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Endless Skyway

As I was walking that ribbon of highway I saw above me that endless skyway...

19 May  2010   Space elevator to low orbit?
23 May  2010   Space Elevator and The Dynamic Grapple!
  8 June 2010   Hooking on when you're off GEO - an even more dynamic grapple.
10 June 2010   Acceleration Matching for Space Elevator Grappling.
  1 Dec  2012   U-Fly-It Satellite and Space Elevator Simulator.


Space elevator to low orbit?

19 May 2010

I once read that you needed to climb a space elevator to geosynchronous altitude to get to orbit. They really meant to say that while you can get to space by climbing a tower to 220 miles, you can't get into orbit that way. Of course, the main idea of a space elevator is climbing to geosynchronous altitude letting go, under weightlessness, to fly where you want to fly. It turns out though that above some point lower than GEO, simply letting go will also result in an orbit. In fact, if you release an object from anywhere between 66% and 131% of the height from the surface to GEO, it will enter an orbit.

Release from any level (from ground up) will result in an "orbit" of sorts. It's just that, below that certain point (66%), dropping will result in an orbit that intersects the atmosphere and reenters less than halfway around the Earth. Release from very low altitude (from within or just outside of the atmosphere) will result in a landing somewhat east of the anchor point. For releases from within the atmosphere there will be no "reentry", of course. For drops just above the atmosphere, there will be a steep, low-energy, cushy, low-stress "reentry of a sort". These would be similar to the mild reentry of Spaceship One. The higher you drop from, the more energetic and stressful the reentries become and the more shallow they become - until you miss the atmosphere altogether when released at or above that special point at 66%.

A nice old fashioned hand-drawn diagram of all this.

Useful Perigees

That special point, the minimum drop-to-orbit point (what I'm calling it) is at an altitude of 23,760 km, just about two thirds (66%) of the way from the surface to GEO. Drops from near this point will result in useful perigees. Dropped from slightly below, a perigee just inside the atmosphere can be put to use for braking to a circular Low Earth Orbit. Drops from slightly above will have perigees well enough outside the atmosphere to go around for a number of swoops before a tiny burn can adjust perigee lower for the same kind of braking.

Drops from between this minimum point and GEO will result in perigees that vary smoothly from LEO to GEO. Drops from between GEO and a maximum drop-to-orbit point will have perigees at the release point and apogees that vary smoothly from GEO to infinity. This maximum drop-to-orbit point is at 46,750 km, about 131% of the way from the surface to GEO. So, the drop-to-orbit range on a cable is from 0.66 to 1.31 of the height from the surface to GEO.

Release at the minimum drop-to-orbit point will result in a very elliptical orbit with an apogee at the height of release and perigee just skimming above the top of the atmosphere for a nice high speed flyby each time. The speed at this perigee would be a significant 30% faster than the speed ISS flys. The ISS flies at a similar altitude, but in a lower-energy circular orbit. So, you couldn't rendezvous with an ISS-altitude station unless you had the ability to make a change in speed (at perigee) of 5100 mph! And then, to get home, you would need a reentry system (heat shield and retro-delta-V) or at least the same 5100 mph delta-V to get back to the cable (actually more than that to get to GEO for a safer less-dynamic reattachment). This totals about half of the ~20,000 mph delta-V needed to lift to LEO from the surface (it's big!).

A reentry system would likely be carried as standard safety equipment anyway for all manned cable ascents (I wouldn't go without one!). With a reentry system on board, you could save rocket power by dumping most of your excess delta-V by "dipping-in" to the atmosphere on successive perigee flybys. This would successively reduce your apogee until a small rocket burn at apogee would elevate your too-low perigee to a nice circular LEO. So, you can fairly simply get to LEO with only a small delta-V. The ability to make that delta-V could come from a reentry system that would be necessary anyway. Just add somewhat bigger tanks to its retro firing system. One safety advantage of this is: if the rocket system fails to fire at the LEO apogee to circularize the orbit, you are already set up for reentry - no strandings.


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