.

Now, directional emission. This has two big problems.

First, it’s a red queens race. To direct your emissions sufficiently to gain stealth will take energy, likely more than you can provide on passive power systems.

Second, it assumes you have a safe direction to point that energy. For the cost of a single space warship, I can fling dozens of sensor satellites into solar orbits. Unless space war is a totally new thing, there is going to be something to see your radiation no matter which way you point it.

The latter problem is also one of the reasons any attempt to trick the observer as to the range simply won’t work.

What we have here is an example of Nicoll’s Law: “It is a truth universally acknowledged that any thread that begins by pointing out why stealth in space is impossible will rapidly turn into a thread focusing on schemes whereby stealth in space might be achieved.”
#9 Benjamin Franz
March 13, 2010

You can ‘prove’ that stealth is impossible in the general case by throwing enough resources at it.

And I can show that it *is* possible in the restricted case _also_ by throwing enough resources at it. For example: I could launch my gigaton mass double pyramid shaped mirror skinned projectile from the 50 AUs out after cooling its core to 1 degree K and letting it passively cool itself the whole trip through sheer thermal mass. It won’t show up on ordinary radar, thermal imaging or visual scans.

And then you can counter with ‘yes, but if I put hundreds of radar stations all over the system I can detect it with side-scatter radar’.

That isn’t a productive way to argue.

The question isn’t if you can detect me if you have unlimited resources.

It is ‘can I hit you in practice without you detecting me’ for realistic levels of investment.

And the answer is clearly: Yes.
#10 Andre Vienne
March 13, 2010

Of course, then you have to get your gigantic mirror-skinned magic spaceship out to 50 AU in the first place. And if it’s incoming, then you’re going to have to decelerate sometime. Depending on how fast you’re going, your destination, and your drive’s capabilities it could be a very long deceleration indeed.

And you just wasted all of that mass on being undetectable. Pity.
#11 Benjamin Franz
March 13, 2010

Why would I decelerate it? It makes a great weapon as is. A gigaton chunk of *anything* hitting at a few tens of kilometers per second makes a very effective weapon.
#12 Benjamin Franz
March 13, 2010

To clarify: I don’t need to haul the mass out to 50 AU. I just need to shape and plate anything already out there in the Kuiper Belt and divert it into an orbit headed into the inner solar system. By the time it arrives in the inner solar system it will be moving at over 35 Kilometers/second and make a very effective weapon against targets like things on planets.
#13 Andre Vienne
March 13, 2010

Yes. Because a weapon that takes almost seven years to hit its target is obviously the best weapon for the job.

Hell, we’ll just get Flash Gordon to stop you. It’s in the same realm of feasibility.
#14 Andre Vienne
March 13, 2010

Seven years minimum, I mean. Assuming you accelerate it yourself at first.

Good luck keeping it on target if you miss.
#15 Rick Pikul
March 13, 2010

First problem with diverting something big from the Kuiper Belt: I don’t need to pick you up on simple radiant heat, you had to fire up your drives to divert it into the inner system.

Once you fire up those drives, I can see you from _very_ far away. That gigatonne ship, with even a poky little chemical thruster giving you 0.1 miligees? I can see you at 63 AU, and not only do I know where you are: I know what kind of drive you have, I know how how big your ship is and I can put constraints on your available deltaV. Moreover, the better drives are actually _easier_ to spot, (the same thrust out of something like a VASIMR would be visible from ~200 AU).

This is using sensors and processing gear that you can buy _now_. The development that brings about the ability to have people spread out enough for space war to matter will also result in the detection becoming better.

You also haven’t quite gotten the multiple sensor platform issue: They are so much easier than any kind of space warship that the sensor network which is easy at any given resource/technology level can beat any attempt at stealth using the next generation systems.

(OK, now who is going to try decoys? FTR: They work, but cost almost as much as the real ship.)
#16 Andy P
March 13, 2010

1. I think you’ve been too quick to dismiss your near solar stealth case. The thermal insulating and reflective materials in s/c thermal control systems can do some pretty astonishing stuff. Look into the thermal design of the Messenger spacecraft now in orbit over Mercury.

http://messenger.jhuapl.edu/spacecraft/thermal.html

You’ll notice that the sun shield is able to maintain room temperatures on the shade side of the shield while the sunlit side is at over 600 Kelvin. What this means is that your close-solar orbiting spacecraft might look like it’s room temperature.

And the other fella will be looking for you against the backdrop of a solar corona and the close in stellar dust disk component of the zodiacal light mentioned in my other post.

Might be pretty easy to hide there.

Another thing you might do in close to the Sun is just make the sun facing side of your s/c highly reflective in the solar spectrum – you should be good to go unless someone is in a lower solar orbit than you are. It doesn’t seem too likely that anyone on the other side of the star is going to be able to see you through the previously mentioned close stellar component of the zodiacal light.

2. Controlling your surface temperature controls the intensity and wavelength that you’re emitting at. Controlling your onboard heat emission, the amount of surface area you have intercepting solar radiation, and the amount of radiating surface area controls your skin temperature. The hard part (for me at least) has been properly estimating the real background. Most folk use some variant on the 22nd magnitude star case or (worse) assume that the 3 kelvin cosmic background is it. If anyone else is interested in more realistic background modelling here’s a resource that I’ve found:

http://irsa.ipac.caltech.edu/IRASdocs/exp.sup/ch10/Ap4.html

v/r
Andy P.
#17 Recall
March 14, 2010

“This is using sensors and processing gear that you can buy _now_. The development that brings about the ability to have people spread out enough for space war to matter will also result in the detection becoming better.”

Not to mention the sheer size of telescopes that become practical.
#18 Benjamin Franz
March 14, 2010

Those who are attacking me over the ‘Flash Gordon’eseque approach are missing my point:

If you are allowed to assume unlimited resources to *detect* an attacker, I’m allowed to assume unlimited resources to *make* an attack.

And it isn’t a productive way to argue.
#19 Andre Vienne
March 14, 2010

Nobody said anything about infinite resources, that I can recall. Probes are cheaper than spaceships, true fact. Probes can be outfitted with telescopes, again, simple enough.

The question is, how can you efficiently manage stealth in space, without limited resources, and without someone else detecting you with the same amount of resources?

I haven’t seen anyone answer that in all of their refrigeration schemes or dodgy rock tricks that are ‘supposed’ to work.
#20 Andre Vienne
March 14, 2010

with limited resources* Stupid brain, why you no work right?
#21 Benjamin Franz
March 14, 2010

I need to throw *ONE* rock at you undetected. You need *HUNDREDS* of detection systems to have a reasonable chance of beating it.

Who is assuming unlimited resources?
#22 Rick Pikul
March 14, 2010

Those detections systems are _ORDERS OF MAGNITUDE CHEAPER_ than the gear needed to fling that rock. The tech needed to do this exists now, and the only really expensive part is that you want to put it in space. If we have interplanetary combat, then interplanetary travel is affordable.

Furthermore, the reason you need many sensor platforms is to detect radiation from the ship’s latent heat. There is nothing you can do to hide your drive, turn that on and you are spotted.

To make things worse, that 0.1 miligee drive? Your transfer burn is going to be measured in weeks. Getting it down to a few days of burn means I can see a chemical drive out to ~200 AU and a high quality plasma drive out to over 500 AU, (and every sensor platform still looks right at you over a dozen times).
#23 Benjamin Franz
March 15, 2010

I can think of at least two ways to make the necessary delta-v changes that don’t require a detectable heat signature. Starting with ‘use a mass driver as a drive’. I don’t have to throw hot stuff. I just have to throw stuff.
#24 Vicki
March 15, 2010

This discussion seems to be treating “hide a spaceship traveling in arbitrary, changeable directions” and “fire a missile that will hit a planet without being shot down” as equivalent problems. Bullets are not methods of transport, and in most scenarios of warfare, there are reasons to want to be able to capture an area or resource rather than destroying it. (Yes, ICBMs and Apollo both use rockets, but they have rather different constraints.)

The moment you send out stealthed missiles on long approach orbits that you can’t stop yourself, your enemy has little reason to surrender or negotiate, because their cities, oceans, or bases are going to be damaged equally much whether or not they give you what you want. (All you can offer them is advance warning of where to evacuate, and depending on the size and aim of the missile, it might not help much.)

That means that for many purposes, you need to be able to communicate with that “rock” Benjamin is talking about throwing, and either destroy it (which means the ever-problematic long-distance self-destruct button–I don’t need to find the thing if I can figure out your codes) or change its course, which at least complicates the hardware. Even if it’s “We can throw rocks at them, Man. We will,” the rocks need to be somewhat steerable, so you can abort the attack if the other side surrenders.

It might also be useful to be able to re-direct or abort the attack so you don’t smash Denver after your troops capture it.
#25 Doug M.
March 15, 2010

“I don’t have to throw hot stuff. I just have to throw stuff.”

Your mass driver needs a power plant. If it’s going to throw generate significant amounts of thrust, it needs a /big/ power plant.

You must now hide that power plant’s heat signature.

Doug M.
#26 Rick Pikul
March 15, 2010

Sorry, using a mass driver won’t hide you either. All it will do is to move where the really hot spot is.

That gigatonne of rock/ice/whatever? If you want the 0.1 miligee I’ve used in my calculations, you’re going to running a power plant rated for hundreds of gigawatts if you are willing to use over 90% of your craft as propellant and also be spotable at ~30 AU[1].

To make things worse, it’s not like accelerating your propellant isn’t going to also significantly heat it.

[1] The shorter the detection range, the higher the mass ratio. Getting the detection range down to 20 AU at 0.1 miligee means a mass ratio of almost 250.
#27 Keith Morrison
March 15, 2010

The one thing I see the pro-stealth people do…constantly…is assume asymmetry of either technology or ability or both, and always on the side of the side attempting the stealth. Which, given the state of technology, is completely ass-backwards.

Right now, for a very large but not impossible budget (in comparison to US military spending) you could set up a system that could cover the solar system from Earth orbit out with passive infrared sensors that can scan the entire sky every few hours and catch pretty much anything trying to approach Earth.
#28 Noimporta
March 16, 2010

It appears as if the idea of stealthing satellites, if not space battleships, has been around a while:

http://www.fas.org/spp/military/program/track/stealth.pdf
#29 MPL
April 3, 2010

“Stealth” is a relative concept, you need to describe what it is you’re trying to evade detection by, and for how long.

Hiding a long term biologically-staffed observation mission would be extremely hard. Probabilistically hiding a useful percentage of automated attack vehicles long enough to make interception impossible might be very easy.

Re: “ever-problematic long-distance self-destruct button”, assuming you have long distance communications, codes are not a problem: anything that expensive can afford to have a computer on board that can quickly process modern cryptography. The chance that a society that has space weapons doesn’t have secure digital signatures seems very small.
#30 Haji
October 10, 2011

I strongly disagree with this analysis. First, and foremost, 100% efficient conduction breaks the laws of thermodynamics (entropy!). That means, some heat will be retained, and that means, the entire shell will heat up, untill the temperatures are at equilibrum (the systems try to reach equality of temperature, not energy). For example, the temperature of Ceres during daytime is 239K, which means, that for cross-section of 25m^2 we have total output of 4.5kW. However, this assumes you have to beat only 1 sensor. If there are several sensors (for example, Earth, Mars, Jupiter) and you have bigger cross-section (say, 10 times bigger on the side, with the 25m^2 being the smallest, directed at Earth), the amount of energy will rise, in this case to 45kW . This is what I could think of on the spot, there are probably more things to consider.
#31 SF
March 28, 2012

What do we think of the possibility of meta-materials which make the ship “invisible” to heat?
http://www.bbc.co.uk/news/science-environment-17518210