Quick Dumb Question
If you were to go far back in time, GPS systems would be useless because there are no satellites, correct?
Is there a system, in use today, that can tell you your relative position on the face of the Earth without use of satellites, and not requiring any input from the user?
Is there a system, in use today, that can tell you your relative position on the face of the Earth without use of satellites, and not requiring any input from the user?
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I always thought if it was a clear night, a person with the right knowledge could do that. At least decently enough to travel?
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For a self-contained device that can tell your your current location, there are various inertial navigation systems with varying levels of accuracy. The MK 39 MOD 3A Ring Laser Gyro (http://www.sperrymarine.northropgrumman.com/products/Inertial_Navigation/mk39) is an example of such a device. It's about the size of a small oven, though, not exactly pocket-portable. The more accurate models are closer to refrigerator-size. If I wanted a GPS-like device on my time-travelling vessel, though, something like a ring laser gyro inertial nav system is what I'd want. As long as your time machine transports you only in time and not spatially (relative to the earth) then it should be pretty accurate.
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In short, no.
In long: That depends. What do you mean by "relative position"? How accurate do you want that to be?
What do you mean by "input from the user"?
There are systems in use today that could be combined together with software to find a very imprecise location - Know what date and time it is, take a snapshot of the visible sky, correlate from the height and declination of visible stars on the horizon. That would give you a figure probably somewhere on the accuracy of within forty square miles. We used to practice using lookup tables and star charts for Orienteering in Boy Scouts. I don't think anyone's actually implemented such a thing in hardware because A: image processing not terribly advanced until recently and B: GPS satellites.
There's also the possibility of using which craters are visible on the surface of the moon, along with the elevation, and knowing the date and time (the moon currently shows the same features to a given longitude on every orbit - it "rolls" around the earth), but again no extant portable off-the-shelf hardware modules and the moon is technically a satellite.
so, not really, no. And the computational methods for working it out don't work if you don't have a way of keeping and knowing time.
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I think everyone has already given you the best answers possible. A sextant, (or to a limited degree an astrolabe, or octant, or quadrant) will work. They'll give you your latitude no matter what era you're in if you work off of the sun and if you know the day of the year. Finding your longitude, however, is tricky.
There are digital star trackers that can identify stars from a database, and if you input an accurate time they'll spit out your position. Finding accurate time might be a struggle for time travellers, of course. And no star tracker will work if you're so far back in time that the stars have shifted positions.
If you have far-future travellers, you know what I'd have them do? Launch their own GPS. A pocket rocket can put up a microsatellite. You'd still have to give it a precise time, and you might only get a reading from it once every 90 minutes (the rest of the time it'd be over the horizon), but it'd be better than your other options.
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