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Assume plenty of delta-v is available but it's very slow.

At first glance it looks easy enough, get capture and spiral in. However, we have that big bully in the sky, aka Luna. Is it possible to bring an asteroid in to a lower orbit assuming a very low acceleration? Obviously you have to stay far away to avoid going splat or even getting tossed about by the moon.

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    $\begingroup$ I see. I'm of the "Space is big. camp so I assumed it's certainly possible with a reasonable rate of inwards spiral. I wonder if you want to add some feeling for how slow "a very low acceleration" would decrease the orbit? Are you thinking of a decrease in semi-major axis of 100,000 km per month, or perhaps per year for example (near the lunar altitude)? $\endgroup$ – uhoh Oct 25 '19 at 7:29
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    $\begingroup$ @uhoh I'm picturing something like using solar power to operate mass drivers or the like. Accelerations measured in a reasonably small number of microgravities, the process from capture to final orbit taking years. (I'm picturing bringing back something in the ballpark of a mile across, with the intent of building a mining/manufacturing base in a fairly low orbit.) $\endgroup$ – Loren Pechtel Oct 25 '19 at 7:47
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    $\begingroup$ I'm guessing you could deliberately fly close by the moon and have it lower your orbit enough to get some aerobraking. I have no idea if that would be the most practical way, but at least it sounds interesting. $\endgroup$ – Bit Chaser Oct 27 '19 at 2:44
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    $\begingroup$ @bitchaser You don't get meaningful aerobraking for something that large. I also don't think a trajectory like that would be allowed, flubbing it could be an extinction event. Nobody's going to allow a trajectory that in event of an engine failure or small mistake would come down. $\endgroup$ – Loren Pechtel Oct 27 '19 at 6:31
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    $\begingroup$ @JamesJenkins I'm picturing permanent, at least until the miners chew the whole thing up. The basic issue of the question is how to get past the moon when you don't have the acceleration to dodge. $\endgroup$ – Loren Pechtel Nov 14 '19 at 18:42
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"Assume lots of delta V"

If you're using chemical rockets that would mean propellent mass comparable or greater than the asteroid mass. A quick chart:

enter image description here

Exhaust velocity for hydrogen/oxygen is about 4.4 km/s. 3/4.4 = ~ln(2). So every 3 km/s added to the delta V budget about doubles over all mass.

It's quite plausible to have solar powered hall thrusters with an exhaust velocity of 30 km/s. However given Hall thrusters and solar panels of reasonable mass, acceleration is excruciatingly slow even for a relatively low mass asteroid.

Hasnain, Lamb and Ross wrote a paper Capturing Near Earth Asteroids Around Earth. Hasnain, Lamb and Ross look at two delta Vs:
1) Delta V to nudge an asteroid's heliocentric orbit so the rock passes through the earth's sphere of influence.
2) Once in Earth's sphere influence, the delta V to make the hyperbolic orbit an elliptical capture orbit about the earth.

There are near earth asteroids that already pass close to the earth/moon system. If nudged early enough in their orbit they can be made to pass through the earth's sphere of influence with relatively little delta V. And there is a lot of time to accomplish the nudge so high ISP ion engines can be used to accomplish the first step.

Once in earth's sphere of influence and if the moon is in the right position, a lunar swing by can be used to shed velocity making a hyperbolic orbit into an elliptical capture orbit.

enter image description here

Above is an illustration how a lunar swing by can drop an asteroid's velocity from around 2 km/s in the lunar neighborhood to 1.2 km/s which is below earth's escape velocity at that distance from earth.

If I understand the Keck Report correctly, they say it could take .17 km/s to park a rock in an earth capture orbit and they say it could be done with Hall Thrusters.

On the bottom of page 15 of the Keck Report they talk about safety. They specify retrieving a small carbonaceous asteroid that would burn up harmlessly in the upper atmosphere should it go off course and impact the earth.

The also specify parking the rock in a loose lunar orbit so it'd be a good distance from earth, another safeguard against impact.

These safety measures work against your scenario of an ore body in low earth orbit.

Also to get from a loose escape orbit to a low earth orbit takes a lot of delta V. A general rule of thumb going from coplanar orbits with a low thrust trajectory is subtract high orbit velocity from low orbit velocity. See Adler's answer to my question General guideliness for modeling a low thrust ion spiral

So this means you need a delta V budget in the neighborhood of 6 or 7 km/s to spiral down to LEO. If using chemical that would mean using about quadruple the mass of the asteroid in propellent. If using ion I'm guessing it would take centuries to spiral down.

So I'd say it's not plausible to park an asteroid in LEO.

It is plausible, in my opinion, to park a rock at EML2. Which would be a great place for a water rich carbonaceous asteroid. A potential propellent source at EML2 would be a possible game changer.

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  • $\begingroup$ Chemical is obviously out of the question. I wasn't worrying about the exact mechanism, I figured the power source would be solar and didn't worry about exactly how that's converted to thrust, Hall effect thrusters are the sort of thing I had in mind--as you say, excruciatingly slow. No ducking Luna, you have to work past it. I considered a gravity assist off the moon but I don't think that would be safe enough. $\endgroup$ – Loren Pechtel Nov 18 '19 at 4:32
  • $\begingroup$ @LorenPechtel A gravity assist from lunar is about the only plausible way to capture a rock. It's not something to be avoided. Power source for the Keck's proposal is solar. But that doesn't eliminate the need for tonnes of xenon for just .17 km/s delta V. Solar's not a magic wand that eliminates the need for reaction mass. $\endgroup$ – HopDavid Nov 18 '19 at 14:10
  • $\begingroup$ I was picturing using the slag from refining the asteroid as your reaction mass. We can accelerate it to high speed, the exact means used to do so isn't really relevant as this is an orbital mechanics question, not a rocketry question. $\endgroup$ – Loren Pechtel Nov 19 '19 at 5:08
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Even if it is possible we should not do it.

Low Earth orbits do decay over years, decades, centuries or millennias. Low orbits decay faster than higher orbits. If we do not want the asteroid to hit the surface of Earth sometime, we have to do station keeping forever.

Only a very small asteroid would fully disintegrate during atmospherical reentry but not a larger one.

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  • $\begingroup$ An asteroid entering Earth's atmosphere from a decayed LEO orbit wouldn't be all too dangerous. The shallow angle at which it hits the atmosphere would leave it plenty of time to burn up before it hits anything and it would also be much slower than typical near-Earth asteroids. Also, if it's set into an orbit with, say, a decay time of 50 years, that gives humans plenty of time to reboost it (or use it for asteroid mining practice) $\endgroup$ – Dragongeek Nov 13 '19 at 13:25
  • $\begingroup$ Spacecraft are light. Asteroids are heavy. They'll fall much slower. And I'm picturing something like 500 miles up--high enough not to be an issue, low enough for easy access for mining. $\endgroup$ – Loren Pechtel Nov 14 '19 at 18:38
  • $\begingroup$ @Dragongeek What I'm picturing would be catastrophic if it actually came down. It's not going to meaningfully burn, it will be the world's biggest bowling ball until it runs into a piece of terrain sticking up and then it will be an incredible splat. $\endgroup$ – Loren Pechtel Nov 14 '19 at 18:40
  • $\begingroup$ Aren't the interstellar velocity asteroids the main concerns? Oumuamua would've demolished huge swathes of land at 26.33 km/s- but if you placed it in orbit to slowly decay into the Earth... it wouldn't have the speeds to be a planet destroyer; just a city destroyer, right? Given that's still bad... $\endgroup$ – Magic Octopus Urn Nov 18 '19 at 16:10

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