Rendezvous

The Soyuz spend days rendezvousing with the Space Station. A tether demands capture within seconds. The grapple end of the tether is accelerated upward by the tension in the tether (about 1.1 Gs) while gravity is pulling the rocket back to Earth (1 G). So the rocket can match position and velocity with the end of the tether, but not acceleration. This means the hookup has to happen fast, like within a second or two. This has not been demonstrated yet (as of 9/2007) and is clearly non-trivial.

However, there are a few difficult high speed rendezvous that humans have mastered.

Airplanes land on aircraft carriers even though they are moving much slower, pitching up and down in the waves, with winds shifting.
In the early days of spy-sats, film canisters coming back from space on small parachutes were snatched out of the air by airplanes.
In the Fulton Extraction System a rescue was made by having the downed pilot let up a helium balloon on a rope and then an airplane came by and grabbed the rope and pulled the man up into the air.
Anti-missile missiles have to get very near a missile coming the other direction at high speed without any cooperation on tracking from the other missile.
Inin-air refueling
The airport at Courchevel ski resort is sloped at 18 degrees. Going taking off it is like a ski-jump and landing is done going uphill.
Train mail pickup/dropoff. Trains could pickup and drop off mail at 70 MPH using a bar with a hook that turned around when the fast moving package hooked on.

Each of these examples are a bit amazing really. So while this rendezvous is difficult, with the high speed computers, differential GPS, etc. that we have today it should be possible. The question is how can we do it very reliably without too much weight.

We can either transfer the payload from the rocket to the tether or attach the whole rocket and payload to the tether. If the rocket is attached to the tether it can go around the Earth and release when it will be able to glide back to the launch site. This saves the cost and trouble of bringing the rocket back to the launch site. The downside is this takes a stronger tether than if only the payload is attached to the tether.

Using two stages to get to the tether might be interesting. The first stage could land very close to the launch site or maybe even fly back and land at the launch site. The second stage could be small enough that it could stay attached to the tether and ride around the Earth without requiring so much more strength in the tether.

For the rendezvous to work, the rocket has to get to the right place at the right time with very little room for error. To do this it needs to know exactly where the tether is and where the rocket is. A system using the GPS satellites has been shown to have 6.5 meter accuracy during the ballistic phase of a suborbital rocket flight. With differential GPS on the tether and on the rocket we should be able to get much better. Getting the differential information to both will require some communications, but we will want this anyway. It may even be necessary to have a differential GPS reference station on the tether sending info to the rocket. We can also have optical and or radar on the tether and or rocket. It seems possible to know both positions to within less than a meter.

The EU plans to have their Galileo system up in 2011, which will be like GPS but with 1 meter accuracy and 10 cm with ground stations. The US has plans for a GPS-III with better than 1 meter accuracy to be operational around 2012. Far out in space you can not use these systems, but 100 km high is well below these sats and so they should work fine.

A sort of harpoon gun on the end of the tether could shoot something on the payload or rocket. The harpoon could go through a hoop and then spring open when it hits the payload so it can not be pulled back through the hoop. This could happen very fast. The computer aiming the harpoon would have to take into account the different accelerations as it would take a little time for the harpoon to get to the target. With something like this the rocket may just need to get within 50 meters of the tether so the harpoon can hit the target.

A variation is to shoot a net at the payload that can close very quickly on the backside of the payload after getting to the payload. The net would be on a cable so that once it closed around the payload the payload would be secured.