How to broadcast Earth's position to someone in the future?

Question

Using current technology, what could I do to optimize the odds of being located by time-traveling humans a thousand years from now? The accuracy must be such that they could "transport" me out of a 10-meter box at a specific date and time, within a 60-second window. Oh, and to minimize the butterfly effect, all interaction must take place inside the 10-meter box. No search parties walking or flying around and disturbing the timeline; they must beam in and beam out of that box!

Here are my ideas:

To find Earth's rough location, I'm wondering if I could send a radio signal, perhaps from multiple towers. A cloaked ship in the region could zero in on the signal? Would this even be necessary? A civilization capable of time travel could surely calculate Earth's flight path, or am I underestimating the difficulty?

Also GPS coordinates may not be meaningful to folks 1000 years from now, so use planetary alignments. Schedule the extraction on Hawaii, when the sun is directly overhead. This is known as Lahaina noon and occurs once a year, when telephone poles cast no shadows (provided they are perpendicular). This ensures that the extraction point is precisely aligned with the center of the Earth and the center of the Sun.

BTW, I'm able to write instructions to the future time travelers (digital or hard-copy), e.g. "look for the big island" or "I'm the bald guy in the blue shirt."

EDIT: Here's the synopsis:

Tom, my modern-day protagonist, has a fiancee who has either been kidnapped into the future, or incinerated. Since Tom has no time machine, he must create an organization that will endure long enough for a time machine to be built that can come back and rescue her. The sole purpose of this organization is to survive political upheaval, collapse of civilization and even destruction of Earth, and to ensure that a time machine will be built to come back and rescue his fiancee (OK that's two purposes).

Using this organization, Tom will pass along information relevant to the rescue, e.g. dates, locations, maps, etc. Chances are, this info will be sufficient to locate his fiancee, but he wants to increase the odds.

Answer 1

Are you able to send graphics? Or print them. If GPS coordinates may not be meaningful in 1000 years, why assume that your use of English will be? (Or any current language) If they can find the earth itself and if they can make use of an instruction such as "look for the big island" then they could use a map. A full set of maps would be my preference. One of the earth. Then the ocean region. Then the Hawaiian islands. Then the area. Town. Neighborhood. Building. Floor/location in building. Or cave. Or underground. Wherever you plan to hang out for 1000 years.

Answer 2

First, we must assume that they can find Earth. They wont be able to simply calculate its position. Let's start with the assumption from this answer that we know the eccentricity of Earth's orbit around the sun to 8 significant figures. That implies our understanding of our position in space with respect to the sun may be off by 1,400m. We simply can't measure our position any more accurately than that, so that's the best we could write down. And that's just one source of error in one direction.

Having the time travelers observe the Earth before the day you do the teleport will help pin that down. Also it will help with another vicious issue: time tag errors. The Earth is rotating around the sun at roughly 30km/s. That means your 10m box in space is like a 300us box in time. If they aren't calibrating their process with respect to the earth, they're going to have a mighty short window where your box is actually where you say it is.

Since they're observing things and can move through time, I would make the box a "logical" box, based on geographic locations. There's plenty of time to survey the planet and get a good fix on our concept of latitude and longitude.

However, given that this is a story, there's some value in being flashy. We have a lot of events whose position in space and time is very well understood. For example, we know the precise position of nearly every nuclear bomb detonated because military engineers are sticklers for that kind of information. You can go find exactly where these events occurred.

More than seventy years after the test, residual radiation at the site is about ten times higher than normal background radiation in the area. The amount of radioactive exposure received during a one-hour visit to the site is about half of the total radiation exposure which a U.S. adult receives on an average day from natural and medical sources (Trinity)

And just for fun, I'd play games with the precise time tags, just because they amuse me.

Any time traveler should have been able to pinpoint the precise location of the first atomic bomb detonation. There would be no event quite like that in all of time. A great cusp in time and space where literally the entire world turned, and held still, all in one brief moment as future history was written.

Tom's disappearance was a much less momentous occasion. Pinpointing it in time from over a thousand years in the future required a bit more direct of an approach. Tom looked around to see if anyone was looking, and then swung a leg over the fence between himself and Trinity -- the true site of the first atomic explosion. He told himself "this is the moment," but he knew he was lying to himself. The moment was yet to come. None the less he breathed an audible sigh of relief when he found the device nestled in the rocks where only a fool would brave the radioactivity. Not that there was much radioactivity left, but there's just enough to help a time-traveler ensure nobody accidentally finds your clock before its time.

Tom opened the face of the device. The gleaming counter inside stared back out at him, counting 2,295,711,060 seconds upwards, with a fast moving blur of digits to the right. 2.3 billion seconds since world changed on that one night in 1945. Something about this felt fitting. Below the timer were two buttons: pause and cancel. One press of the pause button would anchor this moment in time, and his journey would begin.

Tom thumbed the pause button, closed the device, and threw it into the rocks a few feet away. This is the moment, he thought. In 10 seconds, the clock would fuse, indelibly marking that paused moment into its circuitry. If he were to sprint over to the rocks and clock the cancel button, the process would stop forevermore. This moment would vanish into history like so many moments before it.

Tom stood still. A glimmer of fear rippled through him. The cancel button was a nice failsafe, decreasing the likelihood of his actions rippling through time like the infamous butterfly flapping its wings. He could still reach out and keep time sane. But she was still waiting. "Is-has still waiting," he thought, remembering that time travel was going to require some new tenses.

Ten seconds later, the clock made the tiniest noise as it locked the time in forevermore. But Tom did not hear it. Ten seconds is a long time, but once that moment is anchored in time and space, it happens in an instant. The clock fused, and Tom vanished, all in one moment. And that was all.

Correction: that is-had been all.*

Bloody timeless tenses.

Answer 3

yes, radio beacons from multiple towers. 3KW 1296MHz has been bounced off the moon. morse code might work, an optimized packed pulse stream encoding protocol would be better. the more towers, the wider range allowable for the box to be placed. the towers would also have cellular receivers - your device could, when transport is needed, start pinging the towers every few seconds, with the nearest three towers broadcasting distance to the box, including unit of measurement. the challenge is the SOL propagation delay plus encode/decode delay of the signal, relative to the delta of position. one technique is, if that propagation delay can be established on the receiver side, it can be compensated for.

as long as you are in line-of-sight, that should be enough for the time-travelers to get a dynamic fix on you, without resort to gps, etc.

EDIT: alternatively and more simply, if feasible, a single radio beacon mounted on top of the box :)