This is a sketch from a post I did in 2009 about moving asteroids using their own rotational energy to sling ISRU mass to change their orbit.
With Jons’ last post, I got to speculating about other ways of getting mass from an asteroid back to Earth. What if the exploring spacecraft carried a tether to the asteroid that was long enough to serve as a beanstalk. Instead of carting the selected boulder(s) all the way home, the beanstalk is used to sling a number of samples to Cislunar space to be caught by some TBD craft.
Instead of the thousand ton boulders slung in the original post, ten or so tons per throw would send a sizable mass to explore and exploit close to home while leaving the spacecraft in the field for a continuing mission. While as in the previous it would be necessary to wait for launch windows to use the tether, the time between arrival and window could be spent exploring the body in question and organizing multiple throws. When the window opens, the ten (or one or thirty) ton samples could be sent Earthward every time the asteroid rotates. A four hour asteroid rotational day would give six launches per Earth day. A window a week long could have forty or so samples heading home at once.
If the asteroid is considered explored by that time to the limits of the available craft, it is time to head to the next target. One way of doing that would be for the spacecraft to climb the tether to well past astrosync orbit to a point calculated to sling it to the next body to be explored. At the right time, the tether is cut loose at the asteroid end to send the vehicle and its’ tether to a new little unexplored world. Once there, the cycle is repeated. It would seem that the craft could explore and exploit indefinitely without running out of propellant.
For a second phase of exploitation, tethers are left attached to the asteroids for use by future visitors. Eventually, spacecraft could visit dozens of rocks during an operational lifetime to prospect for different substances or to test new techniques in a variety of locations.
Certain asteroids would be exceptionally useful in a third phase if they proved exceptionally well suited for transportation hubs. Instead of slinging small robotic prospectors to other rocks, long beanstalks could relay humans and cargo to Mars and other points of interest throughout the inner solar system.