by antonio glez
Tags: clock, longitude, mathematical, obtain
 P: 39 archeoastronomist are bufled at polinesian finding out longitude without a clock here the concept i just found out how to prove: you have a dial with two geared counterotating needles you move by hand every rotation of the sun around you you rotate a needle ten times with which the other needle will rotate another ten times in opposite sense a question i think easy is how many times will cross each needle the sun? well, like one follows the sun and the other goes against it one will count one more and the other one less that is 9 and 11 how many would they count along 10 days? 90 and 110 and how many will they count in those ten days if besides you give a revolution to earth(warning tricky question) well my minds so weak i have to simplify i know in greenwhich they count 110 and 90 but i cant make in my mind the simultaneous rotation around the globe so i make first the ten days stopped and ill move in a second around the globe in the end and check the count now my weak mind can see that in greenwhich i count 110 and 90 for each needle crossing the sun, now i make a light fast trip around the globe: so if both needles are at 12 and i make a light fast revolution following the sun going east the sun will move with respect to BOTH needles west but for one needle going west counts as POSITIVE while for the other going west counts as NEGATIVE, for theyre counterotating so ill have to add one and substract one to each other to whatever count so if i count 110 and 90 in greenwhich travelling around the globe ill count one more and one less of each, 111 and 89 or 109 and 91 depending the sense i travel, which will allow me to know longitude i think theres an easier demonstration: in greenwhich one needel will move with speed x with respect to the sun clockwise and the other with speed y counterclockwise with respect to the sun so as soon as you change longitude speeds will be x+z and y-z for the added velocity of the sun counts as clockwise in x and counterclockwise in y
Mentor
P: 12,037
 a question i think easy is how many times will cross each needle the sun?
Sure, but where is the point in turning those needles?
The sun does not rotate around you. And you do not count rotations of earth with that device, you count "days" as seen by your (probably changing) longitude.

 so if i count 110 and 90 in greenwhich travelling around the globe ill count one more and one less of each, 111 and 89 or 109 and 91 depending the sense i travel, which will allow me to know longitude
No, you'll see 11 or 9 days (depending on the direction, while Greenwich sees 10), and have [120 and 100] or [100 and 80] crossings.

Unless you use a clock to power those needles to rotate 10 times in 24 hours. But then you don't need the needles any more, as you have a clock.
 P: 3,093 Are you talking about the antekythera device? http://en.wikipedia.org/wiki/Antikythera_mechanism
 P: 39 Could this be a mathematical way to obtain longitude without clock? Please help maybe the antichitera did this who knows the idea is based in this concept, basically you have one needle which points to a VIRTUAL stellar body that rises east and sets west and the other needle aims to a VIRTUAL stellar body which rises west and sets east then as phileas phog depending of going west or east youll count one more of one virtual star and one less of the other virtual star, and viceversa if you had gone opposite sense: http://upload.wikimedia.org/wikipedi..._Denoument.jpg edit: if you have a handclock with counterotating needles and you spin the whole clock youll count an extra turn from an outside reference in one needle and lack one turn in the other needle, and if you turn the clock the other sense viceversa
P: 39
 Quote by mfb No, you'll see 11 or 9 days (depending on the direction, while Greenwich sees 10), and have [120 and 100] or [100 and 80] crossings.
well even in the worse case that shows my idea to work if not as well as i wish just with certain aproximation:

if you go one sense you get a ratio for crossings of 120/100 while the other sense 100/80, while in greenwhich you always get a ratio 11/9=12.222...

so though not with high precision, in the worse of cases, checking the ratio of crossings you could find out longitude, though i belive with this method if works as i think you can get high precision

if you go around the globe in one sense you get 120/100=1.2

the other sense 100/80=1.25

so if you had a ratio of 1.2125 you travelled 180º(and this neglecting the verne effect)
 P: 825 You cannot get an absolute longitude with your device, which should be clear due to the elemental symmetry of the problem, so you could only measure deviations when you move from a known longitude to another longitude like from Greenwich to somewhere else, but even that doesn't work. You will always need a clock. You see the sun moving because you are in a rotating reference frame. If you move on the surface of the earth changing the rotation speed of your reference frame the sun simply moves slower or faster. The position of your cogwheels is the result of geometry, and will look the same if the sun has moved by the same angle with respect to you, regardless of the time it took to do so. Maybe the advantage of that Polynesian device is that you just need high precision of your clock and not high accuracy, but I doubt that Polynesians had clocks of the necessary precision.
 Sci Advisor Thanks PF Gold P: 12,253 Whatever methods the Polynesians used for their navigation, we have no idea of how reliable they were. What percent of the journeys actually took them where they wanted to go? Also, they were probably as ingenious as we are (probably more so, out of necessity) so they would have made a virtue of necessity and, if they actually made landfall, they got on with life where they had arrived.
 Mentor P: 12,037 @antonio glez: Your concept always needs a clock, even if it turns 10 times per day instead of 2 times (like a conventional 12h-clock). If you check your arguments carefully, you already assume that those needles are a clock.
 Sci Advisor Thanks PF Gold P: 12,253 There were alternative ideas for navigation which involved observing the Moon and the Jovian Moons to establish a 'universal time' without carrying a clock with you. They weren't a total failure either and could probably be better nowadays with decent telescopes.
Mentor
P: 12,037
 Quote by sophiecentaur They weren't a total failure either and could probably be better nowadays with decent telescopes.
Sure, you can measure those moons to get the current time with a precision of a second with a good telescope today. But if you can use modern technology, wouldn't it be easier to use a GPS receiver ? This gives your location with an uncertainy of a few meters (and time with nanosecond precision, if you like).
 Sci Advisor Thanks PF Gold P: 12,253 I can't see the North Koreans being able to blow the moons of Jupiter out of the sky, though. (Or an extremist US government holding us all to ransom, either).
 P: 39 the big problem for me is that i cant solve this problem for im dislexic so its very difficult for me to distinguish clockwise from counterclockwise if in greenwhich its alway 90 and 110 crossings during ten days and as if someone pointed travelling around the globe would be 120 and 100 or 100 and 80 that backs up my idea as working for it not working you should get 121 and 99 for 121/99=110/90 the idea is this concept adding it a counterotaing needle http://www.youtube.com/watch?v=sWhYS4hcDic edit: by the way theres missinformation on this subject, the usefull solution to the longitude problem wasnt using a mechanical clock for they acumulate error and voyages lasted maybe years the solution was using the angle between sun and and moon as a 28 day universal clock
Mentor
P: 12,037
 Quote by sophiecentaur I can't see the North Koreans being able to blow the moons of Jupiter out of the sky, though. (Or an extremist US government holding us all to ransom, either).
Well, use a modern clock then. If the US government (or North Korea) has and uses enough bombs to break all clocks on earth (including wrist watches), latitute estimation is probably not your most urgent problem.

 Quote by antonio glez if in greenwhich its alway 90 and 110 crossings during ten days and as if someone pointed travelling around the globe would be 120 and 100 or 100 and 80 that backs up my idea as working
Yes, if you have a clock. Or a local man telling you the longitude so you can calculate the expected number of crossings for that longitude.
 P: 3,093 There is a way to use a ship's sextant to compute the longitude but using a clock was way simpler: http://en.wikipedia.org/wiki/Sextant with some details of how it was done here: http://en.wikipedia.org/wiki/Longitude in contrast the polynesians used information from the stars and waves to navigate to known islands having discovered them by chance: http://en.wikipedia.org/wiki/Polynesian_navigation
 P: 39 thanks a lot with your help i figured out where i went wrong: basically if one virtual star to which a needle points to half its speed as you change longitude the other halfs it as well with which doesnt work but imagine you use a mechanical clock with counterotating needles: the clock has such an speed that during a day one needle crosses the sun 9 times and the other 11 if the clock during 10 days has a delay of 24 hours, huge delay, needles will cross the sun 90-1 and 110-1 times, expecting in greenwhich 90 and 110 crossings while after a revolution to earth it would be expected 89 and 111 so 110/90=1.22222:expectted ratio of crossing in greenwhich 109/89=1.22471:ratio of crossings in greenwhich with a 24 hour mistake in clocks during 10 days 111/89=1.24719:expected ratio of crossings after a revolution to earth with no error in the clock so 1.22222 is a 0º as 1.24719 is at 360 so 1.24719-1.22222=0.02497 1.22471-1.22222=0.00249 so 0.02497 variation of crossings is at 360º variation of longitude as 0.00249 variation of croosing is at the error of estimated longitude in greenwhich with a 24 hour error in the clock along ten days 9.971% with this system with a 24 hour error in the clock that traditionally would lead to a 360º error in longitude you just get 0.09971*360=35.89907º so with the traditional system a 24 hour error implies a 360 º error in longitude while with my system implies a 35º error
 Mentor P: 12,037 The traditional way would be to compare the clock (keeping Greenwich time) to the position of the sun or stars (giving access to a local time). Precision is just limited by the precision of the clock and the observations of the sun. With a wrist watch, the shadow of a roof and some stones to mark positions, it is possible to get a precision of <5 minutes. This corresponds to ~1° or about twice the diameter of the sun. This gives a maximal deviation of ~100km. With better devices, you can reduce the uncertainty a lot.
 P: 39 i recall reading dont rememeber where that the captains of the royal navy had orders to light an explosive charge in the navigation instruments case the ship was captured as i see it, if im right in my last point, with this opposite needle clock method you could diminish the expected error, 10 times, in the traditional method of comparing local and greenwhich time, something similar to magnify precision of the sextant with a nonius so if the moon is actually a 28 day universal clock its precision can be magnified ten times with this method with which it becomes a 2.8 day clock for the effects so i think the polinesian could have figured this out and use the moon-sun angle dial to power clocks with opposite sense needles and by keeping count of time wit respect to the sun or moon obtain longitude quite precisely with a very basic mechanical device
 Mentor P: 12,037 There is no expected error in the traditional method with a clock. Your method does not represent the traditional method, and would lead to a large error not present there.

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