Celestial Navigation Math

TabletClass.com - www.tabletclass.com Math. This video explains the basics of how math is used in celestial navigation. When people first started to navigate by stars a massive explosion in trade and culture developed. Celestial navigation requires the use of a sextant, clock and nautical table but most importantly it requires mathematics. SPECIAL NOTE: The earth is round/oval, so my use of right triangles is a simple math model to explain the basic concepts of navigating by the stars. However, the actual math needed to perform celestial navigation involves trigonometry on a sphere- which is very advance math- as such you should watch the video knowing that right angle trigonometry is not actually used in navigation because the earth is a sphere.

[@castaway123100]

Thanks! This is the best overview I've seen so far. I watched a few other videos that went into great detail, but, they NEVER illustrated what those details were accomplishing. The drawing and simple explanation create context for the detailed math involved.

[@DD-lr6ne]

Acreedores, excelente descripción

[@spelunkerd]

This video deserves a 'part B' where you work through an actual example. Good work on part A, best description I've found so far.

[@edshannon4426]

Kudos to you sir! Most explanations of this process bury the pupil in jargon without first giving a simple conceptual explanation. I for one, thank you very much.

[@johnlbales2773]

Ed Shannon Agree 100%. Thank you. Great job.

[@davecorley5514]

Good first-order explanation. Fifty three years ago I took two, three-hour classes on navigation over two semesters. One semester was devoted to celestial navigation. It was a part of my training as a midshipman at the US Naval Academy. Forty years ago, I served as Navigator on two nuclear submarines. To take celestial observations, we had to attach a specialized sextant to the bottom of our periscope and be at periscope depth for the duration of the observation at nearly constant course and speed. The fixes we obtained were usually very inaccurate when compared to modern electronic navigation fixes - errors of +/- 5 miles or more were common. Modern gps fixes with errors less than six feet are quicker and don’t require extended time at periscope depth. But, we’d take celestial fixes through the scope every year just to stay in practice. An operational difficulty for submarines is that celestial fixes are best taken near twilight (near sunrise or sunset) to be able to view both stars/moon and horizon at the same time. That meant that bad guys would know when a sub had to be at periscope depth to take these observations. Not good. So, we avoided celestial navigation in favor of electronic navigation fixes - GPS, NAVSAT, LORAN-C, OMEGA, bottom contour fixes. We also had two inertial navigation systems that maintained estimated position of the sub using gyroscopes and accelerometers. The more accurate explanation is that the LOP of a celestial observation represents the intersection of a cone extending from the star towards the earth that intersects with the surface of the ocean’s surface. In the open ocean that intersection describes a circle. And that circle is the LOP. Observation of the altitude of at least two other celestial objects, corrected to the time of the first observation, yields two more circular lines of position. With no measurement or instrument errors, these three LOPs intersect at a point on the ocean’s surface. The point is the fix position at the time of the first observation. Because the surface of the ocean is spherical, then linear geometry will not yield an accurate enough fix. Instead, spherical geometry is used to generate the tables in H. O. Pub 229. The navigator/quartermaster does not have to know spherical geometry, but they must know how to look up the star’s parameters for the time nearest the observation. And several corrections must be made in order to optimize the accuracy of the celestial fix.

[@raymondlowry8564]

I was also in the Navy ( in the early ‘70’s) as a Quartermaster. Your presentation brought back some fond memories, for instance how satisfied we would get achieving a pinwheel fix when shooting stars. Not always easy when your vessel is rolling and pitching. I wonder if ships still carry Chronometers? In any case, nice job Sir.

[@TNEWHAT]

Negative, am a quartermaster currently and mostly everything is based on VMS better known as electronic navigation.

[@DivergentDroid]

You claim: " The thing is, it is very easy to prove that cel nav requires the globe. The single fact that no flat earther has ever accomplished cel nav without the globe is proof." - NO Not gonna cut it son! You just used a strawman fallacy which is also begging the question to back your claim instead of actual evidence. I'm sure you meant it as a red herring too! 3 fallacies! Look them up son. Show me you taking an elevation angle without a straight horizontal baseline. You Cannot do it!

[@robertlafleur5179]

⁠​⁠@@DivergentDroid_’’No flat earther has ever accomplished cel nav without the globe…’’_ I’m sure you won’t let this be and will do a Flat Earth CN demonstration right now, right? I wonder why no flat earther has ever done it? Don’t tell me that Earth being a globe is stopping you. When has facts ever stopped a flerf making a fool of himself?

[@MyNameIsNobody57]

In case anyone is wondering what "H0229" is, it's a Nautical Almanac. "A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea. Wikipedia"

[@albertsarigumba4706]

Table 249 not, HO 229 Sir!!!..

[@seankivler1957]

By the previous comments in response to your 'H0229', Its' a wonder any of you found your way back to shore!... So, dare I ask this 'confused' bunch, how this differs from an Ephemeris?...

[@seikibrian8641]

Sean Kivler -- There are many ephemerides, with different formats and layouts. H.O. 229 and H.O. 249 are particular publications designed specifically for navigation.

[@tortillafilms]

Those Manuals ,are correct : 229 & 249 Sight reduction Tables/air nav.

[@TheHarshRealm]

229 is sight reduction tables. The air, or nautical almanac is a book reproduced yearly. I have a set of 229 onboard that was printed in the 70’s and they are still correct.

[@surveyore7]

Good 'general' explanation. As a surveyor and one who did astronomic observations for nuclear weapon delivery systems, we used this technique primarily to establish direction. We also used it to establish and or verify our location against predetermined markers on the ground (called trigstones). This method whereby you use two or more astronomic observations to locate your position in marine navigation, we also call 'resection'. Other points that have 'known' data sets could be church steeples for instance. I spent 12yrs in Europe doing exactly that, most of which was before 'GPS'. I 'trig traversed many kilometers, bringing directional and coordinate control to where I anticipated a 'firing point would be needed. Mostly this trig traverse occurred in winter where trig stones were covered in over 3ft of snow. Later as technology became more 'developed' they brought a navigation system (gyros and accelerometers) through my points previously established with trig traverse, and found my data to agree with a 1:50,000 Accuracy ratio. Yes we used T2 theodolites and 'math' as well as star finders, and emphemiris.

[@TheJarhead70]

Thank you for your service. I was a Marine NCO and later in my career an Army Officer. I did operate a pair of LPC's (leather personnel carriers). I am new to sailing and will use D.R. plots with running fixes to support electronic navigation. Great information. Regards Jarhead 66

[@Uhlan_]

Armed only with a sextant, a book, some math, AND A CLOCK!

[@hunterplayshd3820]

Right, that's what was weird to me. What if you don't know what time it is?

[@Rebius]

HunterPlaysHD in the old times, when sailors didn't had a watch on board were perfectly fine just by guessing the time and were pretty good at that, didn't had as much nonsence to care about like our modern culture and it was also extremely important and useful as you can see ;)

[@wuteverfloatsurkayak]

Rebius They also used the stars to tell time.

[@2adamast]

+leigh tyrrell An astrolabe can tell time with stars. But local time only, no way to know if 3 a.m. is New York local time or a local time 300 miles more east.

[@zengerz]

astrolabes prove geocentric universe too :)

[@Sharkman6275]

That was most simple explanation for celestial navigation I have ever heard! Thank you!

[@tabletclass]

Hello and Thank you for your service as well. Before I was a Navy Officer I was in the Marine Corps (enlisted 87 -91) - Semper Fi. As you stated navigation uses several skills and methods. Knowing how to DR is key as it's too difficult to update your position with celestial nav only.

[@davidjacobson9463]

Thank you for this incredible "Navigation" documentation. I've just been "getting into it"; so again TY!

[@hughheron4532]

Finally someone xplained this in a way that the average joe can understand.Hats off to you sir.

[@rawnukles]

The two LOP circles would intersect at two points, two fixes. I guess I third star would tell you which fix was the right one.

[@wuteverfloatsurkayak]

rawnukles I thought of the same thing. If you are alert and knowedgable enough to calculate this, you could probably estimate where you're at based on velocity and your previous known position and thus you would probably already know which of the two points was accurate; but the third LOP would eliminate the wrong position with certainty.

[@Argos100i]

+rawnukles The second intersection is probably in some other ocean, so the navigator does have a clue.

[@rawnukles]

Of course common sense rules out the second intercept.

[@user-pf2hv8qw1s]

Yes you could rule out the second fix unless the two circles were tangential to each other. In that case they will only intersect at one point.

[@garychap8384]

rawnuckles, in practice the error margin takes care of that, also... as wuteverfloatsurkayak said ... you have other techniques such as the running fix... one LOP+DR gives you an EP (Estimated Position) In actual fact, it's typically less important to know where you ARE than where you're NOT ... so, you'd typically be more concerned with best avoidance than perfect position. In practice, trying to be too accurate is very dangerous. For example, when you take three bearings and transfer these to a chart you typically get a triangle, not a point. It is so tempting to say "I am within this triangle" ... but to be inside of the triangle you'd need all bearings to be off in the same direction ... all bearings, however tight, will be off to one side or the other with near equal probability - so there is actually more chance that you are NOT inside the triangle! Technically, your actual position would map as a blurry donut, with an area of decreased likelihood inside. So, always accept the error margins with dignity! Never try to convince yourself of where you ARE ... but simply seek to be damned sure about where you're absolutely NOT (rocks, wrecks, windfarms, coastlines, busy TSS's, etc) ... and keep checking to make sure you remain 'NOT THERE' during your passage. Having even had my chart-plotters GPS throw me a silly offset now and then, I'm far less concerned about where I truly am these days ; ) I know, that sounds weird, but it's a fact we sailors all have to accept sooner or later : )

[@michaeldowning1533]

Hello, I know absolutely nothing about navigation. Isaw this film"Adrift" a true story about a Couple (man and women) who were given the Job of sailing this well equipped yacht across the Pacific. Sadly they ran into a fierce storm, the boat got completely wrecked, the man (an English guy) was thrown overboard and sadly died and the American lady came to to find all navigation equipment completely destroyed except a sextant.She is seen looking through this sextant to try and find her position and it was the vastness of the sea that she was in that made me realise the importance of knowing something about knowing where you are and which direction to want to go. Your simple but clear description of finding our roughly where you are at sea was great. Thank you. I'll have to get that book with the funny title..

[@jorgepinal3621]

Great starting point, thanks ! So to cap it off celestial map to know one or two stars sextant the HO-229 Accurate time (know what time zone) What would it happen if I want to take the measurement during the day? Again Thanks,

[@roohif]

The line you draw from the observer to the GP of the star at 4:53 is *INCORRECT.* The line of sight between the observer and the star, and the line between the GP and the star are *PARALLEL* - it's not a triangle. The reason you see the star at 50 degrees elevation is because you are 40 degrees of a sphere away from the GP of the star. At 69 miles per degree, that makes the distance to the GP equal to 2760 miles.

[@sleepingwarrior4618]

Roohif, is that line of sight a straight line? Or is it subjected to 7/6r? It's subjected to 7/6r isn't it.....so that means to can't get a 90° anywhere as well.....funny looking triangle that.

[@golfkilo6227]

@@sleepingwarrior4618 There is no need for a triangle, actually.

[@roohif]

@@sleepingwarrior4618 The line of sight is curved in reality. The whole idea behind 7/6r is to make it straight so the geometry is easier, you frikkin numpty. Watch my recent JTolan video and you’ll see how it works.

[@marcg1686]

@@sleepingwarrior4618 The line of sight is refracted, hence the altitude correction table in the Nautical Almanac.

[@poly_hexamethyl]

5:00 Isn't this pretty misleading? I mean, the base of that triangle isn't a straight line, but follows the curvature of the earth. And the horizons at the observation point and the point underneath the star aren't parallel. I think it would make more sense to draw the earth as a circle and then you can see that the observed angle of the star above the horizon will be 90 degrees minus the angle at the center of the earth between the two points, which is how you get the distance. Another misleading feature of the diagram in the video is that the star is in reality essentially infinitely far away (compared to distances on earth), so the light from the star hitting the two points on earth is essentially parallel, which is important for the geometry to work.

[@thesextantthesunandtheholy4274]

Earth radius value has been debunked with footage of the horizon beyond 9.41 miles away from a one foot eye height. The sextant works only on a flat surface. The radius for the circles of equal altitude can not be curved as a curved line does not provide a vertex for the 90° angle. This instructions given here, in this video are redundant if spherical trigonometry is to be usef. This dude is a religious, globe believing, fundamentalist moron.

[@wattdaflat5286]

@@thesextantthesunandtheholy4274 Wow, very interesting. How does the sextant work on a flat earth, then?

[@wattdaflat5286]

@flatearthlogic dot net Ok, you have an angle to a star of 45 degrees with a bubble sextant (no need for dip correction), how do you calculate your distance to the GP??

[@tabletclass]

Thank you for that wonderful comment. Clearly you know what you are talking about and bring back a lot of "rusty" memories for me when I was a Navy Navigator. The goal of my video was to give students a general sense of the mathematics that go into celestial navigation. Of course I find it amazing that we can use the starts to locate our location on earth so I try to motivate students by using real life examples of math to become more interested in the subject.

[@frankmiller95]

From personal experience, the sight reduction tables are a massive time saver. Unless there's a dog on board, who eats them, they're preferable to Ageton, which l, ah, never learned. .

[@tabletclass]

Hi Brian- I agree with your comments; finding your position using a sextant really is an amazing feeling as it connects you with so much history of how people navigated in the past

[@flattenthecurve8623]

It only works on a Flat Earth.

[@MISHA12314]

It's easy to measure "altitude" of a celestial body, correct according to height above horizon, upper or lower limb, etc. Subtract from 90 degrees. This is your distance from the body in nautical miles. Best to shoot body's that are due north or south for latitude, and due east or west for longitude. Position of bodies are listed in the "nautical almanac" in longitude and latitude according to date and time. Each "fix" results in a triange on the map, or a distance in nautical miles when subtracted from 90 degrees, to the body. Problems develop because maps are not true d/t curvature of the earth. The map triangle can have three 90 degree angles which is 270 degrees (or more!), so conventional trig is worthless except for figuring the distance to the body with your calculated position on a distance line from the GP (geographical position, aka long. and lat.). Also, you must assume longitude to get latitude, and vice versa. So, at best, especially with a time that is off (one second = 1 nautical mile), problems develop regarding actual position vs. calculated position. Also, arcs drawn on a map are not true circles (grid lines on the map do not make a true square). There are "cheat sheets" that can be used for celestial navigation, which seem more accurate than the actual hand computed fixes. Corrections are often made using a "trafrail log" which measures distance covered (not corrected for current!). In short, oh brave explorer, be sure to have a modern system such as GPS to guarantee accuracy of your navigational skill and provide information when the weather is bad to keep you out of trouble!. There's a reason celestial navigation has taken a back burner. It's fun to play with to see the difficulties, but that's about it. Thanks for the site!

[@peterbeefchicken5237]

Thanks a lot for the details! It may even save someone from big troubles.

[@seikibrian8641]

+ Thomas Dobyns "It's easy to measure "altitude" of a celestial body, correct according to height above horizon, upper or lower limb, etc. Subtract from 90 degrees. This is your distance from the body in nautical miles." To be precise, it's your distance from the point ON EARTH that the body is directly overhead of, not the distance FROM THE CELESTIAL BODY...which would be 207,560 (moon), 80,776,388 (sun), or more nautical miles away.

[@seankivler1957]

... and how, pray tell, will we EVER measure and compute the 'PZS' triangle?

[@baubljos103]

I watched your video to educate myself about sextant use and celestial navigation because it relates to the controversy about whether the oceans are curved - or flat. Based on your video, I'm inclined to infer that the LOP (line of position) and the 900 mile leg of your triangle - are flat. In addition, based on your video illustrations I infer that the ocean must be flat in order for the sextant/navigation method to be effective.

[@iveneverseensuchbehaviorin5367]

the stars are in a celestial sphere. i know you dont understand what that means but it means the earth isnt flat

[@baubljos103]

@@iveneverseensuchbehaviorin5367 Rather doubtful that you could possibly know what another person "understands", because you can't read minds. So the basis of your claim is bogus. As to the flat/curve hypothesis, the sextant presumes that the measured distances are flat. Similarly, engineers presume that earth is flat when they design bridges and other structures, and airlines fly flat over the flat earth.

[@iveneverseensuchbehaviorin5367]

@@baubljos103 you say my claim is bogus but yet dont say why. makes me think you dont understand it. a sextant gives you the angle something is off the horizon, nothing to do with flat or curved.

[@baubljos103]

@@iveneverseensuchbehaviorin5367 Well technically I wrote the "BASIS of your claim is bogus" and I explained why. It's bogus because it's impossible for you to know what other people "understand". That's not knowable because you cannot read minds. As to the sextant angles - they are all flat , ie horizontal - and perpendicular. Not curved. You know the word "horizon"??? You know what it means? It mean horizontal - flat at zero degrees.

[@iveneverseensuchbehaviorin5367]

@@baubljos103 okay so you dont understand why a celestial sphere debunks the flat earth, youre just upset i called you out on it. so are you saying the horizon rises to eye level? Because the tons of evidence saying the horizon doesnt rise to eye level would debunk your claim about the sextant correct?

[@Ratlins9]

Superb video, the ability to break down a sophisticated method of navigation for laymen to understand shows high intelligence. Thank you!

[@kamisview]

Best explanation I've heard wasn't even looking for this but I just got hooked.

[@alexxchavezee]

@1:45 skip to

[@iveneverseensuchbehaviorin5367]

flat earthers sure talk big when they dont even have a map yet

[@AlexZander688]

Read the description for the video: "SPECIAL NOTE: The earth is round/oval, so my use of right triangles is a simple math model to explain the basic concepts of navigating by the stars. However, the actual math needed to perform celestial navigation involves trigonometry on a sphere- which is very advance math- as such you should watch the video knowing that right angle trigonometry is not actually used in navigation because the earth is a sphere."

[@tabletclass]

Thanks for the great feedback. I agree with your comments. When I made the video I just kind of created it as I was think about it. Nevertheless the topic of navigation and teaching the mathematics around the subject is huge and offers several approaches. Thanks for watching!

[@jochenludewig8857]

Very well done!! Being a total novice with this skill I have been looking for some decent & basic information re positioning/sextant use for a while.....I found your KZbin clip and now understand the principles involved. You ARE a legend. Thank you from a layman in Australia

[@dbeierl]

Unfortunately he neglected the basic principle that a difference in observed angle to something as far away as a star can only arise by your own self being aligned in a different direction because you're standing on a sphere. The actual divergence of angle of light rays falling from a star onto any point on earth is far too small to measure with a handheld instrument.

[@richardcranium8408]

5:05 “I’m not going to get into the math because that’s not the purpose of the video.”. Huh? Why title your video like that then?

[@Somethingisntright64]

The radius of your “Circle of Equal Altitude” for star A would be 2400 NM, not 900 NM. ZD = 90* - Ho x 60NM/*

[@davesantiago1827]

Yes and what does this prove? It proves the earth is FLAT. Cant have 90 degrees on a sphere thats dropping away from you at 8 inches per mile squared. Im not trying to be condescending. Im just trying to make people see the truth.

[@Somethingisntright64]

@@davesantiago1827 90 degrees to the subpoint of the body. Your position is somewhere other than the subpoint which allows you to derive the zenith distance.

[@davesantiago1827]

@@Somethingisntright64 sorry for the aggression. I thought you were in another thread I was arguing with someone

[@davesantiago1827]

@@Somethingisntright64 yes so you have your zenith pulled from a celestial object then to horizon to you. 90 degrees every which way on a circle of equal elevation. Proves the earth is a flat plane. Its a fact that cannot be denied.

[@TheIsmaelIsaac]

Just checking to see where the 60 nm to get 900 or 2400 miles came from??

[@tabletclass]

Hi Ken- thanks for watching the video I'm glad you enjoyed it. I'm a math teacher however I love engineering and other science topics as well....

[@Rick-tb4so]

I have tried to learn celestial navigation for years reading books ...failed..videos...failed and then you came along, Your video is OUTSTANDING and easy to follow and I finally get it.........THANK YOU.....

[@johnx9318]

minute and a half in - still waiting for some information. any more waffle?

[@mikenaugz88]

John X welcome to KZbin, just click 5 or 10 min in and rewind till it starts to make sence.... like i do lol

[@reginaldwigglebottom4731]

No shit! I left during the 3rd minute of disclaimers. Fuck it, I’d rather be lost

[@TacMind]

Flat Earth brought me here. Thank you for your video

[@flat4life]

This would be impossible to do on a globe. Sextants prove flat earth.

[@marcg1686]

​@@flat4life Why would this be impossible on a globe?

[@flat4life]

@@marcg1686 How do you get a 90° triangle on a curved surface? Not to mention, this 90° triangle spins around in a circle… It only works on a flat surface, it can’t work on a globe.

[@marcg1686]

@@flat4life We don't use 90° triangles when conducting celestial navigation.

[@flat4life]

@@marcg1686 Yes you do, you use 90° right triangles it’s right there in the very video that we just watched. He actually shows a graphic.

[@antoniothales4721]

Congratulations!!! Your video is a lot easy to understand and well explained. Please keep with the classes, I am learning a lot. Thank you

[@alfaproximacentauri5335]

I think this is completly wrong.... how can you calculate this '900' miles having ONLY three angles? Please note the distance to any star is -comparing to the size of the Earth- practically infinite. So I think the author of this video is showing wrong triangle.

[@alfaproximacentauri5335]

***** I am not saying the celestial navigation method is wrong. I am saying the explanation provided by post author is wrong. Look at the triangle he shows: first of all if you have only angles, then you can not say anything about lengths of triangle sides. In addition, assuming the distance of 900 NM is correct: the angle is 50deg, tan(50 deg ) = 1.2, so the distance to the star would be 900 NM * 1.2 = 1080 NM. Not so far, really.....

[@19Koty96]

eh, nautical mile is not a unit of distance, it's a unit of angle ;)

[@duane816]

wouldn't a nautical mile be a measurement of distance (6076 feet) and latitude and longitude be a measurement of angle (degrees)?

[@19Koty96]

nautical mile is angular distance ))) go figure nautical mile is a section of arc (on a "spherical" surface) defined by its angle

[@denisrogers4543]

nautical miles are units of distance. one degree at the center of the earth represents a distance of 60 nautical miles on the surface of the earth. There are 5,400 nautical miles between the equator and either pole.

[@Frups12345678]

Congratulations TabletClass Math, you have now become a flat earth poster boy! I understand that it was never your intention and you tried to prevent it by writing: "SPECIAL NOTE: The earth is round/oval, so my use of right triangles is a simple math model to explain the basic concepts of navigating by the stars. However, the actual math needed to perform celestial navigation involves trigonometry on a sphere- which is very advance math- as such you should watch the video knowing that right angle trigonometry is not actually used in navigation because the earth is a sphere.". This however is of no relevance in the flat earth cult, so congratulations to your new found fame!

[@tabletclass]

hello- I have not anymore videos however I may look into creating more- I love navigation and find it very interesting to see how math is used to find your location

[@sam111880]

ok curious how the book was created so that one can associate the right stars,sun, celestial objects to the times/locations of them. Like it seems easy to measure the angle with a sextant and time with a clock but math being trig is not to difficult either but nautical table don't get how that could be create accurately and one to associate the right objects with.

[@seikibrian8641]

The tables were produced based on empirical evidence. The stars were/are measured from a known position on earth -- the Royal Observatory at Greenwich being a famous one -- and tables devised from those observations. Then one needed only to use calculations to determine how far away from the observatory you were.

[@q.e.d.9112]

sam111880 The fixed stars all rotate in unison. Observatories around the world have, over the centuries, fixed their position on an imaginary “Celestial Sphere”, using a system similar to latitude and longitude on the terrestrial globe. On this celestial sphere the prime point, equivalent to Longitude 0 on the equator is a point in space known as the First Point of Aries. From this point each star’s position on the sphere is given by two numbers. Its Declination (latitude on the celestial sphere) and its Hour Angle (also known as its Right Ascension) which is its celestial longitude. These figures are fixed for each star just as the latitude and longitude of places are fixed, on the terrestrial sphere. To find the Zenith point of any star (the latitude and longitude where that star is directly overhead) we first look up its Declination and Hour Angle. These can be found in a Nautical Almanack or an Ephemeris. Then we look for the Greenwich Hour Angle of the First Point of Aries for the nearest hour. This is the location of that point on the equator measured round from longitude 0 (Greenwich). We can now find our zenith point. It’s latitude is the star’s declination. It’s longitude is its Hour Angle measured around from the GHA of Aries. This requires either the addition of the two hour angles or a subtraction. It is best done by sketching out on a circle representing the equator. Mark a point as longitude 0, with E and W marked. Estimate Aries GHA and mark that. Then from that point estimate the star’s HA and mark that. You should now be able to figure out whether you add or subtract and whether the longitude of your terrestrial zenith point is E or W. Now you’ve got to the nearest hour, your longitude is changing by 1degree westwards every 4 minutes. I hope this has been useful. It sounds complicated and because it uses nomenclature from several centuries ago it IS rather more so than we could make it today. But then again, today we’d just use GPS.

[@solahudinudin906]

hi you use flat earth model. Interesting.

[@carl203crazy2]

Sorry, he is using a bad example that means nothing. And celestial math is sphere based.. NOT flat.

[@dejanhaskovic5204]

WHAT AN IDIOT YOU ARE!

[@carl203crazy2]

Really? I think teaching celestial math for over twenty years contradicts your immature response.

[@garychap8384]

Solahudin ... yes, I laughed at that too : ) There's _"simplifying"_ ... and then there's _"playing into the hands of the flat-earth idiots"_ and, however well intentioned, this is definitely achieving the latter ; )

[@19Koty96]

The funniest part about trigonometry is, that it works regardless of what you take as base.

[@FTFEOfficial]

Uh...that's all wrong...there are NO triangles in celestial navigation...

[@paulwielgosz6046]

Unless you are directly under the celestial reference the triangle is a result of the elevation

[@stellerpolaris]

​@paulwielgosz6046 idk why people fight so hard about the gp of the elevation angle making a right angle triangle from the gp at the horizon to your location in the boat.

[@stellerpolaris]

Ohh what are you talking about?

[@iveneverseensuchbehaviorin5367]

@@stellerpolaris There is no triangles in celestial navigation, how hard is that to understand?

[@dqf9830]

There are spherical triangles

[@southerntexashomestead5028]

Awesome class. If current teachers would use this method of teaching more students would grasp the skills of mathematics and value it's usefulness. Great job!

[@TrueCourse]

Thanks very much for clarifying celestial navigation. I've been on bridge watch and noticed some of the JOs and QMs plotting away and I wasn't quite sure how thing worked. Which ship were you on?

[@sakichatzichristidis8932]

need to be more to the point too long intro

[@hillside6401]

Proving earth is flat earth. Very nice 👍🏻

[@mactallica9293]

You clearly don't understand navigation. Or trigonometry

[@hillside6401]

@@mactallica9293 o nice why don’t you explain why I don’t. Oh yeah I actually do and you don’t. That’s why you don’t elaborate sphere boy. Gtfoh

[@iveneverseensuchbehaviorin5367]

@@hillside6401 flat earthers dont know how to celestial navigate, you cant find one who can do it

[@hillside6401]

@@iveneverseensuchbehaviorin5367 I have several times with my grandpa. Have you? We even used our sextants upside down. Great proof of flat earth. You don’t have to like it. 😁

[@iveneverseensuchbehaviorin5367]

@@hillside6401 you can say anything you want, you wont demonstrate how to use a sextant to find your location because no flerf ever has. They couldnt explain how to do it because that requires saying the earth is a sphere. so all you flerfs do is lie lie lie.

[@elizabethkoetje6536]

This is awesome, thanks! I've always been interested in both astronomy and history, so this was very cool to learn! The internet is an amazing thing.

[@DianMeidiani]

how to make accurate measurement in choppy water? as the ship up down movement would interfere with the observation.

[@certified_boogeyman]

Proof the earth is flat

[@iveneverseensuchbehaviorin5367]

not one flerf knows how celestial navigation works. proof flat earth is a scam

[@iveneverseensuchbehaviorin5367]

proof flerfs cant defend their claims

[@DivergentDroid]

@@iveneverseensuchbehaviorin5367 A sextant is an angle measuring device. Angles are defined as two straight lines meeting at a vertex. It is impossible in math to take an angle from the surface of a sphere as any Cad program will tell you. The celestial navigation books and this video shows you taking an angle from the flat horizontal plane. The books call this the equatorial plane. They also state cel nav uses the horizontal coordinate system. They tell you at sea level you do Not need to correct for height of eye or dip as some call it. The sea level itself is considered the flat horizontal plane cel nav uses to take the angle from as shown in this video. Nothing you do in the tables after that angle is taken will negate the fact you used a flat horizontal plane to obtain the angle. Earth measured Flat by way of elevation angles. No way you can get out of this.

[@iveneverseensuchbehaviorin5367]

@@DivergentDroid the line from the sextant to the horizon is a straight line, destroyed your huge paragraph in an instant

[@DivergentDroid]

@@iveneverseensuchbehaviorin5367 Are you Daft? It didn't destroy my position, it agreed with it. Don't you understand you cannot have ANY straight lines on a sphere? If that's the best you can do to rebut my paragraph then I say Welcome to Flat Earth!

[@dataderivations2737]

I'm studying the "Sextant Crop CIrcle" and this information exchange was most helpful for the linguistic studies being performed.

[@ilovefredreika]

Thank you for this wonderful Video! Finally somebody explains it simply!!

[@carl203crazy2]

John.. Please delete this video. You are embarrassing the rest of us who know how this is done. Your use of 'thing' and the totally wrong distance in your example is just poor. If you are going to reference an example, use the proper terms and correct information. 50 deg observed altitude equates to 2400 nm from the stars geographic position. Which is tabulated in a book by-the-way. And, You do not need a major in mathematical study to determine this fact. It's simple multiplication. Oh.. I think it's HO pub 229? really? maybe it's something else. Maybe a Nautical Almanac? Maybe Sight Reduction Table? Sorry, I couldn't watch past the 900 mile thing... 17yrs ocean navigation, U.S. Navy Instructor (Celestial Navigation) Good luck

[@deaconallan]

As a former ships captain (merchant), and a navigator for many years, before the advent of GPS, although we did have DECCA and in the western hemisphere LORAN, these did not reach out to sea, and were only useful near land. Thus, celestial navigation at sea. Basically, three items are needed: a quality sextant, a good accurate timepiece (Chronometer), and sight tables, I prefer to use the Air Almanac because it was much simpler than HO229 and sights can be worked out much faster. A stopwatch is also helpful. Although I have been retired for 14 years, my sextant and stopwatch reside on a shelf in my study.

[@marcg1686]

Did you ever try to determine Hc using a calculator? I also started with HO249 but I only use a calculator now. Way easier.

[@saishyamnilgiri1]

Thank you! I enjoyed this video. You taught me some thing very important on Astro Navigation. I has got me closer to my goal. Thanks once again and God bless you.

[@JamieSmith-fz2mz]

A very simple conceptual explanation. As a sailor, I love it. I also like that it works if I don't have a phone or a GPS or any other technology. Except I need a sextant, and a timepiece, and knowledge of stars, and a book (H0229), and a pen. The lesson I'm taking from this is to keep my Garmin charged and drop it in the water. Just giving you grief. Your explanation is great.

[@jonathanpatterson3659]

Question, I am planning on applying for Navy ROTC to become a naval officer, what math level would do you believe is expected for all junior level officers? Math isn't best subject for me but I am not bad, just slow at it. I had planned on enlisting and rating as a QM but now I am pushing to be an officer, I just want to know what kind of math levels I should study up on more.

[@tabletclass]

I'm the same way- more data the better. Thanks for the great input on the videos, I think I might brush up on MoBoards and do a intro video; all the best! John

[@some-other-time]

This is so concise -- a perfect refresher!

[@armedmariner]

I like idea of part B - an example. I want to see how you look stuff up in the book. I want to know how to derive the “900mi” LOP circle. Having said all that - BRAVO to you for making this easy to understand. I love navigation. Always have. Always will. My dad once took me for a ride in a heavy snowstorm in NH. He pulls off a dirt road and parks. He shows me on a topo map roughly where on that road we were. He then showed me a roughly parallel road a few miles distant from the one we were on. He produced a compass. Oriented it to the map. Showed me how to find a heading. He said “you think you can walk that heading and come out on that other road?” I mean SURE - it was a long way away but if I could come close to following that heading it was gonna be as easy as shooting fish in a barrel. Out I went into the woods all alone with that compass. Heart beating. Sweating too. But I followed that heading. I came out on that road probably 3 hours later. It was getting dark in the sky and I just waited. I heard a car coming. It was dad in the old Chrysler Newport. He pulls up and rolls the window down and says “I think you know how to keep from getting lost now right?” YUP. Every kid should be given that experience. I loved him for that. What a great thing to build confidence. Thanks Dad!!

[@twocyclediesel1280]

It’s a great experience to navigate through the woods like that. I hiked way back in the Adirondacks once. Simple heading in, I came back out on a 180 degree opposite bearing. I was deer hunting so I was meandering a little as I walked. After all, the road I was parked on ran east / west, and I was heading south. Couldn’t be easier. I got to the road at dusk...where’s my car? I walked east to the first bend in the road, no car. Walked back the other way to the next bend, no car 😆 I was getting very cold and anytime I was walking in one direction, I’m thinking that I could be walking the wrong way! It was a bad feeling. I obviously found it eventually and that heat felt so good. I learned from that. Always add a little intentional error into the bearing so when you get to the road, you definitely know, “OK, I hit the road, now I have to go east (or west) to find my car”. I think the official term is “aiming off” in the “BEMAC” book. “Be expert with a map and compass” I do love working with a topo map and compass, good times.

[@armedmariner]

@@twocyclediesel1280 when sailing, common practice is to “pinch to windward” - you can’t sail directly into the wind but you go as close as you can. You try to navigate so that as you approach your destination harbor or anchorage you only need to steer downwind to get where you are going. Easier than fighting upwind tacking one side then the other. It’s common to say “keep steering high” up into the wind - as high as possible. I absolutely love navigation. There is a book I have that I treasure called We The Navigators. About Polynesian sailors who could sail hundreds of miles between islands with NO navigation instruments. Those guys are a dead breed now. The book was written by a scholar who studied their last generation. He unfolds a ton of stuff that was revealed to him in the course of sailing with those guys. Phenomenal what navigation THINKING can do for you if you keep your senses about you.

[@twocyclediesel1280]

@@armedmariner That’s very interesting, I’m going to get that book. Thank you! I live on a huge river in the SE near the sound and would love to get into sailing. Unfortunately I’ve seen, and worked on a few too many boats that have sunk. I’ve decided I don’t want the hassle of owning one. It must be a great feeling tho. My grandparents lived on a lake in the already mentioned Adirondacks. They had a “mini fish” sailboat and I had so much fun with that as a kid. A bigger boat, and all the skills involved in sailing and navigating...must be a blast! Thinking about how ppl, like the Polynesians, did what they did is truly amazing.

[@shahzalak650]

best explanation so far for this topic found on this platform

[@tabletclass]

I know what you mean- MoBoard problems were great especially when doing things like winds for a helo. A radar screen can be used as a MoBoard so you can plot contacts on your screen and get a CPA; then determine what course correction is needed to open up a safe distance; this stuff is really important for large vessels as you need lots of time and distance to manuver

[@RipMK747]

Thanks man!!! really got the hang of it with your simple and clear explanation!! Cheers

[@MoosesValley]

I used to be able to do Celestial Navigation with a Sextant, a clock, and a current Nautical Almanac - the book of tables for the positions of the closest stars, our solar system's other planets, and our sun during the day. The math wasn't hard. The more difficult math was in the construction of the tables for each celestial object for the coming year. I'm pretty rusty now, but it wasn't hard. Using a Sextant requires some practice to get good readings, and is especially difficult on rough seas, in windy conditions, and/or in small boats. Get regular practice, take readings for 3 stars, and you will soon get your position amazingly accurately.

[@juanjuanruso9180]

Very simple, very clear. Excelente ...Thanks a lot !

[@sam111880]

basically nautical tables seem difficult to create and had to be update over time even more difficult to old cartographers for earth map make. Because everything is moving around so how do you even know enough things will always be at a fix location so you can do the calculation... and don't forget the other aspect being how to figure out whats what up in the sky

[@garychap8384]

In actual fact, stars are relatively static in relationship to each other, and can be treat as such. This being the case, they're highly dependable and predictable. Our own sun is similarly highly predictable and, as you know, it relates to time well. In fact, noon-sights are still among the most useful. So, the difficulty problem you mention exists pretty much only with the motions of the planets, which are harder to calculate tables for and, if you've ever followed them, do appear to reverse direction in the sky ... however, with the notable exception of Venus, they tend not to be reliably visible for navigation anyway. You certainly can (and I have) navigate off Jupiter, Saturn, Mars and Mercury... but it's tricky to locate them, they're too easily lost in haze and too often they're lost in sunset or sunrise glows ... but it's always fun, when the chance arises ; ) But wherever navigation is the primary aim, then the planets tend to be overlooked in favour of easier sightings such as the moon, sun and particular stars.

[@KarlBrau]

Excelent video!!!!! Now I understood how a sextant works. Thanks!!!

[@tabletclass]

Thank you! I so happy you enjoyed the video

[@tabletclass]

hello demmy- maybe sometime in the future I can put together a video on various coordinate systems. Thanks for the suggestion and feedback- keep learning!

[@jackiechan3691]

Erm ....please explain why You fix Ya spot by using a refracted horizon (so no straight line for an angle) then Ya use 3 stars n with triangulation... giving You a massive massive area of Ya position of equal altitude.. but then comment we live on a sphere? After jus using a tool to debunk the sphere!! What Ya been smoking? You can not get a right angle on a globe n no plumb lines hang down vertical perpendicular to horizontal wherever Ya are on earth .. forget pre supposing balls n molten iron cores, Ya jus destroyed Your entire presentation lol

[@tabletclass]

to actually plot a fix on a map/chart it rather involved; my goal was to give a general understanding of the process but in actual practice it takes training to develop ad transfer fix data onto a chart

[@steinrich56]

Brilliant little vid..! You explained it so well. Greetings, and many thanks, from Australia.

[@premchoudhary6998]

Could u explain y we prefer long by chron in morning and intercept in evening?

[@tabletclass]

Hello, QM rate is excellent! You will be on the bridge (pilot house) of the ship and see all the action; also you wont feel trapped inside the ship. As to the math I would get really good at working with decimals. Also you could learn how about angle measurement in terms of degrees-minutes-seconds. However the post important thing is to learn from those senior QM; listen to what they say. It will take a few deployments but you will master all the critical skills of nav at sea-good luck!

[@tabletclass]

Hi Bruce. Thanks for watching the video. Yes indeed I think you should study the process more and it's really a joy to be able to navigate by the stars. I wish you all the best and thanks once more for watching my video... John

[@hengirmen]

Thx for the video man i was just loking for it to help a friend but i learned the idea much faster than my own lessons

[@steadmanuhlich6734]

Nice illustration of the concept

[@gordonlwilliamson]

Extremely clear and well done exceptionally well done.

[@tabletclass]

navigating by the stars has evolved over 1000s of years; some of the ancient methods used basic tools just to hold study the latitude of the north start; this keep navigators on a one Lat. until they reached the coast; at which time they switched to piloting along the coast; the use of a sextant was introduced much later on as science and math evolved as well..

[@demmz80]

thank you so much sir,i'm hoping for that sooner,and i will learned farther more about it and hopefully it could quench my confusion regarding such things

[@tabletclass]

Celestial navigation was developed over 1000s of years. At first navigators used more basic methods before developing the sextant, book or clock. However these methods could not produce a fix so navigators never knew their exact position. It was not until the 1600s where accurate clocks where made to handle the rough movements for ships at sea that navigators could determine longitude - then the art of celestial navigation became more like what the video described.

[@MooonrakerCom]

If i am on a vessel in the middle of nowhere and all i have is accurate time, ie GMT and a sextant with pencil and paper,,,with nothing else at all in the way of almanacs and tables etc. Is there any information i can glean from the equipment at hand and how do i get it.

[@BobbieGWhiz]

A "Noon Sight" of the sun can give you a reasonable longitude. But you need to know the sun's declination (latitude) to figure out your latitude. If you happen to be navigating on an equinox then you know the declination is zero, or on a solstice the declination is +/- 23.4 degrees. Then you can figure your latitude. Or you can use Polaris, the North Star" to get a a pretty good idea of your latitude, as the measured angle from your sextant is more or less your latitude.

[@carl203crazy2]

The angle or altitude to polaris all night will give you a latitude, at least within a degree or so without corrections. The sun at apparent noon will give a longitude when the time of the event is converted to longitude. If you have extended knowledge of the suns declinations during the year you can also estimate a latitude at apparent noon from the altitude observed and adding/subtracting the angle from the declination estimate. Will be off for sure, but better than nothing at all.

[@sfzabawa]

Really helpful for a 10,000ft view of celestial navigation. Thanks!

[@leborico]

Best explanation ! very clear ! thank you so much for this !

[@Hurricanes2244]

Thanks for the info! I'll definitely start studying up, Thanks again!

[@CaptDenis]

Very good basic explanation. However, you would use a nautical almanac to find the present position of the celestial body for the date and time, new is issued each year. Then go to the HO 229 to get for lat and long variation or declination. Also, the Bowditch tables will quickly simplify the math for finding the angles. The mariner needs to understand that this is a very simplified explanation due to the exactness of time and high of eye, etc.

[@seanpatrick78]

Nice work! I've been studying cel. nav. for a couple of years now and as you say, it's a great way to learn about trigonometry, history and other subjects. Everything in the video is essentially correct. I heard you say you weren't sure about a couple of things, so here's some very minor corrections: The book you were referring to is actually the Nautical Almanac. The circles of possible positions are called "circles of equal altitude", but when plotting them on a chart, only a small...(cont.)

[@postholedigger8726]

Where does your radial distance from the GP come from? You take a sextant reading of 50 degrees and you know that you are 900 miles from the geographical position. How do you know this? david

[@tabletclass]

On your question about the use of a sextant at night. It's easy to use a sextant however it takes alot of skill to take accurate "shots" of the stars/moon at night especially when your ship is rolling and pitching ; I was never that good as it takes YEARS to develop the skills of master navigators.

[@JoseSanchez-wv4wk]

How did you get the 900 miles from. Than you

[@Sam-Alexander]

Explained how it works but not specifically how I can say where I am after doing all that. I can measure the degrees of both stars then look at the distances but how would I calculate the intersection aka FIX without drawing it ?

[@denisrogers4543]

Excellent insightful comment. The basic principle of celestial navigation is indeed simple. But; These circles of equal altitude can have, and frequently do have, circumferences that span different hemispheres and different oceans. For instance for a sextant altitude of 20 degrees, the radius of such a circle would be 4200 nautical miles, (90 minus sextant altitude x 60) and the circumference could pass through different hemispheres, continents and oceans. The problem -- and the math -- comes in when we attempt to plot those circles of equal altitude on our chart. The method commonly used called the "Intercept Method" was devised in 1875 by a French admiral called Marc St. Hilaire. By selecting a reference position on our chart and computing a sextant altitude from this position for the same time and the same body as for our observed altitude, we can compare these two altitudes and thus have a reference position on our chart from which to plot a line of position. It is in this computing of a reference position on our chart that the spherical trigonometry comes in.

[@strannick2212]

Sir, Just for interest sake, in what navy were you a navigation officer?

[@kraycrunr]

McHales

[@bobschmal389]

Great video, really clear, thanks for sharing

[@arturocubria9398]

First time I watch a video about navigation that I actually understand. Thanks

[@TheSmkngun]

Beautifully explained.

[@bhsfixed]

this is a stellar video

[@islamicknowledgecenter]

What is the name of Application in back ground?

[@gerardhand1954]

Many thanks, you have inspired me to delve further.

[@BRYKS22]

When I did bridge watch on the USS Anchorage I used to always watch the quartermaster do their navigation. I picked the wrong rate...was much more interested in the Navigation part. Been cruising sailboats for a bit now wishing I had a sextant for backup.

[@Macialao]

With star B you have two positions available if we consider full two cricles. Unless the distances are equal.

[@petersushkin]

Hi! Listen, I am from Ukraine, and my native language is Russian. I just wanted to thank you and tell that I couldn’t find more simple and obvious explanation for this topic on my native language! You are awesome, thanks again mate! :)

[@khairilimam265]

How did you define the 900 mi distance?

[@tabletclass]

Hi Eric, Yes indeed you are correct; thanks for watching the video and it's great getting feedback from people the understand the skill involved to celestial navigate

[@flattenthecurve8623]

Excellent Flat Earth Proof. As a surveyor, I can also verify that every survey of every piece of property on earth is measured using horizontal distances.