Scott wasn't asking *HOW* you get the objects to each end of the tether. He was asking whether there were other methods to achieve the same orbital energy gain.

The "trick" is that you are partitioning orbital energy between different parts of the same co-moving body while the tether is strung, and you then separate the body into two objects WITH different intrinsic orbital energies.

This is essential using Tidal force to first separate the two parts of the body and then fling them into different orbits. Tides are due to the gradient of gravity. Across a few tens of metres in a single spaceship, these are normally so tiny as to be unmeasurable (but read Niven's "Neutron Star" for an extreme case). Over several km, the gradients and the associated forces become significant.

Recall the Roche limit for an orbiting body that gets too close to its primary and breaks up. One factor in the Roche limit is the force tending to hold the satellite together. Formally, the Roche equation looks at the self-gravity of a satellite (moon) as the force holding it together. When the Roche limit is exceeded, only the material strength of the satellite remains to hold it together.

A man-made satellite is in the latter category. It is INSIDE the formal Roche limit and if it were made of cotton candy, rather than aerospace composites, it would pull apart and break up due to the tidal forces.

For the tether process, you start by physically disconnecting the two components, except for the (loose) tether. You have then reduced the material strength to zero. A very small push will allow the two components to slowly drift apart. Eventually, tidal forces will accelerate the drift apart. (remember to have a friction damping "stopper" at the end of the cable, or you will reach the end and bounce back, like a badly-adjusted elevator - except you'll come ALL the way back, in space).

The "secret" of the Tether is in the STOPPING force at the end of the travel. As this builds up, you are essentially stressing a "spring" between the two component parts - except it's a force holding them together. When you cut the tether, you release this force and the objects at each end of the tether sail off on their merry way. The lower object has lost energy - which makes for an easier re-entry - and the higher object has gained energy - thus maintaining its orbit.

An impulse of a few newton-seconds can separate many tonnes of mass to a distance of many km along the tether (as per Jacob's partial answer). Then, detaching the tether can result in a massive magnification of the original impulse.