Motives for interstellar warfare

[Ariphaos]

You continue to assume a single energetic burst must be the means by which the rods or whichever objects are being projected instead of a carrier moving at a steady acceleration to get its payload up to the required velocity. You further assume perfect observation, perfect targeting, perfect prediction, and of course perfect operation of every system required to focus a laser on the target zone.

Yeah well, so are you.

I guess I'll qualify this bit of flippancy.

The author gave that the initial launch was known at the soonest possible moment. At that point, if you intend to protect your most valuable targets, you know its exact speed and probable target (or targets). If it's actually off course, no worries. If you protect too many targets, no worries. The result is simply an elementary school train wreck problem. If the train is off the rails, it's missing anyway. There is a very narrow window through which it has to pass in order to strike your planet.

Likewise, a number of much colder (compared to their distance from our Sun), and non-blueshifted objects need to be tracked, and have their mass measured, in order to properly track Earth's position decades into the future. Not just gravitational attraction, but at these scales time dilation will play a role as well (which falls of linearly with distance).

Some pretty impressive feats of measurement are given in both instances.

[Patrick Degan]

Xeriar, it really should not be necessary to point out just why your yottawatt laser idea is a non-starter to begin with. But then, it also should not be necessary to point out another flaw in your argument: your faith in targeting-by-prediction.

Sure, it's more than possible to do a Lorentz calculation of a relativistic object. That's not the problem, however. That comes from one of the conditions you yourself mentioned earlier in this thread concerning what happens when the .9c projectile is ploughing its way through the heliopause. Ablation will no doubt occur as well as braking and quite possibly deflection as well. Which means that both velocity and trajectory are now non-constant values, which junks the prediction set and therefore the targeting solution will have to be recalculated.

The next problem is that thousand kilometre wide focussing lenses massing a half-million metric tons can't exactly be turned on a dime. This is where the reaction-time problem comes in, because it will not be possible to do precision adjustments on the lens angles in the time you have left before the terminal strike occurs, and the closer in the projectile gets toward Earth, the more the interception window shrinks.

Sure, the sun pumps out 4E26 watts of power. Unfortunately, you're not going to have 100% of that output available for this task. Half your collectors will be out of orbital position on the opposite side of the sun at any given time, and you'll have at most the luminosity of the side you have available lenses to focus on the incoming object to work with. Then, there's that pesky Inverse Square Law to consider: intensity halves with the square of distance, which is further reducing the energy available for your lenses to collect and focus into a beam. Additionally, the total amount of power you'll be able to harvest from your collectors and lenses will be delimited by their surface area. This is absolute.

If you had five billion of the aforemetioned 1000km-wide focussing lenses available, you'd still be harvesting only .00008% of the sun's total output as usable power. Assuming that those are in the same orbital distance as the one mentioned in the extract from the laser sailcraft paper quoted earlier.

So much for the yottawatt laser. You'd have a better chance of defending against the incoming R-bomb by putting asteroids or clouds of debris in its path or actually moving the Earth itself out of position —a difficult bit of orbital engineering but possible in principle; though it depends upon how much time there is before hammer-fall.

[Ariphaos]

Sure, it's more than possible to do a Lorentz calculation of a relativistic object. That's not the problem, however. That comes from one of the conditions you yourself mentioned earlier in this thread concerning what happens when the .9c projectile is ploughing its way through the heliopause. Ablation will no doubt occur as well as braking and quite possibly deflection as well. Which means that both velocity and trajectory are now non-constant values, which junks the prediction set and therefore the targeting solution will have to be recalculated.

Same benefit. If parts get deflected, they aren't heading to Earth anymore, now are they? You are covering a focal region the size of the planet to begin with, with a very predictable path length.

Oh, sure, some unlucky satellite might get hit, and in many cases Earth's atmosphere is going to light up, but five light-days is well beyond the heliopause to begin with.

As for the actual deflection caused by the IPM, it's actually fairly negligible. I was hard pressed to come up with a figure of more than a hundred kilometers - unless your star system passes into a nebula, you make one, move your planet, or do something like point your star in their path, if they've got good prediction on your planet's future position, they won't miss.

The next problem is that thousand kilometre wide focussing lenses

Well, five light-days, so, 2.6E10 kilometers.

25,000 km (DSpot) = 2.44 * 2.6E10 * 1E-9 (micrometer, still large) / Dlens

Dlens = 2.44 * 2.6E10 * 1E-9 / 25,000

Dlens = 2.5 meters.

Defense rests. Literally. Especially considering the tiny angular adjustments you'd need to make if you wanted to make them -anyway-.

massing a half-million metric tons can't exactly be turned on a dime. This is where the reaction-time problem comes in, because it will not be possible to do precision adjustments on the lens angles in the time you have left before the terminal strike occurs, and the closer in the projectile gets toward Earth, the more the interception window shrinks.

Er hrm.

Are you under the impression that light pressure + terrestrial IPM will deflect the rods being fired, and if the attackers account for this, they'll hit Earth anyway? Is that why you're bringing this up?

If so, it's pretty baseless, like I said. I needed to cheat to come up with the 100 km IPM deflection.

Sure, the sun pumps out 4E26 watts of power. Unfortunately, you're not going to have 100% of that output available for this task. Half your collectors will be out of orbital position on the opposite side of the sun at any given time, and you'll have at most the luminosity of the side you have available lenses to focus on the incoming object to work with. Then, there's that pesky Inverse Square Law to consider: intensity halves with the square of distance, which is further reducing the energy available for your lenses to collect and focus into a beam. Additionally, the total amount of power you'll be able to harvest from your collectors and lenses will be delimited by their surface area. This is absolute.

Vaporization of any known substance would require something on the order of 15 MW per square meter. For a radius of 12,500 km, that's ~1E20 watts. Since this is occurring at an extreme angle, pumping that up by a few orders of magnitude is desired, though going beyond 1E23 does seem rather silly.

If you had five billion of the aforemetioned 1000km-wide focussing lenses available, you'd still be harvesting only .00008% of the sun's total output as usable power. Assuming that those are in the same orbital distance as the one mentioned in the extract from the laser sailcraft paper quoted earlier.

Well, for the Solar System, you want to put a Dyson Swarm in the Vulcan orbits. I calculated the numbers once and they were truly obscene, but ended up being "Scrape the top three kilometers off of Mercury" when you broke it down into raw materials needed (I'll need to run the numbers again, it's been awhile).

So much for the yottawatt laser. You'd have a better chance of defending against the incoming R-bomb by putting asteroids or clouds of debris in its path or actually moving the Earth itself out of position —a difficult bit of orbital engineering but possible in principle; though it depends upon how much time there is before hammer-fall.

Moving Earth is the most feasible defense for such targeted attacks, as I already mentioned. Building particle screens is really only feasible for systems that you place near insane value on - IE you're actually trucking matter back from Tau Ceti to build it.

Besides, you need this same sort of power generation capability to fire your RKVs in the first place.

Beyond and because of all that, sunshine and happiness > your RKVs.

[Patrick Degan]

Sure, it's more than possible to do a Lorentz calculation of a relativistic object. That's not the problem, however. That comes from one of the conditions you yourself mentioned earlier in this thread concerning what happens when the .9c projectile is ploughing its way through the heliopause. Ablation will no doubt occur as well as braking and quite possibly deflection as well. Which means that both velocity and trajectory are now non-constant values, which junks the prediction set and therefore the targeting solution will have to be recalculated.

Same benefit. If parts get deflected, they aren't heading to Earth anymore, now are they? You are covering a focal region the size of the planet to begin with, with a very predictable path length.

Oh, sure, some unlucky satellite might get hit, and in many cases Earth's atmosphere is going to light up, but five light-days is well beyond the heliopause to begin with.

As for the actual deflection caused by the IPM, it's actually fairly negligible. I was hard pressed to come up with a figure of more than a hundred kilometers - unless your star system passes into a nebula, you make one, move your planet, or do something like point your star in their path, if they've got good prediction on your planet's future position, they won't miss.

Uh huh. Nevermind that the beam won't have a dwell on the target for long enough to actually effect it. Nor can the beam be shifted to track the target with such a large focussing lens being utilised for it.

The next problem is that thousand kilometre wide focussing lenses

Well, five light-days, so, 2.6E10 kilometers.

25,000 km (DSpot) = 2.44 * 2.6E10 * 1E-9 (micrometer, still large) / Dlens

Dlens = 2.44 * 2.6E10 * 1E-9 / 25,000

Dlens = 2.5 meters.

Defense rests. Literally. Especially considering the tiny angular adjustments you'd need to make if you wanted to make them -anyway-.

Still don't get the essential problem, do you? At a velocity of .99c, the target would cross that dwell spot (which we'll use for purposes of argument here) in about eight-tenths of a second. It won't contact the target long enough to do anything to it and you can't adjust the lens afterward given how long it would take to shift such a massive object by even a degree.

massing a half-million metric tons can't exactly be turned on a dime. This is where the reaction-time problem comes in, because it will not be possible to do precision adjustments on the lens angles in the time you have left before the terminal strike occurs, and the closer in the projectile gets toward Earth, the more the interception window shrinks.

Er hrm.

Are you under the impression that light pressure + terrestrial IPM will deflect the rods being fired, and if the attackers account for this, they'll hit Earth anyway? Is that why you're bringing this up?

If so, it's pretty baseless, like I said.

I'm not responsible for your fantasies.

I needed to cheat to come up with the 100 km IPM deflection.

Then your evaluation is fairly well useless given its basis on wholly arbitrary numbers you've plucked out of thin air.

Sure, the sun pumps out 4E26 watts of power. Unfortunately, you're not going to have 100% of that output available for this task. Half your collectors will be out of orbital position on the opposite side of the sun at any given time, and you'll have at most the luminosity of the side you have available lenses to focus on the incoming object to work with. Then, there's that pesky Inverse Square Law to consider: intensity halves with the square of distance, which is further reducing the energy available for your lenses to collect and focus into a beam. Additionally, the total amount of power you'll be able to harvest from your collectors and lenses will be delimited by their surface area. This is absolute.

Vaporization of any known substance would require something on the order of 15 MW per square meter. For a radius of 12,500 km, that's ~1E20 watts. Since this is occurring at an extreme angle, pumping that up by a few orders of magnitude is desired, though going beyond 1E23 does seem rather silly.

It also requires sufficient contact time for that process to actually occur. But then this is among the many aspects of this problem you are deliberately choosing to ignore. Just as you are pointedly ignoring the figures provided by the aforementioned laser sailcraft paper describing the 1000 km focussing lens which do not support your conclusions.

If you had five billion of the aforemetioned 1000km-wide focussing lenses available, you'd still be harvesting only .00008% of the sun's total output as usable power. Assuming that those are in the same orbital distance as the one mentioned in the extract from the laser sailcraft paper quoted earlier.

Well, for the Solar System, you want to put a Dyson Swarm in the Vulcan orbits. I calculated the numbers once and they were truly obscene, but ended up being "Scrape the top three kilometers off of Mercury" when you broke it down into raw materials needed (I'll need to run the numbers again, it's been awhile).

Are you seriously under the impression that a Dyson Swarm is nothing but focussing lenses? Please say that's not what you're really suggesting here.

And, um, if you mean an inter-Mercurial orbit, you have to realise that this would not be an ideal place for anything you actually want to stay in long term solar orbit.

So much for the yottawatt laser. You'd have a better chance of defending against the incoming R-bomb by putting asteroids or clouds of debris in its path or actually moving the Earth itself out of position —a difficult bit of orbital engineering but possible in principle; though it depends upon how much time there is before hammer-fall.

Moving Earth is the most feasible defense for such targeted attacks, as I already mentioned. Building particle screens is really only feasible for systems that you place near insane value on - IE you're actually trucking matter back from Tau Ceti to build it.

Besides, you need this same sort of power generation capability to fire your RKVs in the first place.

Or you use antimatter rockets on steady acceleration. Doesn't matter if it takes a while to get up to speed.

Beyond and because of all that, sunshine and happiness > your RKVs.

As you wish...

[Darth Smiley]

Topic drift much?

The point is WHY two spacefaring civilizations might fight each other. We've already agreed that 'kill them before they kill us' is a plausible motive. And barring excessive amounts of handwavium, it is easy to kill a planet from a freaking long way away. Killing dipersed habitats is another issue, but...I digress. The exact mechanics aren't neccessary.

For plausible motives, what about political gain on the originating planet? I could definitely see a situation where a political faction trumps up 'the alien threat' to stay in power (or raise taxes).

[Ariphaos]

Uh huh. Nevermind that the beam won't have a dwell on the target for long enough to actually effect it. Nor can the beam be shifted to track the target with such a large focussing lens being utilised for it.

2.5 meters is large? Especially as slowly as it has to track in the beginning.

Incident angle is 180 gm x 129,600 gm so it's about 36 million kilometers long, while covering the affected area.

Still don't get the essential problem, do you? At a velocity of .99c, the target would cross that dwell spot (which we'll use for purposes of argument here) in about eight-tenths of a second. It won't contact the target long enough to do anything to it and you can't adjust the lens afterward given how long it would take to shift such a massive object by even a degree.

How is something 2.5 meters wide massive? How is anything going to cross 36 gigameters in .8 seconds?

Even beyond that, at that range (5 light days), how would turning even a megameter lens be a problem? -Earth- turns orders of magnitude faster than a lens four hundred thousand times beyond the needed size would have to.

I'm not responsible for your fantasies.

But apparently, I'm responsible for doing your math, and instead of showing any of your own (beyond utterly pointless and obvious stuff like 'it would take a lot of orbiters to make a Swarm!), or even acknowledging mine, you spew lines like this.

Then your evaluation is fairly well useless given its basis on wholly arbitrary numbers you've plucked out of thin air.

Are you offering to show the relevant math, or you going to continue this hypocrisy, thus forcing me to do it for you again.

It also requires sufficient contact time for that process to actually occur. But then this is among the many aspects of this problem you are deliberately choosing to ignore. Just as you are pointedly ignoring the figures provided by the aforementioned laser sailcraft paper describing the 1000 km focussing lens which do not support your conclusions.

1: I disproved the need for a 1,000 km focusing lens several posts ago, using the same equation you provided me. Which you have repeatedly ignored, yet somehow are getting on a horse and complaining about me ignoring something.
2: Pre-trigonometric math is enough to prove you wrong on the length of the targeting window. I thought it was too obvious to need pointing out.

I have endeavored to answer every last point of yours. If I have missed something, point it out to me, and I will apologize. You, however, have missed a very important refutation, and have done so for multiple posts now, even after I've pointed it out multiple times.

Are you seriously under the impression that a Dyson Swarm is nothing but focussing lenses? Please say that's not what you're really suggesting here.

Nope, a silicate collection array, most likely, but I'm seriously beginning to worry about your grasp on math.

And, um, if you mean an inter-Mercurial orbit, you have to realise that this would not be an ideal place for anything you actually want to stay in long term solar orbit.

Vulcan orbits are between .08 AU and .21 AU, roughly, and stable enough for a Dyson Swarm's purposes (losing some is inevitable, of course, but compared to the number you need to make in stable outer shells, why build it anywhere else?

Or you use antimatter rockets on steady acceleration. Doesn't matter if it takes a while to get up to speed.

...you believe that building an antimatter rocket, and hiding its gamma ray output is more feasible than harnessing the power of your parent star?

...and keep the entire apparatus trained on a target a nanoarcsecond wide while doing so, given the amount of AM you are using.

As you wish...

Apparently, you didn't quite get the math last time.

Was there a problem with me showing that a 1,000 km lens could reasonably focus on a planet out to a hundred light-years, using infrared wavelengths?

Was there a problem with me showing the defensive lens only needs to be 2.5 meters, using the same infrared wavelengths?

Was there a problem with my claim that light pressure and the Interplanetary medium would cause a negligible amount of course deflection? Do I have to write this out for you too, since you seem so incapable?

Is there a problem with me pointing out the angle of the defensive laser, which means that the focal beam is going to remain on target for ten minutes (on average), assuming it -doesn't move-? If the firing array is in front of Earth instead, it won't be off target until some time after the projectiles are.

[Ender]

Topic drift much?

The point is WHY two spacefaring civilizations might fight each other. We've already agreed that 'kill them before they kill us' is a plausible motive. And barring excessive amounts of handwavium, it is easy to kill a planet from a freaking long way away. Killing dipersed habitats is another issue, but...I digress. The exact mechanics aren't neccessary.

For plausible motives, what about political gain on the originating planet? I could definitely see a situation where a political faction trumps up 'the alien threat' to stay in power (or raise taxes).

Problem is time - political pressures and gains tend to be - relatively - short term. Whereas travel times to another star system are definitely not.

[Patrick Degan]

Two points which need immediate response:

Still don't get the essential problem, do you? At a velocity of .99c, the target would cross that dwell spot (which we'll use for purposes of argument here) in about eight-tenths of a second. It won't contact the target long enough to do anything to it and you can't adjust the lens afterward given how long it would take to shift such a massive object by even a degree.

How is something 2.5 meters wide massive? How is anything going to cross 36 gigameters in .8 seconds?

YOU said a dwell spot of 25,000 kilometres, remember? Basic mathematics: 25,000 km/(299,792.458km/sec) equals a transit time of .0842 second —eight hundredths of a second, actually (my slipup but one which magnifies the problem for you). And I seriously cannot believe that you believe this an impossibility given the velocities we're talking about.

Even beyond that, at that range (5 light days), how would turning even a megameter lens be a problem? -Earth- turns orders of magnitude faster than a lens four hundred thousand times beyond the needed size would have to.

EARTH turns orders of magnitude faster because it's been doing so for the last 4.5 billion years on the momentum imparted to it when it formed out of the accretion disk. This Red Herring of yours aside, you cannot be serious that reaction-thrusters could produce a precision change of inertia in a half-million tonne object in moments. Unless you're now going to propose that the things are actually equipped with the Handwavium Drive instead.

[Patrick Degan]

Oh, and as for your insistence that you've actually demonstrated anything, Xeriar, according to the formula R(t)=0.61*D(L/R[l]) calculating beam diffraction over distance in which R(t) is beam radius at target in metres, D is distance to target from emitter, L is wavelength of laser and R[l] is radius of laser lens, a laser in the mid-infrared range (2700 nanometres) fired through a 2.5 metre lens (your figure) over a distance of 2.6E10 km (also your figure) results in a beam spread of ~28,000 km at the target zone.

That means there is effectively no focus to the beam. You actually do need a large lens to ensure tighter focus over greater distance (also so that the heat of the beam doesn't melt the lens before any effective work can be done). A 1000km lens, on the other hand, results in a beam spread of only 107 metres at a target zone 10 lightdays out from Earth.

[Ariphaos]

YOU said a dwell spot of 25,000 kilometres, remember? Basic mathematics: 25,000 km/(299,792.458km/sec) equals a transit time of .0842 second —eight hundredths of a second, actually (my slipup but one which magnifies the problem for you). And I seriously cannot believe that you believe this an impossibility given the velocities we're talking about.

...do I need to draw a picture for you?



Notice the red line is staying within the focal path of the beam for longer than the actual width of the beam at this point.

EARTH turns orders of magnitude faster because it's been doing so for the last 4.5 billion years on the momentum imparted to it when it formed out of the accretion disk. This Red Herring of yours aside, you cannot be serious that reaction-thrusters could produce a precision change of inertia in a half-million tonne object in moments. Unless you're now going to propose that the things are actually equipped with the Handwavium Drive instead.

...says the guy who is proposing the use of an antimatter rocket to send this thing off in the first place (I wonder if the neutrino emissions would go unnoticed). Since I already proved that only 2.5 meter lenses would be needed several posts ago, you repeatedly ignoring it and accusing me of bringing forth a red herring is...

Since you seem incapable of doing relevant math, .716 degrees, over 4.5 days, comes out to 6.63 milliarcseconds per second (on average, it's not scaling linearly). Over these 4.5 days the limbs of the unneeded 1,000 km lens would move 6.25 kilometers at the extremes.

I'm not sure what sort of magic drive you believe is required, since a great deal of load balancing is possible across a plane.

[Patrick Degan]

YOU said a dwell spot of 25,000 kilometres, remember? Basic mathematics: 25,000 km/(299,792.458km/sec) equals a transit time of .0842 second —eight hundredths of a second, actually (my slipup but one which magnifies the problem for you). And I seriously cannot believe that you believe this an impossibility given the velocities we're talking about.

...do I need to draw a picture for you?

I presume you'll be using your crayons.

Notice the red line is staying within the focal path of the beam for longer than the actual width of the beam at this point.

So I suppose that whole concept of beam diffraction over distance just sailed over that pointy head of yours.

EARTH turns orders of magnitude faster because it's been doing so for the last 4.5 billion years on the momentum imparted to it when it formed out of the accretion disk. This Red Herring of yours aside, you cannot be serious that reaction-thrusters could produce a precision change of inertia in a half-million tonne object in moments. Unless you're now going to propose that the things are actually equipped with the Handwavium Drive instead.

...says the guy who is proposing the use of an antimatter rocket to send this thing off in the first place (I wonder if the neutrino emissions would go unnoticed). Since I already proved that only 2.5 meter lenses would be needed several posts ago, you repeatedly ignoring it and accusing me of bringing forth a red herring is...

Actually, the figures regarding beam diffraction over distance shows how far off you truly are in most of your assumptions but you'll just go on ignoring those, I suppose.

Since you seem incapable of doing relevant math, .716 degrees, over 4.5 days, comes out to 6.63 milliarcseconds per second (on average, it's not scaling linearly). Over these 4.5 days the limbs of the unneeded 1,000 km lens would move 6.25 kilometers at the extremes.

I'm not sure what sort of magic drive you believe is required, since a great deal of load balancing is possible across a plane.

Uh huh. 4.5 days to try to maintain a constant dwell on an object moving at better than .99c, with a beam which is spread out over a diametre of 28,000km at the target zone which means the beam intensity isn't worth jack shit for any purpose...

[Ariphaos]

That means there is effectively no focus to the beam. You actually do need a large lens to ensure tighter focus over greater distance (also so that the heat of the beam doesn't melt the lens before any effective work can be done). A 1000km lens, on the other hand, results in a beam spread of only 107 metres at a target zone 10 lightdays out from Earth.

So, are you claiming that the energy magically vanishes for a diffused beam, or what? Yes, a laser would ideally be pulsed and mode-locked - those issues are tangential to the point.

I'm not claiming one lens is doing the firing, either. Only that something much smaller than a megameter lens is necessary, which you have a strange fixation on.

[Patrick Degan]

That means there is effectively no focus to the beam. You actually do need a large lens to ensure tighter focus over greater distance (also so that the heat of the beam doesn't melt the lens before any effective work can be done). A 1000km lens, on the other hand, results in a beam spread of only 107 metres at a target zone 10 lightdays out from Earth.

So, are you claiming that the energy magically vanishes for a diffused beam, or what? Yes, a laser would ideally be pulsed and mode-locked - those issues are tangential to the point.

I'm not claiming one lens is doing the firing, either. Only that something much smaller than a megameter lens is necessary, which you have a strange fixation on.

You're on drugs, right? You SERIOUSLY imagine that an unfocussed laser beam deposting its energy over thousands of square kilometres is going to be doing any effective work on anything?!

[Ariphaos]

You're on drugs, right? You SERIOUSLY imagine that an unfocussed laser beam deposting its energy over thousands of square kilometres is going to be doing any effective work on anything?!

So, taking this red herring back to the 2.5 meter level, we have a few quadrillion (their number does not really matter) of these focusing their unfocused beams at said distance, all of them covering the same area at the target spot.

By my last post, I suggested an energy density of 15 GW/M^2, using a fraction of a percent of the Sun's energy. Lorentz contraction means it's experiencing roughly 330 GW/M^2 at .999 c.

You are claiming, then, that at this energy level, no significant work is being done? What happens to it? Does it pass through your RKV's unharmed? Does it bounce off without changing it's momentum? What?

[Flagg]

I think the most likely reason aside from religion or a 'them vs us' scenario is kind of obvious. That or I'm a total idiot.

Interstellar disaster, like a gamma ray burst. You have a powerful interstellar civilization that suddenly has to flee it's systems just to survive. This would require a nearby interstellar civilization far enough away from the disaster area to have no appreciable damage, yet close enough to be within range of the refugee ships. Assuming that the intact civilization is large enough that there are no 'empty' systems within range for the refugees to utilize and colonize, then that could make a decent staging ground for an interstellar war.

[Patrick Degan]

You're on drugs, right? You SERIOUSLY imagine that an unfocussed laser beam deposting its energy over thousands of square kilometres is going to be doing any effective work on anything?!

So, taking this red herring back to the 2.5 meter level, we have a few quadrillion (their number does not really matter) of these focusing their unfocused beams at said distance, all of them covering the same area at the target spot. By my last post, I suggested an energy density of 15 GW/M^2, using a fraction of a percent of the Sun's energy. Lorentz contraction means it's experiencing roughly 330 GW/M^2 at .999 c.

You are claiming, then, that at this energy level, no significant work is being done? What happens to it? Does it pass through your RKV's unharmed? Does it bounce off without changing it's momentum? What?

Doesn't work that way, Sunshine. The relevant formula used here is, according to the folks at Atomic Rocket:

Bpt = BP/(π * (D * tan(θ/2))^2)

where:
Bpt = Beam intensity at target (megawatts per square metre)
BP = Beam Power at laser aperture (megawatts)
D = range to target (metres)
θ = Theta = Beam divergence angle (radians or degrees)
π = 3.14159...

—because you are attempting to intersect one point of a circle with a straight line, and in this case the circle has a radius of 2.6E13 metres.

Using a 2700 nanometre beam (mid-infrared range), the figures work out to:

Bpt = 6500/(π * (2.6E13 * tan(0.000019/2))^2)

or a beam power at target point of ~1.033E-23W/m^2

Using a quadrillion lenses, you might get that figure up to .00000001W/m^2. Of course, this assumes that none of those 2.5 metre lenses would have melted into a thin goo while trying to dump 65GW of heat through them. Which, BTW, is one of the reasons why a lens of 1000km diametre was proposed as the model for the cited laser sailcraft paper so as to lessen thermal stress and keep the lens intact through the lasing operation.

So, kindly tell the rest of the class just what sort of useful work is being done on the target here.

BTW, you've also fundamentally misunderstood the concept of a Dyson Swarm, which is the alternative to Dr. Dyson's Shell —of a constellation of solar collection satellites and full-scale orbital habitats in nested orbits around the sun, not simply a large collection of focussing lenses. The concept also has problems due to ultimate limits on the number of structures which could be placed in orbit before they'd start eclipsing one another periodically as well as perturbing each others' orbits. Which is one reason why a quadrillion structures would be unlikely.

[Surlethe]

Patrick, I calculate theta = 1.22(L/R) = 1.22(2.7e-6 m/2.5 m) = 1.317e-6. Then, using your numbers, I input 6500/(pi(2.6e13*tan((1.317e-6)/2))^2) to get 2.3e-8 MW/m^2. I'm not sure if this is correct or incorrect.

EDIT: I'm doing something wrong. Google calculator just gave me 7e-12 MW/m^2. But this is still six orders of magnitude greater than your result.

[Shadowtraveler]

Programming Error (see Star Control 2).

[Beowulf]

Not to mention that you're apparently misunderstanding his proposal. Stick several quadrillion mirrors into close solar orbit. These mirrors will be useful for power generation, so it's useful for them to exist. If an attack is detected, use said mirrors to direct a beam towards the attack. This results in a beam with a wavelength varying between far infrared and extreme UV. The peak will be at about 500nm, so we'll use that for the wavelength. The mirrors can be ball-parked at about 2.5m, let's say. In a vulcan orbit, the sun has an insolation of about 12kW/m^2

Using the equations from atomic rocket: BPT = BP/(π * (D * tan(θ/2))^2), where θ = 1.22*L/RL. We come up with: BPT = .012/(pi * (2.6E13 * tan(1.22*5E-7/(2*2.5)))^2) = 3.79633926 × 10E-16. (plugged into google)

Comes out to needing about 2.6 quintillion mirrors to get a flux of 1GW/m^2. Rather high. Increase the size of the mirrors to 100m, however, and you get the much more manageable number of 1.6 quadrillion (though that still is rather high). Given that you could use solar pressure itself to manage the perturbations, you don't have to worry too much about them screwing each other orbits up. Of course, that's just mirrors reflecting. You'd need more because some wouldn't be able to reflect in the right direction. On the other hand, those same mirrors could reflect into other mirrors which can.

If you take into account the increase in flux from the Lorentz factor at .99c, your necessary number of mirrors drops by another sixth, approximately.

It's still a completely insane number of mirror satellites though. Of course, the RKV attacking civ needs an approximately equivalent power generation capability to manage an attack. A 1kiloton mass requires 5e23 J of energy to get it up to speed. The mirror array gives that amount in about 5 seconds. With thermal limits, you could feasibly use only half the thermal power. Even if you take weeks to come up to speed, you only lower the amount of generation capacity required by six orders of magnitude. And you'd still need to power your civilization for those weeks.

Assuming a RKV of 1x1x127m dimensions (about 1 kiloton of mass), it'll recieve about 1GW. It takes about 11MJ/m^3 to boil it away (0K to boiling point of iron). Thus, the RKV will be gone in about 1 second. (Ballpark figures, doesn't take into account heat of boiling or vaporization, or the decrease in boiling point in vacuum, the shattering effect of the beam, or a host of other factors). Every order of magnitude increase in boiling away the RKV decreases the number of mirrors required by the same magnitude. You want it to take a day, and the number of mirrors drops by 5 orders of magnitude. Makes it a couple million at that point. Increase the diameter of the projectile, and the time drops further.

Aiming the beam array isn't much of a problem because the RKV is coming effectively straight at the sun.

[Ariphaos]

Doesn't work that way, Sunshine. The relevant formula used here is, according to the folks at Atomic Rocket:

Bpt = BP/(π * (D * tan(θ/2))^2)

where:
Bpt = Beam intensity at target (megawatts per square metre)
BP = Beam Power at laser aperture (megawatts)
D = range to target (metres)
θ = Theta = Beam divergence angle (radians or degrees)
π = 3.14159...

Interesting, the calculator linked to from that site is giving some extremely different results.

Let's see, divergence angle equation is:
θ = 1.22 L/RL

θ = 1.22 * 1E-6/1.25 = 0.000000976
tan θ/2 = 4.88e-7

Bpt = PowIn/(3.1416 * (2.6E13 * 4.88e-7)^2)
Bpt = PowIn/505,750,374,046,025

The divisor is exactly the same as the target area in square meters for said laser according to RT = 0.61 * D * L / RL, who would have guessed the laser beam does not magically lose power over distance!?

It's a collection of them coming up with the total power output, that's why I said the number of individual mirrors didn't matter (for our purposes). If there needs to be 1E20 of them because they can only handle 6.5 kilowatts, well, same deal.

In any case, it seems about 2% of the Sun's light would be needed for a power density of 15 GW/sqm (my bad), or 7.7E24 watts total input. Whatever.

—because you are attempting to intersect one point of a circle with a straight line, and in this case the circle has a radius of 2.6E13 metres.

Using a 2700 nanometre beam (mid-infrared range), the figures work out to:

Bpt = 6500/(π * (2.6E13 * tan(0.000019/2))^2)

or a beam power at target point of ~1.033E-23W/m^2

1: You calculated the diffraction angle wrong. See above. Running that equation is exactly the same as calculating the size of the target, then dividing the total input power by said size. It's just an equation to skip that part.
2: The input power into a single mirror is irrelevant - If it's 6.5 kilowatts per mirror, then there would be more of them (though it would probably be closer to 150 kw/mirror/lens/whatever the appropriate intensity is at 30 gm from the Sun).

Using a quadrillion lenses, you might get that figure up to .00000001W/m^2. Of course, this assumes that none of those 2.5 metre lenses would have melted into a thin goo while trying to dump 65GW of heat through them. Which, BTW, is one of the reasons why a lens of 1000km diametre was proposed as the model for the cited laser sailcraft paper so as to lessen thermal stress and keep the lens intact through the lasing operation.

Irrelevant. See above. We want a diffuse beam to cover any possible trajectory of approach.

So, kindly tell the rest of the class just what sort of useful work is being done on the target here.

Nifty calculator linked from Atomic Rocket

Multiplying the input power by 22.5, we get 1.73E26 for the total power in. This is vaporizing nearly 8 cm of tungsten per second (- from the RKV's point of view) on the face. I wish there was an input variable for the incident angle for the lateral component. Let's see

At 89.92 degrees, a specific slice of the angled beam would be 18 gm long (initially), either divide the input power by cos θ, or multiply the total area by 18,000/25. The former is easier since I can plug it into the calculator. 2.4E23.

For .1 mm/sec of tungsten vaporized initially along the side of the RKV, rising to 1 mm/sec after 4.5 days, with linear growth. Ignoring whatever lateral force it experiences, we get

t = 4.5 * 86400 / 22.5 = 17,280 seconds
(.1 + 1)/2 * 17,280 = 95,040 mm vaporized from the side and
79 * 17,280 = 1,365,120 mm vaporized from the front.

Assuming the target is tungsten.

(Duty cycle and duration of 1, obviously)

BTW, you've also fundamentally misunderstood the concept of a Dyson Swarm, which is the alternative to Dr. Dyson's Shell —of a constellation of solar collection satellites and full-scale orbital habitats in nested orbits around the sun, not simply a large collection of focussing lenses. The concept also has problems due to ultimate limits on the number of structures which could be placed in orbit before they'd start eclipsing one another periodically as well as perturbing each others' orbits. Which is one reason why a quadrillion structures would be unlikely.

Well, the Swarm itself is the collection satellites. They need to transmit their power somehow, so... how are they going to do it?

And what -else- should I call the result? Seriously.

As for the sheer number I speak of, the Vulcans have over 15 gm of radial space to orbit safely in. While it's a given that they won't be able to cover the entire Sun, that's a lot of space to put objects with trivial masses in.

[Ariphaos]

Not to mention that you're apparently misunderstanding his proposal. Stick several quadrillion mirrors into close solar orbit. These mirrors will be useful for power generation, so it's useful for them to exist. If an attack is detected, use said mirrors to direct a beam towards the attack. This results in a beam with a wavelength varying between far infrared and extreme UV. The peak will be at about 500nm, so we'll use that for the wavelength. The mirrors can be ball-parked at about 2.5m, let's say. In a vulcan orbit, the sun has an insolation of about 12kW/m^2

You will notice I said mirrors first, I went to lasers because Patrick had some sort of insistence on them. Honestly it will come down to if collectors can beat the efficiency provided by mirrors. If solar collectors can be made to exceed 80% efficiency, then by all means use them and raw laser output instead.

Comes out to needing about 2.6 quintillion mirrors to get a flux of 1GW/m^2. Rather high. Increase the size of the mirrors to 100m, however, and you get the much more manageable number of 1.6 quadrillion (though that still is rather high). Given that you could use solar pressure itself to manage the perturbations, you don't have to worry too much about them screwing each other orbits up. Of course, that's just mirrors reflecting. You'd need more because some wouldn't be able to reflect in the right direction. On the other hand, those same mirrors could reflect into other mirrors which can.

The entire 2.5 meter thing is absurd, yes. The point isn't there number, the point was his silliness about beam diffraction and somehow not being able to focus on an Earth-sized target at five light days. -that- is why I sued 2.5 meters, it's the smallest size that could be used to cover the relevant target area.

Naturally, any civilization is going to want as large of collectors/mirrors as possible to maneuver at reasonable speeds. I'd probably go for a kilometer instead. If you need a bigger lens/mirror (though I've honestly no idea why), build another one they can point at.

If you take into account the increase in flux from the Lorentz factor at .99c, your necessary number of mirrors drops by another sixth, approximately.

.999c, or ~22.46 (I used 22.5). I think this actually would end up ablating through the local fluff (.26 particles / cc), so it's probably faster than desired. Note that most of the galaxy is a bit more than 1 particle/cc.

At .99c, the defense would begin out at 50 light days, and there would actually be nearly a half day to make reasonable corrections as needed. This would be another reason why you'd want large mirrors, of course.

It's still a completely insane number of mirror satellites though. Of course, the RKV attacking civ needs an approximately equivalent power generation capability to manage an attack. A 1kiloton mass requires 5e23 J of energy to get it up to speed. The mirror array gives that amount in about 5 seconds. With thermal limits, you could feasibly use only half the thermal power. Even if you take weeks to come up to speed, you only lower the amount of generation capacity required by six orders of magnitude. And you'd still need to power your civilization for those weeks.

I still want to hear how this thing is better powered by antimatter rockets, according to Patrick.

[Ariphaos]

At 89.92 degrees, a specific slice of the angled beam would be 18 gm long (initially), either multiply the input power by cos θ, or multiply the total area by 18,000/25. The former is easier since I can plug it into the calculator. 2.4E23.

Ghetto edit >_>

Also, I've been using micrometer wavelengths consistently, so I'm sticking by them. Since a micrometer is already longer than peak Solar output, there's no reason to use a longer wavelength for these exercises.

[Patrick Degan]

Since it appears I was off in several aspects of my maths, I will have to concede this argument for the present time.

[Nyrath]

Topic drift much?

The point is WHY two spacefaring civilizations might fight each other.

The standard motives for aliens to contact Earthmen from 1950's SF novels are, according to Solomon Golumb:

* Help!
* Buy!
* Convert!
* Vacate!
* Negotiate!
* Work!
* Discuss!

Most of them can become motives for interstellar combat if you add the clause "...or DIE!"

[Guardsman Bass]

Back to motive-

The Killing Star has an interesting hypothesis, but I think even that is too anthropocentric. Why necessarily would most civilization's technological development lead to rocketry at all? There are plenty of imaginable pathways for humanity that could have skipped rocketry in its current forms, or trapped us in technological stagnation. I think it's far more likely that whatever civilizations exist in the universe, most of them probably do not reach rocketry and don't care, and those that do are very scattered.

It's still an interesting motive for interstellar warfare, though.