One of the aspects of most sci fi time travel representations that I find most challenging for my suspension of disbelief is this idea of people travelling through time and not travelling through space. You see the person in the time machine while the world transforms around them; mountains rising, seas forming, dinosaurs roaming past them, etc.
This is implausible for many reasons. The earth rotates, it also orbits around the sun, and the sun orbits the centre of the Milky Way, etc. Even if the existing 3D momentum was preserved and the time machine was at rest relative to its position on the earth, you have problems with continental drift, mountains and oceans changing the relative altitude of the land, etc. Ultimately, you'd end up either embedded in earth, drowning, or plummeting to an untimely (no pun intended) death. In point of fact, I often wonder if that's the reason that the conundrum of time travel (if it's possible, where are all the time travellers in our past?) is satisfied - they're all dead because they landed unsafely. But, I digress.
It struck me that for short term time travel hops (hours, possibly days) preservation of 3D momentum (especially angular momentum) is probably fine. Anything more than that and you risk getting your shoes stuck in the pavement because you left in winter and forgot to incorporate the expansion due to heat for when you landed in summer.
On the other hand, for longer hops, we have a ready-built navigation solution that's already in regular use around the planet every single day; GPS!
If your time machine had some limited 3D movement available to it and could access the GPS signals from throughout the lifespan of the system, then the GPS signals could be used (firstly) to pinpoint the time you want to arrive, and (secondly) to pinpoint the location in space you want to arrive. Marry it with Google Earth and altitude data across the planet for the same time, and you arrive safely every time, more or less.
So; perhaps the reason we haven't seen too many time travellers up until now is that they couldn't navigate to their location because now is when GPS is more reliable and mainstream as a technology. They should be popping up like rabbits any day now (although if they're adept at hiding in our the modern world, this could account for the massive proliferation of new technology in this current age - think about it).
But; is that really the problem?
So here's the question - Is it possible to use GPS signal data from now back through the time of its inception to extrapolate landing sites for time travel machines back past the point where GPS was available?
If so, how would you do it, and what margin of error could you expect as you went back further and further?
For the purposes of this question, let's assume that you have a time signal receiver that can receive the signals from GPS satellites during any and all points of their operation from the past, present and future and that this temporal 'map' of signals is what you use to pinpoint your landing location.
As I see it, the problem with extrapolating a location from GPS into the past is that GPS works via 'relative' signal reception, meaning that the GPS satellites know where they are relative to each other and the Earth, and that the GPS device on the ground uses that information to pinpoint its own location based on the timing of the signals from each satellite in a form of triangulation. In other words, the satellites aren't aware of their 'absolute' location in space, and therefore you can't extrapolate back past their existence to form a map of the earth's journey through space, at least not in a conventional manner.
Hence the question; is there an (un)conventional way to get back past the GPS era safely in my time machine?