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Is there one? Or could you simply fire on any target within your sensor range and hit so long as it isn't so far away it'll have moved out of the path of the beam by the time the light travels that far?

As a bonus question, would relativistic missiles have the same effective range as lasers in space, or would they be shorter/longer?

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Two very interesting but quite different questions here.

Lasers can be built at such scales that you could fire them at other star systems and deliver energy. Robert L Forward did the calculations for an interstellar starship powered by massive laser driven lightsail. Of course to power it, you needed terawatts of energy to drive the laser, and a lens over a thousand kilometres in diameter to focus the laser on the target spacecraft light years away. Scaling the idea even further, you can create a Nicoll Dyson Beam and destroy entire solar systems across the galaxy

enter image description here

This is strategic level weaponry, and requires either a cooperative target, like the laser sail starship, or a slow moving and predictable target, since moving at the speed of light a Nichol Dyson Beam fired from Earth will still take 4 years to reach Alpha Centauri.

For more "tactical" level weapons, such as ones needed for spaceship to spaceship combat in the solar system, you can build huge "Ravening Beams of Death" (RBoD) which can vaporize metals and ceramics in milliseconds at a light second range, illuminate and scorch targets out to a light hour, but in any practical sense, the maximum combat range of a laser being used to target another spacecraft or accelerating object is one light second.

enter image description here

FEL RBoD tuned to fire X-rays. To get the idea of scale, the accelerator ring is a kilometre along the long axis Details on the Atomic Rockets Conventional Weapons page

This allows the firing platform to identify targets 300,000 km away, take aim and fire, with only a one second delay between firing the weapon and the beam striking the target. This means there is only a second delay to see effects on the target, and you can quickly adjust for the target's attempt to break target lock.

For RKKV's (relativistic kinetic kill vehicle), the problem is much different. The vehicle is moving at close to the speed of light, in order to deliver the maximum amount of energy into the target.

Since it is moving at close to the speed of light, it is essentially coming right behind its own light cone, and essentially invisible to the target. Even if you somehow see the RKKV on its inbound run, you only know its position in the past, and not its current position. Trying to aim at it with any sort of conventional weapon would simply be a wild guess.

RKKVs do have one weakness, however. The vehicle is moving at such a high speed that even striking a hydrogen atom in deep space would release an immense amount of energy. If it seems that being attacked by RKKV's is a possibility, then putting shells of dust or gas around the solar system and target planets would cause the RKKV to be heavily damaged or even destroyed well in advance of it reaching the inner solar system. The sudden release of energy in deep space as these things run into the shells of gas and dust would provide warning that something is happening, and provide a clue to the direction of the attack, allowing you to send a counter wave of your own RKKV's, or fire a Dyson Nicholl beam back at the attacking star system.

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  • $\begingroup$ What about in ship to ship combat? Would such gas or dust shields protect large ships or asteroids or would the shields be too thin to sufficiently damage the projectile? $\endgroup$ – Z.Schroeder Oct 18 '16 at 0:21
  • $\begingroup$ The effect of an RKKV impacting a dust cloud will be the release of the same amount of energy as if it were to strike a planet, only spread over a longer period of time. Your spaceship cannot have a cloud that large, and if it is close enough to the erosion track in the cloud, the ship will be destroyed by the radiation release. RKKV's are Planet Busters, and any ship unlucky enough to be in the path of an RKKV will sacrifice itself to save the planet..... $\endgroup$ – Thucydides Oct 18 '16 at 1:30
  • $\begingroup$ Laser weapons are always countered with reflective shields, so effective protection is not dust, but something which will reflect the waves. For ships I have no idea, for planetary defense it can be artificial cloud generation with reflective metal content, but it is still huge effort with low efficiency. $\endgroup$ – Sonic Oct 18 '16 at 9:19
  • $\begingroup$ High energy lasers will not be stopped by simple reflective shields. Even highly efficient dielectric materials reflecting 99.99% of the incoming beam are still absorbing megawatts of energy or more in a very concentrated area and over a very short time frame. The error will evaporate or otherwise fail. $\endgroup$ – Thucydides Oct 18 '16 at 17:47
  • $\begingroup$ Well why not refract them insetead, with refractive metamaterials you can just bend the light so that it shoots out behind the vessel and does no damage. $\endgroup$ – Efialtes Apr 1 '18 at 21:27
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Well, if there was no limit to the power and focusing mirrors. Lasers have an attenuation length, where they will lose energy and lose focus overtime, thus losing power. In open space ,there isn't much dust and such to interfere with the laser, and it's hard for the laser to convert to waste heat, but that will still have some effect.

The attenuation length varies based off the magnetic spectrum of laser you use. A red visible light laser has about... 200,000 meters attenuation length, in Earth's atmosphere (conditions effect this). Can't remember how much it is in space. But that's a very offhand, undetailed estimate.

These pages go into more details about the attenuation lengths of lasers, and the former is a great overview to lasers in general:

http://www.projectrho.com/public_html/rocket/sidearmenergy.php

Attenuation of a laser in space?

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    $\begingroup$ The attenuation length of light beams in space is measured in light-years -- lots of them. The limiting effect for space-based laser weapons is likely to be beam divergence rather than attenuation. $\endgroup$ – Mark Oct 18 '16 at 0:14

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