# Calculating position without key resources

I recently learned the rudiments of celestial navigation, and have been pondering its three basic requirements: a clock, a book of star positions, and a sextant (or device for measuring star inclination).

It got me wondering if someone, classically "trapped on a desert island", could sufficiently observe the stars and write a message-in-a-bottle that would, if picked up, lead rescuers to them if they didn't have any of the necessary items when they landed there (never mind the likelihood of any of these things occurring).

The sextant can be crafted from local items (a couple sticks, a rock, some string, and a fair bit of math), so that's available. Without the book of star positions, the castaway could record his observations and let the message-finders use their book to figure out his location. But that leaves the clock; time is a key element of the data needed to use celestial navigation, at least the way it's classically done.

So, the question is two-pronged: how can you tell time at night with some measure of accuracy? and what methods of star observation are useful for determining position without knowing the time?

• Commented Jan 28, 2016 at 19:38
• @Draco18s - shortest comment ever? Commented Jan 28, 2016 at 19:40
• @AndreiROM Certainly my shortest comment. Commented Jan 28, 2016 at 19:41
• I am puzzled as to the reason for spending time on this. It is hard to imagine a raft so bad that he wouldn't have a better chance of reaching safety than any of his undoubtedly numerous messages in a bottle have of reaching somebody. I mean if he has sails he will navigate toward visible land and be visible to ships and aircraft, he will also actively seek out people upon landfall. In contrast your typical bottle will not seek out people no matter how much you try to instruct it otherwise. The lazy things will just lie there and refuse to cry out or walk towards clearly visible destinations. Commented Jan 28, 2016 at 20:35
• What do the possible searchers have available? Modern authorities are much better at finding people with partial information than their counterparts even a few decades back. Specifically it would not be necessary to have any idea of your location to lead them to you. Commented Jan 28, 2016 at 20:43

If you're in the northern hemisphere, latitude is easy: Using your homemade sticks-and-rocks-and-string sextant, record the angle to Polaris (aka the North Star). Within whatever the margin of error of your homemade sextant is, that is your latitude.

Unfortunately, it's impossible for you to calculate your longitude without a clock and (current year's) almanac. You can, however, record the apparent altitudes of other stars at moments like moonrise/moonset, as well as the apparent altitude of the moon at sunrise/sunset. Take as many of these readings as you can, record them as precisely as you can, and, assuming you can get the message to anyone, they can likely calculate your position within a small enough margin of error to have a reasonable chance of actually finding you.

You have four basic events to time your observations at, sunrise, sunset, moonrise and moonset. Measure the position of one star at at one of those events, and another at a later event. Be sure to describe what the constellations look like. (If you are not able to make a sextant, see what is currently straight up, or at the horizon) That is not going to help you to find your position, but it is enough for the receiver to figure out your longitude. He can then also calculate your day length, giving a reasonable estimate for latitude

You are on an island? Use the tides to measure the time! If you have a steady slope at the shore, you can give your time of observation by a measure of the how high the water reaches. Write down the tide height for all your star positions. Be sure to give a lot of data points,

• I did some reading about tidal cycles. It turns out you can gather a certain amount of information about your location by tracking the tidal cycle pattern. Combined with the longitude, it should reasonably narrow your position. Using the angle of the moon at its peak in the sky, combined with a couple of star positions, should provide a very small search area. Commented Jan 28, 2016 at 22:30

Draw a star map for the entire night sky, dusk till dawn, with indicators of when dawn happened and when dusk happened, along with what your best guess of the date is, and include your sextant readings on the chart.

So as soon as the sun sets draw any stars/constellations that you see, and mark where directly over head is.
As new stars appear over the horizon, add them to your chart, and as new stars are directly over head, mark their position.
Continue until the sun rises.

The people that find the bottle are already going to have an idea of what area you might be in from the prevailing currents.
By figuring out when sunset and sunrise are in that area during that time of the year they can make guesses about what time of night those stars were directly over head. This should get them close enough to where searching only a few islands wouldn't be to hard.

Option B:
Make a couple 1 minute sand dials from what's available around the island.
Maybe a coconut with a small hole, filled with sand up to a line, and then wait for it to all fall down.
It's not hard to get pretty close to a time span of 1 minute just by counting.
Then using those sand dials, build a couple 15 minute sand dials. As soon as the sun sets start the sand dial, and start the next one as soon as soon as the first runs out. Repeat until you've made your observations.

• The two questions I posed were "how can you tell time at night?" and "what methods of star observation are useful for determining position without knowing the time?" Neither of these is addressed by guessing the time or relying on currents. Commented Jan 28, 2016 at 20:24
• @J.D.Ray You are already letting the finders guess the stars from their books. I'm just proposing you let them help figure out the time too. If you know what stars are in the sky directly over head at sunset, and you know when the sun sets at that time of year in that general area, you can get a good guess of what the observer thought was directly over head. Then you look at the chart and see other measurements for other stars, and can see when those stars were in that position, and that gives you the star and time too. Commented Jan 28, 2016 at 20:28
• Unless you are up north and can see the dipper as Draco18s suggested, narrowing the field may be your best option. Commented Jan 28, 2016 at 20:32