I read on Wikipedia something to the effect that basically, you can't deduce longitude simply from physical observation alone. But it seems to me, give the earth's revolution about the sun and it's rotation both parameterized from GMT as the starting point at some known position and time $t=0$ given the relation to near and far objects such as sun/moon and distant stars, it should be quite possible intuitively to know the longitude of the observer.

I could try and be more concrete and find position of GMT as function of time, therefore a map from three spatial coordinates to one temporal or vice versa or use spherical etc. But I figure this should be well known by now this day and age and I can save myself some time.

Additionally I wonder if it can be worked out from sidereal measurements of near and far objects or would additional angles be required?

So basically having no known knowledge of relative position of current longitude or GMT clock, but ability to measure time accurately, can we work out GMT or our current longitude.

  • $\begingroup$ GMT is used, in a manner of speaking, to set the origin of clocks. What do you suppose you are doing when you want to "work out GMT?" $\endgroup$ – user93146 Jun 25 '18 at 14:30
  • $\begingroup$ Well of course, forget GMT, let's just say you want to know the longitude, but longitude degrees from where? You have to pick a starting point. That said I have thought about this. It seems, given an intial position, you can have a time parameterized equation for earth's motion. Thus with 3 celestial bodies, it is enough to triangulate 3 dimensional position, and thus work out the time and longitude. There maybe cases where multiple solutions due to symmetry, I don't care about that. That is what I know. Now it may be that there is even fewer points than 3 to work it out. $\endgroup$ – marshal craft Jun 25 '18 at 17:06
  • $\begingroup$ Some issues with this in real life are one, bodies far away will only have a slight paralax or angle change with minutely and hourly changes in earth position, making it impossible to use alone. Two, many near celestial bodies orbit the sun and themselves have dynamic positions this pretty much ruins it. Now one redeeming concept could be, that because earth orbit is in 2d plane, it may only require 2 bodies, thus one far body or star, and the sun to constrain the 3 dimensional position of the observer, and thus using equation of earth's orbit and period of rotation, deduce longitude. $\endgroup$ – marshal craft Jun 25 '18 at 17:12
  • $\begingroup$ Then further, if longitude are known, GMT. As one can work out local noon and even mean local noon with some equation, thus simply subtracting the longitude or adding to local time, to get GMT. Any matter this is irrelevant to what I want, which is basically a well known solution, mchanized for convenient use, perhaps through period of navigation after 18th century when keplerian orbits well known about. $\endgroup$ – marshal craft Jun 25 '18 at 17:15
  • $\begingroup$ I'm thinking some kind of precise measurement of local sidereal time to local noon or something somehow should be able to work out longitude, using only an accurate clock or watch, rather than having to keep GMT time known always. According to wikipedia, traditional navigation used GMT. So for sailors to know longitude, they had to set a GMT clock and keep it accurate constantly. This method would allow them to set GMT while away from known GMT clock, with unknown longitude, using sidereal time and possibly solar time only. $\endgroup$ – marshal craft Jun 25 '18 at 17:19

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