# longitude without clocks or GPS, but artificial satellites in geosynchronous orbit

Galileo once noted you could calculate longitude, via the moons of Jupiter:

https://en.wikipedia.org/wiki/Longitude#Noting_and_calculating_longitude

Could identifiable satellites be put in orbit that could help someone on the ground determine longitude without telescopes or too much calculation trouble? Would you always need a timepiece, or might this be done only geometrically?

If something was in geostationary orbit at 0 degrees longitude, and was big enough, and you knew your latitude, could you back-calculate your longitude?

If a bunch of satellites were in geostationary orbit, would this do the trick? How stable are those orbits?

• Re: Stability - requires active adjustments regularly, so no natural satellite is going to work. You're almost certainly looking at some variation of a Lunar Distance method, with the benefit that your altitude won't change, and your radius (even if the satellite is large) is effectively zero. For that matter, any readily observable satellite should work, the trick is making the orbit stable and observable enough. – Clockwork-Muse May 28 at 20:52
• What @Clockwork-Muse said. Satellites on the geostationary orbit require permanent station-keeping adjustments, and their lifetime is limited by the amount of fuel they have on board. But you don't need them as long as you have the Moon. As for "too much calculation trouble", that's why officers needed to learn trigonometry... – AlexP May 29 at 1:17
• Glad the Navy went back to learning celestial nav. But is 50m/s per year doable by, say, creating a small magnetic field/sail via solar panels, as noted below? I read that Mariner used the solar sail effect for attitude control. – asylumax May 29 at 2:15
• You could use the positions of Jupiter moons to accurately tell the time. You could accurately forecast the times when each moon would go behind Jupiter and be eclipsed or come out from behind Jupiter. Once you know the time with accuracy you can use the sun or stars to determine longitude. – James Cook May 29 at 14:04
• Although note that at the point that you're able to put any satellite into space, clocks need to be a long-solved problem, and you need pretty accurate ones for a good geostationary orbit. You should also have technology that makes other navigation schemes possible, so the bigger question is going to be "why would you bother"? – Clockwork-Muse May 29 at 15:52

Could identifiable satellites be put in orbit that could help someone on the ground determine longitude without telescopes or too much calculation trouble? Would you always need a timepiece, or might this be done only geometrically?

Yes, you could use such a thing to calculate your longitude geometrically, from any place where the satellite is visible (so, approximately half the world).

The method is identical to that used to calculate latitude by sighting the sun or stars. The trouble is that the sun and stars appear to move east to west, so you don't know the east-west component of their absolute position unless you know the time.

A geostationary object has a different problem: you always know its geocentric position, because it's always the same, no clock required... but a single sighting can only narrow down your position to somewhere along a circle on the Earth's surface. If you also know your latitude, that narrows your position down to 2 possible points, which will usually be very far away from each other, so it shouldn't be difficult to figure out which one is correct, and thus what your longitude is. If you can see two satellites, two sightings will give you your longitude exactly, no guessing required.

The more satellites you have, though, the harder it will get, because determining your position requires being able to accurately identify which satellite you are sighting. The ideal situation would be to have exactly two satellites visible high in the sky from anywhere in the world. You can't manage that perfectly, but a ring of 5 satellites would work pretty well. Perhaps you could fit them with high-power spotlights (illuminating only the hemisphere from which they are visible, rather than wasting power illuminating all of space) of 5 distinct colors--or just 3 distinct colors, so that any pair of simultaneously-visible satellites is distinguishable, as long as you can can determine which way is north vs south.

Geostationary orbits around Earth are perturbed by lunar gravity, solar gravity, and the obliquity of the Earth, and so require approximately 50m/s of station-keeping delta-V per year.

• I wonder if you could get 50 m/s of deltaV by doing magnetic propulsion or solar radiation tweaking. No propellant required, and this satellite remains in space as long as its control system can run. – asylumax May 28 at 23:28
• @asylumax and this satellite remains in space as long as its control system can run no matter the propulsion used, without a/some fixed Earth based station(s), how can a geostationary satellite compute the corrections it needs to apply? – Adrian Colomitchi May 28 at 23:48
• A ground station would be needed; don't know how smart this all has to be (could it be two or more beacons)? A delta V of 50 m/s seems kind of small, but I don't know what that means in terms of location drift. – asylumax May 28 at 23:54
• Given a suitable telescopic system, no ground station should be strictly necessary, although using one would be simpler. Magnetic propulsion won't be effective at that altitude, but light sails may suffice. – Logan R. Kearsley May 29 at 2:19
• Given a suitable telescopic system, no ground station should be strictly necessary for a while. After some tens of years, tho', when the geostationary satellites drifted enough from their original position... – Adrian Colomitchi May 29 at 5:03