Help with (fictional) celestial navigation

[ceswiedler]

Hi! I'm writing a novel which involves celestial navigation, and I have just-slightly-over-a-landsman's understanding of how it works. Fortunately, I don't need to do any _actual_ navigation, I just need to make sure my plot and descriptions aren't ridiculously inaccurate. I'm hoping that you guys can help.

My main question is this: I know there are lots of different ways of doing celestial navigation. I believe the one I want my protagonist to use is sight reduction of stars. It's important that he is able to plot a position, but not be terribly accurate about that position.

Is it correct to say that if a reasonably-practiced, but certainly non-expert, navigator took sights of 3-5 stars, and then did the correct calculations, that they could end up with 3-5 lines which didn't intersect, therefore only giving a position that was as accurate as the polygonal shape of those lines?

If that were the case, what would the inaccuracy come from? Is there any other method that could be used (moon or sun sights or something like that) to improve the accuracy? I'm looking for the character to have a series of initially-inaccurate plots, and then later realize "oh, all i need to do is XXX" and then get a better position.

Thanks in advance for any help and explanation!

[FamilyVan]

I think I understand your question, and no I don't think it's reasonable. Celestial navigation will result in circular lines of position. Imagine a flashlight is a heavenly body. Shine the flash light at a globe in the dark. As a navigator practising the art of celestial navigation your position line is a circle and you are located some where on the outer ring of light.


Sight your second heavenly body and you have a second circular line of position. The circular lines of position should overlap in two places. Those two places represent two, two point fixes. Your position within 100 miles or so would be at the intersection of one of two those points. You should be able to use your Dead reckoning position to determine which of those to points of position is your position.


The two sights don't need to be simultaneous, for example, you can advance yesterdays fix (via dr) to todays fix, and create a position using the combined information, essentially a running fix using heavenly bodies.


Celestial navigation can be a little hard to explain in a few paragraphs on CF, maybe that brief explanation will help you to understand whats happening from the navigators perspective.

[onestepcsy37]

What familyvan says. Those "circular lines of position" are AKA "circle of equal altitude" because a corrected sextant reading would be exactly the same at any place on the rim of the circle. Thats why you need a second sight.

If you are doing stars and you can take sights on two or more within a few minutes you dont need to advance the circles using your DR.

If you are only using one celestial body then you need to wait, maybe an hour or more, for the body to "move" so your next sight will give you a different circle. And advance the DR, as familyvan says.

[CarstenWL]

took sights of 3-5 stars

Is your person alone on the boat or does he have someone who can help (taking the time and values) and 'announcing' the predicted values for the next object?

If he is alone no way he can do 4 or 5 I would say. For sure not after sunset (a bit easier at dawn because you can identify the objects already before the horizon becomes visible).

My 2cts ;-)

Carsten

[FamilyVan]

Originally Posted by onestepcsy37

What familyvan says. Those "circular lines of position" are AKA "circle of equal altitude" because a corrected sextant reading would be exactly the same at any place on the rim of the circle. Thats why you need a second sight.

If you are doing stars and you can take sights on two or more within a few minutes you dont need to advance the circles using your DR.

If you are only using one celestial body then you need to wait, maybe an hour or more, for the body to "move" so your next sight will give you a different circle. And advance the DR, as familyvan says.

Phew! Thanks for verifying my explanation. I haven't used astro in over 10 years, and never had to use it a lot. I just noticed nobody had responded to the OP's question so I figured I'd get things rolling with some basics I could recall.

[Wotname]

Let me see if I can give a simple explanation of celestial navigation to expand a bit on Family Van's excellent post.

The basic concept is to use a sextant to measure the angle between the heavenly body and the horizon and note the time. Then use maths to compute a line of position (LOP).
Three LOPs are required for a fix.

So the errors occur when any of the above steps contain errors.

The common ones are:
Using a wave top of a nearby wave instead of the true horizon or an indistinct horizon.
Motion of the boat may lead you to get the angle slightly wrong when using the sextant.
Sextant has errors - might have been knocked etc and mirrors require adjustment.
Your time may have errors w.r.t. GMT; you want the accurate to a few seconds.
Your maths can contain errors - misreading the numbers in the nautical almanac or sight reduction tables.

These are the common source of errors.

What you may not realise is that you can only use the stars at dawn and dusk. This is because you need to be able to see the horizon and the star at the same time. So the star has to be in view (no clouds, no sun) and the horizon has to be visible - so dawn and dusk.

The sun can be used anytime (during the day of course) and the moon any time it is visible if the horizon is also visible. Using the sun and moon require you to use either the upper side or the lower side of the sphere (or limb in nautical terms).

So this sometimes causes an error if say you use the upper limb for the sight but entered the data from the almanac for the lower limb - don't ask me how I know this .

The only time you don't need to know the time exactly is when you use the sun (and sextant) at local midday. This will give you the latitude only and does not require time data. The procedure is simple - around local midday say 20 mins before, start measuring the angle between the sun and the horizon. As local midday approaches, the sun will appear to lower closer to the horizon, "kiss" it and start to rise. Note the smallest angle obtained and some simple maths (and the almanac) will give you your latitude.

Yes, there is much more but this will get you started.

[FamilyVan]

Originally Posted by Wotname

Let me see if I can give a simple explanation of celestial navigation to expand a bit on Family Van's excellent post.

The basic concept is to use a sextant to measure the angle between the heavenly body and the horizon and note the time. Then use maths to compute a line of position (LOP).
Three LOPs are required for a fix.

So the errors occur when any of the above steps contain errors.

The common ones are:
Using a wave top of a nearby wave instead of the true horizon or an indistinct horizon.
Motion of the boat may lead you to get the angle slightly wrong when using the sextant.
Sextant has errors - might have been knocked etc and mirrors require adjustment.
Your time may have errors w.r.t. GMT; you want the accurate to a few seconds.
Your maths can contain errors - misreading the numbers in the nautical almanac or sight reduction tables.

These are the common source of errors.

What you may not realise is that you can only use the stars at dawn and dusk. This is because you need to be able to see the horizon and the star at the same time. So the star has to be in view (no clouds, no sun) and the horizon has to be visible - so dawn and dusk.

The sun can be used anytime (during the day of course) and the moon any time it is visible if the horizon is also visible. Using the sun and moon require you to use either the upper side or the lower side of the sphere (or limb in nautical terms).

So this sometimes causes an error if say you use the upper limb for the sight but entered the data from the almanac for the lower limb - don't ask me how I know this .

The only time you don't need to know the time exactly is when you use the sun (and sextant) at local midday. This will give you the latitude only and does not require time data. The procedure is simple - around local midday say 20 mins before, start measuring the angle between the sun and the horizon. As local midday approaches, the sun will appear to lower closer to the horizon, "kiss" it and start to rise. Note the smallest angle obtained and some simple maths (and the almanac) will give you your latitude.

Yes, there is much more but this will get you started.

If you are serious about writing a book including serious navigation elements I would recommend "The Nautical Chart" by Arturo Parez-Reverte. Give it a read, that guy is not a pro-sailor, but did some serious research into navigation.

[El Pinguino]

No problem getting 5 stars if he is used to taking stars and has done his planning...

A way of introducing an error that will result in a big cocked hat?...

The simplest would be if the total correction for each star has been applied incorrectly but that would only give about 5' on each star... noticable but not the end of the earth.

A bigger error would be introduced if he applied all his intercepts the wrong way... now that would look messy.... but an easy fix once he realises what he has done.

PM me and I'll email you some stuff that may make this clearer.

Vasco de Ping

[misssherry]

In theory, only 2 LOPs are needed to get a fix from 2 different celestial bodies (best if they are 90 degrees apart). The reason that 3 LOPs are commonly used is that they form a triangle and it is straightforward to resolve the center of that triangle and call it your fix. In the oddball chance that the 3 LOPs cross at the same point,, you can count your lucky stars. More than 3 LOPs puts the navigator in the position of trying to resolve where to guess where the fix should be placed on the chart. If you make only 2 sightings in a perfect world, where they cross is where you are... or were.

[skipmac]

I think the OP might be confused by some of the explanations. Yes taking a celestial sight will give you a position that is on a circular line. But to be clear, that is a circle thousands of miles long going around the planet. For the actual plotting of the position on a chart the sailor is only looking at a very, very short section of the circle which for practical navigation is essentially a straight line.

[FamilyVan]

Originally Posted by skipmac

I think the OP might be confused by some of the explanations. Yes taking a celestial sight will give you a position that is on a circular line. But to be clear, that is a circle thousands of miles long going around the planet. For the actual plotting of the position on a chart the sailor is only looking at a very, very short section of the circle which for practical navigation is essentially a straight line.

Hence my reference to dead reckoning.

Sent from my SGH-I547C using Cruisers Sailing Forum mobile app

[rhubstuff]

I would recommend the OP read the celestial nav. chapter of any of the many navigation general texts out there. Dutton's, The American Practical Navigator (Bowditch, available online, 35 MB total, chapters 15-23 cover celestial), or Boater's Bowditch, a simplified version. Skipmac is correct in saying that celestial LOPs are plotted as straight lines. And they are plotted on a plotting sheet, not a chart. I'd also suggest that, depending on the time frame of the story, the protagonist use a navigation calculator such as the Celesticomp or one of several computer programs available since the 1980s.

[ceswiedler]

Wow! Thanks, everyone.

I think Wotname and others confirmed what I was thinking: that if you sight 3+ stars "perfectly", then you would get a single point, but if you mess anything up, you get a polygon with 3+ sides. So an inexperienced navigator could get a position with a relatively large margin of error.

If that's even more-or-less true, then I'm happy. This isn't a book about navigation (or even sailing) and so I mostly just don't want to describe the process completely inaccurately.

One thing I didn't realize is that you have to be able to see the horizon, though of course that makes sense. Fortunately, this is science fiction. If you're interested, here's the situation in more detail:

Two kids living on Mars ~100 years in the future steal a rover and run away. A solar flare destroys all of the GPS satellites, leaving them with no way to navigate. One of the kids has a decent amount of training, and has been taught how to sight stars. I'm handwaving the measurement stuff with sci-fi magic: for example I'm saying that gizmos in their helmet will help them measure the angles of stars, and it's easy enough to say that they can do this without actually seeing the horizon.

Now, obviously you could ask why their suit computers are good at measuring the angles of stars but leave the rest of the process and most of the math up to the kids. To that, all I can say is that the story demands it: it can't be impossible, and it can't be easy. If you see something that's fundamentally wrong with what I'm describing, please let me know, but if it's just hard-to-believe-if-you-know-a-lot-about-navigation, then I'm going to have to let it pass unless we can figure out another way to achieve the same end in the story.

One other thing I'd like is to have them come up with some way of improving their largish-polygon plot. Something like sighting one of the moons of Mars (which was suggested in The Martian by Andy Weir if you've read that). I'd like it to be a eureka kind of moment--"hey, we can do XXX and get a more accurate location!" So if anyone has a suggestion along those lines, I'd love to hear it.

Thanks again for letting me hijack your forum for my completely-non-sailing-related question.

chris

[Wotname]

Originally Posted by misssherry

In theory, only 2 LOPs are needed to get a fix from 2 different celestial bodies (best if they are 90 degrees apart). The reason that 3 LOPs are commonly used is that they form a triangle and it is straightforward to resolve the center of that triangle and call it your fix. In the oddball chance that the 3 LOPs cross at the same point,, you can count your lucky stars. More than 3 LOPs puts the navigator in the position of trying to resolve where to guess where the fix should be placed on the chart. If you make only 2 sightings in a perfect world, where they cross is where you are... or were.

In theory, 2 LOPs give two possible fixes, usually a thousand plus miles apart;
In practice, you can usually eliminate one possible position as it will some considerable distant from your DR position.
3 LOPs give only one possible solution.

[skipmac]

Originally Posted by FamilyVan

Hence my reference to dead reckoning.

Sent from my SGH-I547C using Cruisers Sailing Forum mobile app

I saw your reference but I don't think dead reckoning relates to the point I was trying to explain to the OP that is, the circular LOP on the globe is very large and the actual navigation takes place on a chart showing a small area and a very small section of that circle. In practical use that is a straight line. I just thought that someone completely unfamiliar with celestial navigation might be confused by the several posts that referred to the circular line of position.

Also, when you mention dead reckoning you say that is how to resolve which of the two points of intersection of the two LOPs will be your correct position. First, since the two points of intersection of LOPs in celestial are generally hundreds if not thousands of miles apart, if you aren't certain which one is correct you would have to be pretty lost. Plus, if your actual position is 100 miles away from your celestial then you are not doing very well with the celestial. It has been 35 years but as I recall the worst I got even in very rough seas and poor observation conditions was 12-15 mile box.

Second, dead reckoning is navigating from a known point using course, speed and adjustments for current, leeway, etc to deduce your current position. If you don't know where you are to start with from celestial or some other method then dead reckoning won't find you.