On Sun, 14 Dec 2003 22:34:16 GMT, Ray Toews wrote:

I read an article about a theoretical tethered space station, where a
long cable was payed out from the surface and attached to a space
station, there are obvious technical problems to overcome but
notwithstanding them it makes sense in a logical way to attach an
object with a wire to a spinning object but would you be weightless in
this type of station.

Now a stationary object in space must travel at 25000 mph (roughly) to
stay orbital but a cable extending upward from the surface would be
stationary and subject only to local winds. where does the transition
occur? There seems to be gap in my knowledge about how gravity works.

Not at all. You just need a bit of background on how orbital travel works.

[Note the following is waaaay simplified.]

What is "orbit"? Simply stated, an orbit is a combination of satellite
altitude and speed that maintains the satellite at a constant average
distance from the center of the object it's orbiting. For circular orbits,
this velocity is given by the equation:

Velocity = sqrt(mu/(h+re))
(nm/sec)

Where mu is the Gravitational Constant, 62750 nm^3/sec^3
re is the radius of the Earth (3444 nm)
and h is the orbit altitude above the Earth's surface

The big thing to remember is that this altitude/velocity combination is
*inviolate*. Increase your velocity, and you climb into an elliptical
orbit with a higher average altitude or even shoot away, free of the
Earth's gravity. Decrease the velocity, and you drop into an elliptical
orbit with a lower average altitude...too much lower, of course, and you
impact the Earth.

The time it takes to go around the Earth (one orbit) is thus rigidly fixed
by the satellite altitude. The equation for the satellite period is
6.97e-6 x (re + h)^(3/2) (again, re and h in nautical miles).

So, let's look at Operation Skyhook. We can integrate every inch of the
cable, but let's look at a simplification: We have a main station at
Geosynchronous altitude (24-hour orbit) and a "way station" along the cable
at 200 nm (90 minute orbit).

Left to their own devices, the Main Station would require an orbital
velocity of about 10,000 FPS, and the Way Station about 25,000 FPS. The
Main station would float in stately grace, fixed above a spot on the
equator. In truth, though, it doesn't care about what's below it...all it
knows is that it orbits the Earth once every day. The fact that the Earth
turns to keep the same point underneath it is trivial. At the same time,
the Way Station whizzes past underneath, 13 orbits per day.

All right. Let's connect the two with a massless cable. Let's assume the
Main Station remains fixed above the equator, and the Way Station just
magically appears at its 200 nm position.

From the Way Station's point of view, it's going waaaayyyy too slow. It
wants to orbit at 25,000 FPS, but the cable fixes its speed at a lot slower
rate. It wants (has!) to fly at a speed that results in 13 orbits per day,
but is being forced to fly at a rate that only gives one orbit per day. So
it's speed is about 1/13 what it should be.

What is the Way Station going to do? Fall. Unless the Main Station can
haul up on the cable to support its weight, the Way Station will fall to
Earth, dragging the Way Station down with some 19,000-odd nautical miles of
cable. It'll wrap almost all the way around the Earth (isn't science
cool?).

So, how are we going to hold Way Station up?

We'll make the cable longer, past the Main Station, and put another station
further out. This other station will be thus be traveling *faster* than
its orbital velocity, and tugs *outward* on the cable as it tries to fly
into a higher orbit. Pick the distances right, and it balances the
downward pull of the Way Station.

What I understand about Scaled and others Xprize contestants is that
they are suborbital, that is, they are lobbing a craft vertically
upwards as far as they can afford and then falling back to earth when
gravity reaffirmes it's grip.

Not to take anything away from this endeavor but it seems to me a long
way from full orbital flight.

I'll toast to the successes and failures of the people involved in shooting
for the X-Prize. But you're right, They are *not* going into orbit. It's
the space equivalent of the Mongolofier brothers. It's not Gagarin or
Glenn, it's more akin to Alan Shepard. You can shoot straight up and reach
space, but you need about 25,000 FPS of additional delta-V to achieve the
orbital velocity that'll let you stay there.

And when you come down, you have to get rid of all the 25,000 FPS. Orbital
spacecraft take some small portion away with rockets, and scrub off the
rest in atmospheric friction. The X-Prize folks have a far simpler
problem. Hopefully, that'll be addressed in the Y-Prize. :-)

Ron Wanttaja