Assume that the alien marauders have FTL and are roughly equivalent to a type 2 civilization. The defenders are roughly type 1. What is the best approach to eliminating this planet? Note: The aliens dont care about the planet itself-they just need to kill off ALL life on it.
8 Answers
Planets have a lot of really useful materials for a Level II civilization, but it is held by a rather huge amount of gravitational binding energy.
Under the Atomic Rockets Useful Tables tab, we can look up the gravitational binding energy of the Earth as:
2.9 X 10^32J
That's a bit extreme, and gravel sized chunks moving at solar escape velocity are not particularly useful. On the other hand, simply disintegrating the Earth and creating a new asteroid belt leaves the KII civilization with lots of useful matter for building, and that only needs
2.9 X 10^31J
For comparison, the Sun's luminous output per day is
3.3 X 10^31J
If we want to do this in a methodical method, and perhaps be able to sort materials by ionizing them and then separating the elements using magnetic fields and cold traps, a Nicoll-Dyson beam is probably the best method to use. The home star can have its power output formed into a collimated beam, and the offending planet can be evaporated from light years away. Certain issues like lead angles and absorption of the beam by interstellar medium or planets passing through the beam have to be taken into account, but you don't need to divert that much of your sun's energy. The only other issue is time lag, since the beam will be moving at the speed of light. If the target planet is 1900 light years away, then you might have to fix a drink and binge watch your favourite series (Game of Planets is good, although many critics claim the writing took a downwards turn starting at season 3000...).
https://www.artstation.com/artwork/ybElkQ
If you are using your star for something else, sending Von Neumann machines is a cost effective way of doing things. So long as a single working device ends up active in a Solar System, it will start consuming materials and begin reproducing. Since each "generation" doubles (1:2:4:8:16 and so on), the devices increase by geometrical progression. Stopping at an out of the way moon allows the devices to replicate into the billions or trillions, before moving onto the planet you wish to sterilize. Even if they only consume the top 5 kilometres of the planet's surface, they will likely have consumed the entirety of the biosphere, atmosphere, hydrosphere, the biologically productive parts of the lithosphere...
The time investment depends on the reproduction rate of the Von Neumann machines, but since you only need to start with one, it is cheap and effective.
If you are still using your Sun's output, but don't want to wait for Von Neumann machines to take all that time replicating, the last option is using RKKVs (Relativistic Kinetic Kill Vehicles). A great deal of energy can be packed into a body by accelerating it, and moving at relativistic speed bring s that to insane levels. Using the Boom Table again, we see 1kg at 99.99% c releases:
6.3 x 10^18J
A 9.5 earthquake is the next event on the table, releasing twice as much energy (about 3 Gigatons equivalent).
A series of these devices can be used to scour the face of an offending planet, and considering the relatively low amount of energy in any individual RKKV, a KII civilization should be able to churn these out and launch them like potato chips. Targeting the Sun should also have interesting effects, triggering giant solar flares and rendering any space based industry or shelters inoperable as well. Of course, you could simply blanket the entire solar system with RKKVs and reduce it to a massive asteroid belt to mine at a later date.
A stray RKKV hits the Moon. The Range Safety Officer will have a word with you
The thing to remember is the KII civilization absurdly outmatches the KI civilization in energy output by orders of magnitude. They could simply move into the Solar System and start Star Lifting, building a Dyson swarm of their own, instantiate a Matrioshka Brain in the Dyson Swarm, Stellify Jupiter to make another Solar System and even remodel the Oort cloud without stopping to ask permission. They might not even notice that there is a KI civilization, unless it is annoying like a nest of termites, in which case it is dealt with swiftly and efficiently using some of the methods discussed.

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The problem with k2 civilizations - they need to invent some new physics, there're no materials one can manipulate that can withstand the energy fluxes required to redirect the Sun's energy into a tight beam. – Adrian Colomitchi May 18 '20 at 01:55
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It's simple, really - just make an optically perfect mirror the size of the Moon's orbit around the Earth... The Nicholl Dyson beam simply turns the Dyson Swarm into a phased array, so each individual element only has a tiny fraction of the beam's full power. – Thucydides May 18 '20 at 02:06
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optically perfect mirror
see? that's new physics already - haven't seen yet a material the reflects hard X rays, or even act as a reflector for all the usual wavelengths.into a phased array
that requires you to control the phase. Which you can only do if you transform the incoming energy into something controllable and "transportable" - at the current level of physics, this involve efficiencies far from ideal; and so you will need to exhaust the losses – Adrian Colomitchi May 18 '20 at 02:14 -
All this fancy technology sounds a bit like overkill. Why not simply fly there and nuke the entire planet from orbit? If the planet is as advanced as earth, there is literally nothing they can do. And if the attacking civilization is advanced enough to turn suns into giant death stars, then replicating a few gigatons of bombs is something they will be able to offhandedly do while in transit. – mlk May 18 '20 at 07:19
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typo: It's a Nicoll-Dyson beam, not Nicholl. (Can't edit for one character.) – Ross Presser May 18 '20 at 15:06
/alien marauders have FTL /
Accelerate a large and weighty chunk of stuff to FTL. Allow it to impact the earth. The earth will be rendered molten. If you hit it head on it will alter its orbit. If you hit it hard enough it will fall out of orbit into the sun. That will do for life.
FTL is good for lots of stuff.

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Accelerate a large and weighty chunk of stuff to FTL.
This imply the stuff being made of tachyons, which don't interact with normal matter. Or go into a dimension where Earth doesn't project. Now, if you talk making the stuff materialize at the end of FTL travel inside the Earth, that would do the trick. – Adrian Colomitchi May 18 '20 at 01:48 -
@AdrianColomitchi Yah, FTL presents problems, it does. For the impactor to stop the earths orbitI think 0.99c ought to do the trick. – Willk May 18 '20 at 03:14
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You act as if its a relativistic projectile. If it was it would have infinity+1 energy, any impact even with a single atom of dust would cause an infinite mass black hole that expands infinitely at the speed of light. So any FTL would not be relativistic in this method. – Demigan May 18 '20 at 05:41
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1@AdrianColomitchi: Not necessarily. If it’s using a variant on the Alcubierre-white warp drive it would just be a bubble of warped spacetime pushing an impossibly hot layer of incandescent plasma. You wouldn’t even need to impact the planet with your ship to charbroil it. – Joe Bloggs May 18 '20 at 06:28
Most effective? Make the victim civilization kill itself.
If you can wait a while, use mass psychology. E.g. spread conspiracy theories until they have narcissistic type1 strength doofuses and autocrats as leaders. Send some carefully modulated electromagnetic signals to their AWACS-equivalent so they think they are being attacked. Cause counterstrike and wait for mushroom clouds to settle. Easy!

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1@gerrit You bet. They wear "Make Aliens Great Again" caps, these lizard people :-) – Jens May 18 '20 at 09:56
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2We've known for more than 200 years that we're ruled by lizard people, so it's about time they get to work! – gerrit May 18 '20 at 12:16
Create a bio engineered pandemic. Clean and easy.
Have the first wave be asymptomatic and infect as many people as possible. It might still kill the weak and the elderly (1% to 4% death rate) thus alerting the population.
Then mutate the virus for the second wave and increase the death rate to 100% Make sure the technologically retarded type 1 Civ will never be able to find a vaccine by bio engineering the virus in a way that makes it impossible for them to cure it in time.
Bonus: Make it look like the pandemic emerged from a country that s not liked by the rest of the world for added chaos. The pathetic type 1 Civ might exterminate itself before the pandemic does.

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I'm not a disease specialist by any means, but I don't understand what's the point of having a "first wave" of one strain, to follow it up with a "second wave" of a different strain? Because it's a different strain it would have to spread again, harder due to the alerted species. More applicable might be to have long term side effects that become 100% deadly after 3 or 4 months with few (no) symptoms up until then – Nathan May 18 '20 at 10:42
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The first wave infects everyone under the radar, then it mutates within its hosts to become more virulent. The reason the 1st wave should be benign is to not kill the hosts too quickly. – Fred May 18 '20 at 23:52
Give the wrong people a particular set of technology.
Some people just disagree with the world. They just want more power, they might think they would be so much better at it or they just want a particular group of people to disappear (and then find another group to disagree with). Give these people the economic and military might to take over the world and make it akin to North Korea or worse. Make sure there will be multiple of such uncaring warlords and they will happily annihilate most of the world's population for you in war, hunger, disease and possibly radiation. If they dont starve the world you can step in and dispose of the remainder.
If you do it right you could even make these warlords dependend on you. They pay you in resources you will want eventually in exchange for technology and luxury products they can only get from you. You can create scarcity of these products to ensure these warlords will fight each other in order to get it. Once they've worked or fought most of the world's population to death while paying you to do your own job, you take over.

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Ah, but what are your criteria of "effectiveness"?
The "simplest" would probably be, as others said, "drop a big rock on it". Any space-faring civilization, even without FTL, can do that already. With FTL tech it'd be a piece of cake.
Bio-engineer a plague is a bit trickier. You basically need samples of the local fauna, and presumably, local fauna will heavily object to being subjects of experimentations. While evading sensors may not be hard, it is much harder to evade "Mark I Eyeballs".
To ensure 99.99+% eradication, one may need to combine the methods. Hit them with a plague, THEN hit them quickly with a big rock, or several, forcing people into shelters and let the plague spread from there. Any survivors will be too few in number to propagate the species.

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A Dyson sphere
A Dyson sphere is a typical example of what a type 2 civilization should be able to do. So build a dense one around the sun. Blocking only a small percentage of the light that reaches the earth will make it freeze.
Bonus: you get energy from the Dyson. And, if you want to go Nestlé style, you could sell this energy to earthling to heat their planet.
Crashing anything that weights a few tons and travels near the speed of light into a planet is going to kill everybody on the planet. Depending on how their FTL travel works it might just be easy to crash one of the FTL ships into the planet they want to eradicate.

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roughly equivalent to a type 2 civilization
Then they can roughly alter the planet's orbit on a collision course with another. – Adrian Colomitchi May 17 '20 at 22:49