Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: acecharly on 01/10/2012 11:18:01
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If a sky lift were made into space, as has been a topic of conversation on here numerous times, how would relativistic effects impact on such an idea.
If we take the example that GPS satelites in space have to be compensated every day for the effects of relativity or would be upto 10km out of position would this not happen to our lift?
Cheers Ace
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edited after reading Phractality's reply which is better
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Relativity matters for GPS because the GPS clocks need to keep time so precisely. A nanosecond of error in the clocks translates to .3 meter of error in the location of a GPS ground unit.
Relativistic effects might matter slightly when it comes to making the clocks attached to the cable as accurate as those of the GPS satellites. The effects would be greatest for the clock at the upper end of the cable, where the counterweight is located. Depending on the mass of the counterweight, it might be 100,000 to 200,000 km from the center of Earth and going around once per sidereal day. That's about 26,000 to 52,000 km/hr. The relativistic gamma of 52,000 km/hr is about 1.000000001. In special relativity, that would be about .1 millisecond per day. But since the motion is circular, you need general relativity, and I'm pretty sure the cumulative effect would be a lot less than .1 millisecond per day.
EDIT:
Here's a good site for space-elevator design. (http://spaceelevatorwiki.com/wiki/images/6/6d/ActaAstropreprint.pdf)
I don't know which is more important, relative velocity or gravity.
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Nice link, Phractality.
Taking some figures from the paper:
- Maximum Speed of the climber is about 200km/h in order to reach geosynchronous orbit in 1 week. The velocity of the climber will not have a big relativistic effect.
- For most of that climb, knowing the altitude to within 1km is probably sufficient. Once the climber arrives at geosynchronous orbit, really low-tech methods like reed relays provide adequate positioning accuracy to align with a doorway. So centimeter-level accuracy is not really important, most of the time.
- The tether will have various vibration modes including 10 hours and 47 seconds, which will be affected by the climber, the moon and winds. Timing this to nanosecond accuracy does not seem critical.
- The orbital velocity of the counterweight is quite high, and it is further outside Earth's gravitational well than the GPS satellites. So really accurate timing would need a different correction factor than the GPS satellites - but this would only amount to 10s of microseconds per day. This is better than the mechanical timing accuracy that you could achieve for launching satellites into interplanetary orbits.
I can't see any significant relativistic problems with a space tether - and if you needed accurate time, you could always listen in on the GPS satellites far below, or relay the GPS time up the tether via a radio link.
In reality, calculations would probably be done in the frame of reference of Mission Control on Earth's surface, so the time and velocity at various points on the tether doesn't really matter too much, and can be taken into account in the calculations.