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Sorry if this question is not relevant to world-building in any way beside being applicable to some fictions.

Conditions
On Earth in the 21st century, some disaster occurred and telecommunication by satellite is no longer possible. A colony of survivors wants to announce to the others their position. They can send a beam of light into the sky so that it could be seen a distance away. However, the only controls they have over the signal are:

  • Its duration (which is costly to maintain over long periods of time)
  • Its direction (straight up or oblique in a direction)
  • Its intensity (obviously will affect visibility)

With the extent of control over these variables decreasing down the list. How would the colonists be able to announce to observers, who could be anywhere, their exact position?

Some proposals

  1. Communicate distance: somehow, using the three variables to communicate to the observers the distance between the emitter and the receiver, who can then use the direction of the beam to find the location of the emitter.
  2. Send codes: send Morse or binary code of the geographic position of the emitter, although this seem particularly costly.
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  • $\begingroup$ Why is using Morse code costly? It can be done as simply as having a sheet of cloth that you use to bock the light beam. You couldn't send Morse quickly that way, but would that be a problem? $\endgroup$ – John Dallman Jul 16 '16 at 22:40
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I would set the light at a steady angle (I was thinking 45*, but it might depend on the geography of the area what gives the most visibility), and rotate it. Depending on resources, it may be steadily rotated, or spun around every time it's turned on. Periodically, the colony can use Morse code or something similar to announce their intentions, and the exact angle the light is set to - not while the light is rotating, that would make it hard to pick out precise light fluctuations from light movement, but once aimed in each cardinal direction and possibly at each midpoint as well.

What this should do... First, the angle should improve visibility in the direction it's aimed at. It has to reach sideways to be visible - if the beam is straight up, it depends on waste light (from intensity) to be seen from a sideways angle. It also has more chances for the light to hit clouds, fog, or dust, for the light to bounce off of. Turning the light means a colony in any direction will have the best chance to see the beam.

It will also give a crude directional triangulation. When the beam is pointed directly at (or away) from the second colony, it is a point of light. At all other times, it will be an angled beam, slanting back to it's point on the horizon. Twice during its rotation, the beam will be at right angles to the second colony, and can be visible along its length (under some conditions) tracing back to its origin. It is giving itself as a reference point, since it is equally distant to any points that divide its rotation - ie, it is halfway between the points it hits 5 min before and 5 min after the time when it's pointing directly at the second colony. For any time or any points that fall in that 180*.

Finally, distance can be calculated if the geography allows. Given the angles (via morse code), it is possible to find an idea of the distance given a chance to compare any two sides - pythagorean theorem. If the light hits a cliff or mountain, for example, it is possible to judge the height (roughly). This can be compared to the apparent distance from the origin to the height measurement and give some idea of how long the last leg of the triangle is. If the height or the distance to whatever was measuring the height is known, it can be quite accurate to pinpoint the distance to the colony originating the signal. Additionally, if its height can't be accurately measured, it can still be crudely estimated that the higher the beam looks, the farther it's origin.

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If these parties can premediate it, it is fairly easy to light two beacons 10 meters apart and the observer can triangulate their position. If they do not have two beacons, they may move it. But this distance should be discussed before hand.

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I don't know if the maths would work but you could have your beam focused on a star. Then your observers could use basic trig to work out the location of the emitter (on second thought, the moon might be a better target with well-known distance and angle parameters).

You would have to have the beam focused on a known star so that everyone around the world would know which star.

You have two options for this:

  1. Everyone knows before your disaster that such a star would be used as a reference point.

  2. No one knows the star reference point before your disaster. Your survivors use a single binary/morse code to signal the star used, every now and then. Say once a night, week, month, half year etc. Which ever suits your story.

You also need to take into account the curvature of the planet. I think if your light was directed across the planet surface it would only be visible for about 14miles? If it was elevated and still beamed along the planet surface it would be a little further. This is how lighthouses work.

I don't know how it would work if your beam is directed straight up, but believe it would limit the distance available quite considerably from say, the entire world down to a region of a hemisphere.

You also would always be able to deduce the direction and if your other survivors had an old map from before the disaster they could make regional deductions of were the light beam is coming from.

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  • $\begingroup$ Why does pointing the beam at a particular star help? $\endgroup$ – John Dallman Jul 16 '16 at 22:41
  • $\begingroup$ Maybe a star is a bit too far. Maybe use the moon instead. You can get your angle and distance to the moon, you can get a 'rough' angle for the light hitting the moon in relationship to your position and then use trig to work out the distance and angle of the original lightbeam is. FYI I should be asleep, so forgive me if I'm not making complete sense...and trig was never my strong point. $\endgroup$ – EveryBitHelps Jul 16 '16 at 22:48

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