Asteroid as a "free slingshot?" The question Halley's Comet as a "Free Taxi" had an interesting thought, even though it didn't work out. I was wondering about a variation on the idea. Use a cable, as illustrated below. Could this be made anything like practical given reasonable assumptions? 

The idea is 


*

*Wait for an asteroid to fly close to Earth. 

*Put a probe, long cable, and net in its path.

*When the probe has swung through a half circle, it lets go of the cable. 


Thoughts


*

*Military planes have picked up downed pilots with a system something like this. 

*An asteroid of a few tons would be small enough to grab, and large enough to throw a probe. 

*It would take relatively little energy to reach an asteroid that passes near Earth, especially if you don't have to match its speed. 

*The strength of the cable would be a limit on how much speed you could gain. A long cable reduces acceleration, but has more mass. 

*The asteroid might be moving fast. To avoid breaking the cable, you might have to use a rocket to partially catch up. 

*How would you make the net? 

*In the illustration, the probe is slung in the direction the asteroid travels. This might not be an interesting direction. The probe could let go early to choose another direction. But this would reduce the final speed. 

*The probe would acquire spin. You might be able to avoid that by attaching the cable to the probe with a hinge aligned with the probe's center of mass.



Late thought - Add a small rocket to the net. Accelerate the free end of the cable to match velocity with the asteroid while leaving the probe still. Now you don't smash the net, and you still haven't used all that much energy. 
It still may not be a reasonable approach, but it is sounding more possible now. 
 A: Think of shooting a shell from a battleship at an instrument, and designing a device that allows it to hold on and continue working while it is transported by the shell.  That's probably easier than doing the same with an asteroid.
If you take a look at this table of near-earth asteroid approaches, you'll see that the relative velocity column has units of km/s.  We simply have no materials that can cope with such a difference without breaking or crushing.  
Right now, we tend to limit accelerations on launch vehicles to around $4g$ or so.  Lets say we were dedicated and built some instruments that could withstand a very aggressive $40g$.  Now we want it to grab on to an asteroid with a relative velocity of $6 km/s$.  it would require a minimum of $15s$ for the acceleration.  In that time, the asteroid would have moved over $90km$.  We'd need to have some mechanism that is far stronger than anything we have today, and it would have to be able to interact with the object at distances on the order of $100km$.  
