Orbital speed at 30 miles?

Entropist
How fast would a satellite need to travel to mantain an orbit of 30 statue miles above sea level?

Algr
REALLY fast!

autisticmoose
v=(2gr)^.5
g=Gm/r^2

30 miles = 4.828032e5 meters

m = 5.9742e24 kilograms
r = 6.378e6 + 4.828032e5 = 6.8608032e6 meters

( 2 * (6.673e-11 * 5.9742e24 / 6.8608032e6^2) * 6.8608032e6) = 1.078e4

which is roughly 1 km less per second than what the surface requires.

remember orbit and escape velocity are the same. escape velocity can be in one direction away from body to never return from that bodies gravity. which is what you are doing when you orbit, otherwise it would fall to earth eventually.

Entropist
I understood the first response, but not the second.
Sorry, I'm just a science fiction writer.

1.078e4 is what in miles per hour?
Thank you graciously.

remember orbit and escape velocity are the same.

Erm. No.

The formula for orbital velocity (circular orbit):
$$v_{orbital}=\sqrt{\frac{GM}{r}}$$

The formula for escape velocity:
$$v_{esc}=\sqrt{\frac{2 G M}{r}}$$

For normal numbers I get an orbital velocity at 30 miles of 7.89 km/s (sea level is 7.92 km/s , not much higher at all).

Entropist
Thanks a million. That's very helpful.

FYI, the satellite is able to mantain that speed by a tether system that terminates somewhere in Low Eath Orbit.

Please don't tell me it is impossible becasue I've already written it and I don't want to go back.

Gold Member
It's ... tethered to something above it? to make it... yay for fiction!

Entropist
Tether systems have real potential that scientists are working on right now.
Basically, the satellite is tethered to a buoy higher up in orbit. Becasue higher orbits are slower, the higher bouy pulls on the lower satellite like a waterskier behind a boat. Very fuel efficient.
They can also be used to pull a satellite out of orbit to reduce space junk.

My main source is a Scientific American volumn that did a cover story on tethers a couple years ago.

My story pushes the design limits of the technology, however, becasue I need a satellite to orbit as low as 32 miles. Not sure if this is theoretically possible, but ... you know.. fiction.

Algr
If something is connected to a tether, then it likely isn't orbiting in a normal way. Something tethered to a buoy higher up in orbit would not be orbiting at all, but hanging from the tether. It would then move at the speed of the buoy. 32 miles would be the top of the stratosphere, likely enough drag to pull your buoy down in time.

I'd also wonder if such an arrangement would be stable. Would gravitational forces cause the object to fling around in a big circle around the bouy? You might actually want this to happen. Aircraft could latch on to the tether when it was lowest/slowest, and be flung into high orbit!

JaredJames
Purely to satisfy my own curiosity, why 32 miles?

Anyhow, I don't see how this system could be very fuel efficient unless the buoy is in an orbit of ~71,955km (that's one hell of a long and strong cable).

Entropist
I needed an ozone-making machine inside or just above the Ozone layer.

I stay a bit foggy about how far up the tethers go into orbit, in hopes that the reader doesnt care.

Tethers can be miles long. The ones that have already been made are simply cables of Kevlar.

JaredJames
I needed an ozone-making machine inside or just above the Ozone layer.

Works for me. Are you compensating for the varying heights of the ozone between polar and tropical regions?
Tethers can be miles long. The ones that have already been made are simply cables of Kevlar.

There's a bit of a difference between "miles long" and 45,000 miles long (71,950km).

And what do you mean "already been made"? I'm not aware of us having any orbital tethers - nor the capability to produce them. Something to do with carbon nanotubes and their lack of availability. Kevlar just won't cut it I'm afraid.

Entropist
Thanks for the tip. I did not know that the Ozone Layer had different alltitudes. Is it lower at the Poles, or higher?

NASA has been experimenting with tethers since the 60s. Granted most of the experiemtns were not sucessful, and the tethers werent very long.

The Scientific American article was published in August 2004. It may be on line.