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.