Momentum from GTO

There are many upper stages in geosynchronous transfer orbit (GTO), at perigee they have a velocity of about 10.5 kilometres per second, although this reduces gradually over years as they slowly decay.

If a suborbital vehicle could attach a tether to one of these stages at perigee, it could be towed most of the way into orbit.

To get into LEO requires 7 km/sec.

If the payload and the stage are equal mass, then the payload would be accelerated by 5 km/sec and the GTO stage would be decelerated the same amount.

Accelerating by 5 km/sec requires about 50 G acceleration for ten seconds, which would traverse a distance of 25 kilometres (the length of tether required).

Alternative profile would factor by ten, e.g. 500 G for one second, traverses 2.5 kilometres (shorter length of tether but higher stress).

The tether would be on a spool with a controlled resistance (e.g. friction brake, or dashpot, or E-M brake) to soften the initial jerk at contact, then, pay out the tether at the right rate to control the acceleration to the planned profile.

The practicalities of attaching a cable to an object moving at 10.5 km/sec are daunting. In this profile the suborbital vehicle would already need to boost itself to 2 km/sec, as the 5 km/sec is not enough to reach orbit. Therefore the relative speed would be 8.5 km/sec (2km/sec less).

Capture perhaps via a light weight structure made of a 3-D web of kevlar strands (or something stronger), like a large bullet proof vest in which the GTO stage becomes embedded. Size, maybe a few hundreds metres across. The webbing could be within an inflatable sphere a few hundred metres diameter, or alternatively shaped as a tetrahedron for simplicity of geometry.
The mechanics of high speed collisions are difficult to analyze. At such speeds, the flexibility of the strands become irrelevant, they behave more like solid bars. The stage would be severely damaged, one would need to devise a configuration which would not shred the GTO stage into a zillion fragments. The kevlar strands would probably be stronger than the stage material.
Wikipedia reports that some remarkable new developments are emerging for new materials being used in bullet proof vests.
http://en.wikipedia.org/wiki/Bulletproof_vest
Researchers in the U.S. and separately in the Hebrew University are on their way to create artificial spider silk that will be super strong, yet light and flexible.
American company ApNano have developed a nanocomposite based on Tungsten Disulfide able to withstand shocks generated by a steel projectile traveling at velocities of up to 1.5 km/second. During the tests, the material proved to be so strong that after the impact the samples remained essentially unmarred. Under isostatic pressure tests it is stable up to at least 350 tons/cm².
Most upper stages are composed of Aluminum alloys (softer than steel), with some graphite composites.

Work on this article has outpaced copyediting on it. You can help Spacepedia by formatting, editing, or tidying it.