Over time, would I exert less effort mining a large asteroid or collecting small asteroids, assuming both have similar compositions?

Question

Suppose there are two asteroids, one very large (larger than a football field) and one very small (roughly the size of a refrigerator). Assume they have similar compositions and are at equal distances from my current location. My hypothetical goal is to begin collecting these smaller, "refrigerator-sized" chunks of material -- by any means -- and use them for some purpose that is unrelated to the question.

Would I be better off going to the large asteroid and setting up a mining operation, or locating and collecting the asteroid that is already the size I'm interested in? What if instead of a single chunk, I began identifying, locating, and retrieving smaller asteroids that are already near the size I am interested in? Would the effort I am putting out depend on the asteroid's composition, and would the hypothetical mining operation cost less effort over time as compared to hunting down the appropriate chunks?

Some more specific parameters:

• For the first part of the question, assume I've identified the first two asteroids in different parts of the asteroid belt, but they're approximately the same distance from my location. Let's call it 1 AU.
• I would like to return any contents to an arbitrary point in open space, not under great influence of any nearby bodies. The vehicle carrying the payload should be capable of either coming to a stop at this location, or slowing enough for another, larger device to capture it. I'm not so much concerned about the details of this procedure for the question, more the actual retrieval of the material instead of the delivery.
• Primary candidates for retrieval would be M-type asteroids. They are desirable for identification and retrieval due to their moderate brightness and metal content.

Answer 1

Your best bet is mining the smallest single rock that provides as much material as you need.

Suppose you mine a bunch of little rocks--you have to expend Δv to move between each rock--energy that you don't expend when you're mining a single rock. On the other hand the bigger the rock the more Δv you will expend lifting your cargo against it.

Note that the means by which you lift your cargo matters here, you very well might be better off with a rock big enough to mount some sort of throwing system. Throwing your stuff home from Ceres is going to take a lot less work than bringing it home by rocket from your football field.

Answer 2

This is more complicated than just how far away, or the size of the asteroid.

If the material is on the surface and easily harvest-able then the smaller asteroids are going to be more efficient to mine.

But if you need to extract large amounts of ore to get any usable amount of material, then a larger asteroid where you can set up something to mine and at least pre-process if not fully process the ore is going to be more efficient. On small asteroids you would need to move the asteroid to someplace where it can be harvested for the ore.

The first asteroids that are likely to be targeted to set up to mine will be larger and have multiple mineral targets. Since ever operation is going to require a certain base effort you will be able to leverage that base infrastructure to build out for multiple mining targets. Smaller targets will require some medium to mine the ore, load the ore into carriers, and transport the ore to some place to be refined.

Answer 3

A problem with asteroids is revisit times. The more earth like an asteroid's orbit, the greater the synodic period. Let T1 be period of one body and T2 period of 2nd body. The synodic period is |(T1*T2)/(T1-T2)|.

For example if the period of a near earth asteroid were 1.1 years, synodic period with earth would be (1.1*1) / (1.1-1) which would be 11 years. Moreover the lowest delta V rendezvous assumes a tangent transfer orbit that just touches earth's orbit as well as just touches the asteroid's orbit near aphelion. This makes launch windows even more infrequent.

We have no experience mining asteroids. Learning how will be a process of trial and error. For a conventional earthly mine, establishing necessary infrastructure would take multiple trips. This would be especially true of an asteroid mine where we're learning as we go.

Let's say it will take 10 missions to the asteroid before we have a working mine. If launch windows are 11 or more years apart, that'd take more than a century.

To eliminate the problem of revisit times, it would be a good idea to park the rock in high lunar orbit. For many rocks, this can be done with a tiny amount of delta V. Once parked in lunar orbit, launch windows open every two weeks and trip times are less than a week. Revisit times are no longer a show stopper. It becomes much more plausible to establish working infrastructure within a short time frame.

We could possibly park small rocks in lunar orbits. But even if delta V is quite small, it's way beyond our present abilities to park larger rocks.

Edit: Another consideration is safety. Should a retrieval go awry and a rock impact the earth, it should be small enough that it would burn up harmlessly in the upper atmosphere.