I have a concept for an asteroid mining station. The metal ingots that are processed are fired out of a railgun towards Earth. How could I slow the ingots down before reaching Earth to avoid accidentally causing an extinction-level event?
Edit: The ingots are about 2-3 tons.
You need to dissipate kinetic energy, which can be accomplished in many different ways.
You could build a "reverse railgun" that catches the incoming ingots. Instead of using stored energy to accelerate the ingots to high speed, the reverse apparatus gently slows the ingots over a long barrel, capturing and storing the kinetic energy as electrical power for use elsewhere.
You could also build an identical railgun to the one that fired the original projectile, and just fire an identical projectile to collide with the first one. Two ingots of the same mass moving at the same speed in opposite directions will collide, and assuming the collision is inelastic, all the kinetic energy will be dissipated and both ingots will come to a stop. This might be a catastrophic collision that destroys the projectiles, though. Alternatively, you could fire lots of small projectiles that would have the same effect in aggregate, but have less energetic collisions.
Since you're firing a ballistic projectile that carries no propellant, you're going to need some external mass or force to affect the projectile. You need to either aim the projectile at whatever provides the mass/force, or bring the mass/force to the projectile.
To steal an idea from one of Peter F. Hamilton's books: aerobraking!
Cast your metal chunks into foam metal blunt-body re-entry capsules. Coat the blunt end with spare rock and whatever else you can synthesise or scavenge from your asteroid mining activities. Attach a suitable solar-powered transponder to them, and shoot them into a suitable re-entry trajectory.
If your shooting isn't quite up to scratch, you can add some little rocket engines to them too... nothing expensive, as shipping them back is impractical. Just enough to do a bit of mid- and end-course correction.
On impact with earth's atmosphere they'll slow right down, and the stuff you've plastered the blunt end with will heat up and burn off in an exciting and pretty way, rapidly slowing the capsule down. Its terminal speed won't be exactly sedate, but it'll be quite restrained. Let it splash down in the ocean. Beauty of foam metal: it can be less dense than water! Send boats out to retrieve these in bulk, between volleys from your mining facilities.
The transponder helps with both keeping an eye on incoming metal packages, and recovering after splashdown.
Trying to use these as weapons would be futile as they'd just be too soft and slow to cause any serious property damage, and too hard to aim to hit anything in space or even any specific targets on the Earth, for that matter. Don't worry about exitinction-level events... the Chixulub impactor that killed off most of the dinosaurs was 1012 tonnes. Your multi-tonne slugs are billions of times smaller. Without clever engineering like I've just suggested, it'd be easy to have most of the metal simply burn up on re-entry.
Fire them slowly.
You do not need your ingots to be cooking along like comets. They don't need to punch thru armor. You don't even need orbital speed. You hardly need any speed at all. They just have to get there. Its not like they are going to go sour if they are late.
Earth will accelerate them some on the way in. Earth actually might accelerate them a lot. The moon is a safer bet. It is smaller. Your slowpoke ingots will ease up to the moon then get a little frisky on the way down. You will not lose any mass to atmospheric friction because Luna is naked. Neither will you have induced eddy currents and ohmic heating because Luna does not go in for that magnetic field stuff.
Your ingots will land with a thump. It is a characteristic thump. Detectors on the moon will triangulate the landing site. Then your robot will go fetch the ingot.
Your foundry is on the moon too. Fewer environmental regulations.
Use a skyhook
It is a more feasible (and fun) version of the space elevator, where the big cable is rotating on itself instead of one side being attached to earth.
The skyhook has the advantage to be able to store energy easily when it receives ingots by rotating faster. You can then use this energy to send back supplies to the mining station.
You can also combine this approach to the other ones mentioned.
The foundry is equipped with a "catcher" - a series of superconducting coils that generate a very strong magnetic field. This is the reverse of the famous magnet-in-the-copper-tube experiment.
As a result, a large portion of the incoming projectile's kinetic energy is converted into thermal energy inside the ingot, pre-heating it and making it easier to melt.
You would also not need to send them with excessive speeds, because all you're interested in is throughput. If you shoot one of them every ten minutes, they will arrive on average one every ten minutes - after several weeks or a whole year on a longer orbit, it's not that big a difference. And shooting slower ingots requires less power.
As @puppetsock pointed out, you don't get away from conservation of momentum: you have some three million kgm/s to go around, so if the smelter masses one million tons, it's going to be moving three m/s in the same direction as the incoming ingot after the catch. Even if it's just 1% of GEO speed, that's still too much (also because you won't be catching just the one ingot).
One economic possibility is having ingots coming from two opposite directions. Whatever the orbit it's in, the smelter is going to need some "downtime" when it's too risky or just impossible to send ingots towards it, so you're going to always need more than one smelter, and adjust its working cycle so it receives ingots just in some points of its orbit. At that point, if it lies e.g. on the ecliptic, it can receive ingots when it's at its greatest incoming elongation; its orbital speed will be reduced by each ingot. Then, the railgun will address the same number of ingots towards the opposite maximum elongation point, and the smelter will intercept them and have its orbital speed increased accordingly, compensating the earlier loss.
When the smelter, as seen from the incoming ingots, is in front or behind the Earth, another smelter will be approaching the maximum elongation points.
The simplest way would be to use gravity assists between the moon and earth to cause the ingots to enter a high, stable, but probably fairly eccentric orbit. Basically, the process would go: metals get extracted and refined in asteroid belt => ingots get shot "backwards" (retrograde) from the perspective of the asteroid's orbit around the sun => the ingots "fall" (follow an orbit with a lower perihelion) towards earth => the ingots get close enough the the earth-moon system to be pulled off course => the ingots follow some precalculated path between the earth and moon, each pass of which slows them down a bit more => the ingots are picked up by an orbital craft and brought to a processing facility.
Advantages of this approach:
-Doesn't require anything to be attached to the ingots. You could include a transponder for safety reasons, but assuming the railgun is reasonably accurate it should be pretty simple to plan the route beforehand and warn any ships to steer clear. Even if it veers off course for one reason or another, the ingots would be pretty trivial to detect and track, and if that didn't work for some reason, the chances of it hitting anything are still very low - think of how many satellites or space stations have actually been hit by meteors (i.e. none).
-Doesn't require aero- or lithobraking. Aerobraking is relatively safe (you probably won't end up nuking any major cities), but adding a chaotic, fluid atmosphere and multiplying that uncertainty over potentially millions of ingots means that some are bound to veer off course. Even de-orbiting objects from low earth orbit is inherently unpredictable. Using either type of braking to slow the projectile down into an earth orbit is better, but would lead to at least some loss of material from ablation or, well, from lithobraking. :p
Disadvantages:
-This method would add to the time it takes for the ingots to reach their final orbit. Given the already-considerable time between the asteroid belt and earth, I don't think it would be too substantial, but it is a factor.
-The ingots will probably be put into high, eccentric orbits, since that would take the least number of gravity assists to get into starting from a hyperbolic orbit. The downside would be that it would require more delta-V for the recovery craft the reach them, and even more delta-V to lower and circularize the orbit into something more useful afterwards. Given that your setting has at least some trans-martian travel, orbital maneuvers around earth shouldn't be much of a concern, but it's still something to consider.
Edit: Reading through the other answers, I've also realized that this method wouldn't require any infrastructure on the receiving end. Loss of funding, political upheaval, or even societal or environmental collapse can occur without having to worry about bombarding the planet with dense objects at orbital speeds or losing the payload into interplanetary space. Although I imagine that any rebuilt post-apocalyptic society is going to be very surprised to discover a bunch of refined metal ingots sitting around waiting for them.
Frame challenge. Don't send it to Earth. We don't need it down here.
The whole premise of asteroid mining (outside of some poorly researched sci-fi) has never been to acquire materials that we need down here on Earth. We've got more than enough metal down here to do everything we need. The point of mining metal in space is so that you can build big things in space.
Let's say you want to build a rocket that can send humans to Titan or Europa or whatnot. The amount of material you'd need to get off the the surface of Earth in order to make such a trip in a reasonable amount of time is prohibitively massive and expensive. It'd be far cheaper to build the rocket in orbit from materials that are already up there.
So what you'd be mining for would be materials to build a rocket, and something that will work as fuel for the rocket. You'd need far less fuel than for a rocket constructed on Earth since you don't need to escape our gravity well. So really all you'd need to get off-planet would be the astronauts, food, water, and other basic supplies for them, and enough equipment to be able to construct the rocket in orbit. (If you're doing this on the regular, you've probably been building up the rocket construction facility for some time now, so ultimately all you need are the people and supplies.
So you're firing metal ingots towards your orbital factory with rail-guns. Well, you only need to match the orbital speed of the factory (or close enough that someone can fly out and grab them), not slow them down enough to get them safely to the surface.
As for fuel, well, you're better off mining comets. Comets are made mostly of ice, which is of course frozen water. Water can be split into hydrogen and oxygen, and hydrogen (along with nitrogen) is perfect for making hydrazine, a powerful rocket fuel. You might also find enough ice on the moon for this purpose. (Launching materials from the moon is far less costly than from Earth due to its lower gravity.) And of course you can use the spare oxygen to breathe.
Just follow the Apollo/Soyuz landing system: ablation shield plus parachutes. The Apollo CM weighed around 5.8 tonnes, the Soyuz reentry section (middle section) 2.8 tonnes.
I have seen pre-parachute speed for Soyuz been quoted as 755 feet/s, that's about 820 km/h - that would likely bury the ingot in the center of an impact crater, so you probably want some parachute, though a smaller one than for Apollo/Soyuz might suffice.
Land or water?
At sea, you need a ship. That's more expensive to operate than a truck with a crane on land. OTOH moving the ingots once collected becomes much cheaper on water. (Coastline may be a good idea.)
If something goes wrong (e.g. the thing crashes into the ground due to parachute malfunction or because the ablation shield didn't properly position itself into harm's way) - well, on water, it just sinks, on land, you have to dig it up, but at least it's there.
Shooting material in your manner is expensive from an energy, infrastructure, and safety stand point. The more you have the harder it is to transport also. What if there was a way to reverse all of those things?
Solar sails
solar sails are not made out of gold, and any metal can be used to make solar sails theoretically. So instead of making a transport system for the materials, you can make the materials the transport system. just take your ingots and turn them into large flat solar sails. They won't be as good as NASA's sails but that isn't the point. solar sails require little to no energy besides a small gyro scope and a computer to pilot the craft. The solar sail will need a a solar sail factory, but that is essentially a machine that flattens the material to the needed width and then sends that to a machine that links those thin sheets. The solar sails are very safe, they accelerate slowly and even if they do get into the atmosphere they will burn up. The more material you need to transport the larger you can make your sails, making them more effective. further more, you can transport other things back to earth that can't be made into solar sails using the sails. you can even throw the material with an accelerator and use sails that deploy mid flight to decelerate it. Solar sails are slow, with an acceleration of 0.058 mm/s^2 acceleration it will take 5 and a half years to accelerate to the needed 10 km/s speed and 5 and a half years to decelerate. If you are willing to wait a decade or two you can get it basically for free. If you are willing to spend energy you can use lasers to speed up the acceleration. However, this will be difficult as in order to transfer the power effectively you would need a very big sail or a very accurate laser. However, if you are transferring a lot of material you can make a very large sail without any problem, making the laser not much of a concern.
Have you thought about using the railgun as an engine? Instead of shooting the valuable stuff towards Earth, shoot the mining waste in what ever direction physics needs to bring the asteroid closer to Earth. Once its in a closer orbit to Earth it will be easier to transfer the valuable stuff off the asteroid and onto the Earth with other spacecraft (or point the rail gun at Earth but now you'll be better able to target things to avoid hitting something valuable).
Shoot them in a cargo bay of your space truck, which is accelerated beforehand obiviously.
if you just shoot them out, without guidance and an orbit correction system - you probably will have a hard time even shoot nearby, not to mention hitting the earth.
with guiding block, you provide the energy and general direction and delta-v for your ingots, space truck catches them and its role is to fine-adjust the orbit to make gravitational reverse slingshot maneuver and insert into the orbit of the earth.
also, to cause an extinction event you need to shoot a very big lump of metals as if you shoot them as 1-10-100kg pebble even if it coincidently crosses earth's atmosphere it will be funny sparks in the sky, and people will make wishes when they see them.
Let's say you have the means to accelerate big objects, 1000's of tons, and more.
Then you have all the means for making a canister with cold thrusters, which works on the oxygen you extract from oxides of those metals, which is about 40% by mass of those materials. And using that mass of oxygen you can maneuver to make a proper insertion.
so your asteroid contains everything you need to make a self-delivering package if you are able to provide it with an initial kick.
shape your copper ingots like a coil, your iron ingots like a cylinder, and give the iron ingots a magnetic field. Then shoot them such that they "collide" on the other side of the Earth. By "collide" I mean the cylinder passes through the center of the copper coil. The eddy currents on the copper coil will serve as a dampener and this will result in a controlled inelastic collision.
Before I get into my answer to your question, I'd just like to request that you give me a little warning before you begin your bombardment. I'd like a chance to not be here when death starts raining from the skies, thanks.
Anyway...
Unguided masses shot in the general direction of Earth are going to wander, no matter how tightly you control the firing mechanism. You'd need to spend a tremendous amount of effort on balancing them for starters, and you've already allowed for a 50% variance in mass, each 'shot' would require a fairly large amount of computation, etc. It's a big, expensive job.
Once you solve those problems there are a slew of others just waiting for you at the other end. Firing into a gravity well speeds up your projectiles, so they're going to arrive going faster than they were when you launched them. The Sun's gravity will speed them up while they approach, then the Earth-Moon system will pull them in even faster. You're looking at a very large amount of kinetic energy to try to bleed off once they arrive.
Most of the normal solutions for the problem will fail in the face of this massive kinetic energy. Aero-braking for instance exchanges kinetic energy for heat, which is likely to result in your deliveries vaporizing in the atmosphere. While some of that heat will radiate away into space, the majority of it will get added to the Earth's total heat. Keep it up long enough and... well, we won't have to worry about the next ice age, I guess.
Magnetic capture might be your best option, especially since you can use the process to generate energy. You're going to need a series of large hoops along the expected path, with enough maneuvering capability to get in the right place. A 2-ton projectile moving at high speed will cause a lot of damage to any structure it encounters, so make sure your timing is perfect. Of course the expense of running these gigantic field generators is going to be pretty high, but you're the one that wants to throw kinetic devastators at a populated planet.
Of course you could always just throw them at the moon, assuming you're not using it for anything else. You'll need to mine the ores out once the dust settles, but that's OK.
It would be far more productive to simply strap a drive system on the packages and have them maneuver themselves into an appropriate orbit around the Moon or Earth. Think more drone, less doomsday cannon.
Using rigid origami and a keen knowledge of the mathematics of paper folding, your ingots can sprout stubby wings and guide themselves down with all the dubious grace of a Space Shuttle. (No, I'm not actually saying to have landing gear, but make a landing slow enough that the ingot can be picked up off a sandy erg in solid form) The Space Shuttle can also inform your heat shielding for the way down; cobble it together out of plates of slag from your refining process. (Yes, you'll end up with craters and shed tiles of space slag all over the desert - let the environmentalists whine! It's still better than making a mine on Earth... probably, at least according to the PR department. The thickness of the metal ingot should ensure that not too much is lost if the heat shielding starts coming apart during reentry.)
Calculate an orbit around earth or moon, where the orbital speed is approximately the speed your ingots will achieve by the time they reach that orbit. That's an easy enough task.
The ingots will need small thrusters to fine tune orbital insertion, and orbital timing (eg to not collide with other ingots or processing stations, or be conveniently close), but those can be recovered and reused.
Without some kind of complicated deceleration device attached to each ingot it becomes a complicated problem in orbital mechanics. If time is not of the essence however it should be possible to work out a trajectory that will take your ingots past a series of other gravity wells on the way to Earth. You then use these bodies for a reverse gravity assist.
Gravity assists (or slingshots) are currently used routinely by space agencies to accelerate probes into the outer solar system by having them pass close to a large planet on an angle that causes them to gain velocity from that planet's own orbital momentum around the sun - effectively 'stealing' the velocity from the planet. That planet in turn loses orbital momentum (minutely) by an amount equal to what the probe gained - so that the energy exchange balances out.
Point is the energy exchange works in reverse as well a probe (or ingot) can lose velocity by traveling in a reverse trajectory, 'dumping' velocity into the planet. Again the planes orbital velocity increases to balance out the energy exchange.
The downside is;
you would need to attach maneuver thrusters to each ingot together with a navigation computer and radio link.
It will take years for each ingot to reach Earth but after the first shot arrives every subsequent shot sustains a continuous supply chain with every new ingot arriving in a predicable and reliable sequence.
The plus side is it is very fuel efficient and your ingots can shed most of their velocity while using very little fuel in return.
Why fire them as ingots? Eject them out of the rail gun as plasma, which would condense into metallic dust clouds on the way.
You need to fire them with just enough speed to be able to take a trajectory to Earth. And/or, fire them at powerful arrays of magnets that reduce the speed of the ingots to a more reasonable velocity.
