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OK, let's say that you have an interstellar human population. You've got people who live on different planets in various systems, but you also have people living in space stations in different systems.

Now, given such a society, the ultimate weapon would be a long-range kinetic impactor: something that accelerates a reasonably-sized mass to a substantial percentage of the speed of light, so that it can hit planets and take them out. Eventually.

The obvious problem with such a weapon is that there's basically no "aiming" mechanism possible which is accurate enough across interstellar distances. Even if you knew the locations of all celestial bodies in the target system when you left and could predict their locations by the time the projectile arrives, you still cannot guarantee that you can aim with sufficient accuracy to hit the target location.

No problem; you just install a guidance system in the projectile. It should have some kind of camera that can see stuff, and it should have some minimal reaction mass so that it can perform course corrections based on what it sees.

Which brings me to the question. If you've got a projectile going 0.99c (relative to the target system), would relativistic effects make it difficult to perform the course-corrections needed to strike the target planet (assume it's Earth-sized)?

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    $\begingroup$ Sorry, but why is there no aiming mechanism possible? If you have the power and technology to accelerate a decently sized object to a large fraction of the speed of light, you would definitely be able to fulfill the energy and computation requirements to aim across interstellar distances. After all, the aiming mechanism is "mathematics", and "mathematics", if done correctly, cannot be wrong. $\endgroup$ – Aify Jan 27 '18 at 22:53
  • $\begingroup$ @Aify: Ignoring the question of whether you can even find the exact point in space with sufficient accuracy, we're talking about a circumstance where if you're off by a trillionth of a degree, you miss. That level of precision is below the noise floor of pretty much any system you could use to accelerate such a particle. $\endgroup$ – Nicol Bolas Jan 27 '18 at 23:23
  • $\begingroup$ A planet is a very large object. You mention an "interstellar" human population; how far interstellar are you talking about? We humans have gotten very very good at precision engineering. $\endgroup$ – Aify Jan 27 '18 at 23:25
  • $\begingroup$ @Aify: The distance to Alpha Centauri is about 275731.1 AUs. The size of the Earth is about 4.3*10^-5 AU. To hit the Earth from Alpha Centauri without guidance, you need to be able to aim with a precision of 9 billionths of a degree (and that's before factoring in any precision issues for math predicting the movement of celestial bodies). I feel perfectly comfortable calling that impossible. Or at the very least, unreasonable. $\endgroup$ – Nicol Bolas Jan 27 '18 at 23:41
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    $\begingroup$ To an observer at rest, the projectile would appear to cross 1 AU in about 5 seconds. To an observer traveling on the projectile at .99c, the same 1 AU takes about 0.6 seconds. Seems like plenty of time for an onboard guidance system to calculate minor corrections and begin to implement. $\endgroup$ – user535733 Jan 28 '18 at 2:11
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Light travels at the speed of light regardless of the origin reference frame. But from the point of view of your 0.99c projectile everything will be extremely blue shifted. That's an easy fix, you just make sure that your guidance system can see in an appropriately high frequency.

The weird bit would be in the time dilation effects. Any countermeasure that the target world uses would seem to move with super speed from the point of view of the projectile. So very robust counter-countermeasures that will prevent the weapon from being knocked off course and being unable to correct itself are going to be where you want to focus.

The target planet can't just block it by letting it hit something in between the projectile and the target - you'd still have to deal with 0.99c shrapnel which would suck. So the target needs to find a way to deflect the projectile, and you (the projectile) don't want that. Maybe a cloud of drones that are dragged along or deployed to block anything that might try to deflect our weapon. Or make it an EMP monster that is broadcasting so much interference that the only way to stop it is to try to block it directly and take your chances with the bits - which probably equals a destroyed planet anyway.

If your team can run this thing up to 0.99c, then the target may be able to move their planet out of the way. They might try to blind your projectile or break it up and move their planet once your weapon is on a fixed trajectory. So you'd want different types of guidance systems and a lot of redundancy - maybe even a way to reorient and reset the guidance system if they try to use the cameras as a vector for a cyber attack. If they are going to try to break you up and then move their planet, then you want some way to counter their attack. This could look like active defense laser/missile/drone that is going to knock their defender off course or a very capable thrust system that will help you maneuver around whatever they send at you.

Now if you're going to invest the resources to run a projectile up to 0.99c the answer is probably "all of the above." So the success or failure of the attack comes down to where in this measure/countermeasure/counter-countermeasure chain one side is able to overwhelm or out fox the other.

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You shoot twice

First off, I dispute your assumption that it is so hard to aim at a target. How do you get your projectile to 0.99$c$ in the first place? Well, I would suggest that you push it there with a laser.

You put your projectile into space. You put a gyroscopic stabilizer on it. You then hit it with a laser, and use laser ablation to get it up to speed. The gyroscope will take care of orientation of the ablated material; the narrowness of the laser beam will take care of directing it in a perfectly straight line. Since it will take a while to get your target up to 0.99$c$, so long as the projectile stays on the path of the laser, it will have made it thousands of AU or even an appreciable fraction of light year on target so far. A that point, it can just glide the rest of the way there.

The accuracy will be high, but of course you won't be guaranteed to hit. So you just shoot it a few times. Keep shooting until the planet is dead.

On the other hand...

Why would a relativistic kinetic weapon work if launched at Earth from Alpha Centauri? It is going to take over 4 years to hit. Given the nature of military intelligence, it seems likely that word of the launch would get out. How much good this word does, of course, depends on if there is any FTL communication.

In any case, the points you make about how hard it is to hit a target apply doubly to defending a target. If all you have to do is disrupt a projectile's course by some tiny fraction of an arcsecond, then a few seconds with a TW laser should make sure your projectile misses.

You might have to shoot a bunch of times to ensure you can punch through any defenses on the target.

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The relativistic effects simply make a bad situation worse.

The trouble with terminal guidance is that you need to provide the thrust to change your vector. The bigger the degree of change and the faster that needs to happen, the more thrust you need.

The farther from the target you are at the time of a course correction, the easier that correction will be. That means that the best time to course correct will be at or just after launch since the degree of change will be much smaller and you will have plenty of time to correct that.

If you are 90% of the way to your target (being very generous) before you have a good enough image to make corrections, your angle of defection will be much higher and the time you have to make the change will be much shorter.

Even if you have some scifi tech that doesn't require rocket fuel, the energy requirements are going to be huge. The equipment to perform the maneuver and store the energy will likely be quite large. A larger payload means that the initial launch will be much more expensive.

The relativistic effects give you an even shorter reaction time. It's not that it can't be done but the cost skyrockets.

The only way I see this working is the method E.E. Doc Smith used: accelerate an object to near c and then make it inertialess and tow it in position where it's vector will intercept the target and turn off the inertialess system.

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Well, I think @MParm answer is good enough as it is. I would like to add two cents though.

Why not, while the projectile is flying through space, just let said projectile to have a correction course system with it?

You take aim, make calculations, and shoot it. It happens that the system by some reason added one more zero than it should (it is still pretty new, what did you expect it would happen?) so, to guarantee that the projectile just doesn't go drifting into space, the course correction system onboard will realign the projectile based on the new calculations in relation to its target.

I think that would solve the problem of aiming :) hope it helps.

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At that speed, the planet you're aiming for has to be on the far side of the sun when entering the solar system. Only this way will you even receive enough light to "see" it. Though even that takes great optics. But given that you can acc. to 99c, that should be an easy step. Depending on the projectiles mass, you need to decide where you want to hit. Is it enough to hit the plant's atmosphere? Is it enough to hit it "somewhere" or do you need to hit solid ground (no sea) for maximum effect. Do you want to hit a specific continent? With those questions in mind, you can calculate the maximum distance at which the structures size can be resolved with optics of 'r diameter and thereby the maximum time available for corrections and the energy and mass required (and stored) in order to make the corrections in time.

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When you can't be accurate, you need a decent spread. Therefore I suggest you fire a planet at them. Fill it with planet busters and explode it like a giant cluster grenade upon entering the system.

This has the advantage of costing a planet to take out a planet, making it a relatively limited resource as all good superweapons should be.

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