https://wiki.tfes.org/index.php?title=Special:NewPages&feed=atom&hideredirs=1&limit=50&offset=&namespace=0&username=&tagfilter=&size-mode=max&size=0The Flat Earth Wiki - New pages [en-gb]2020-06-03T21:11:21ZFrom The Flat Earth WikiMediaWiki 1.33.1https://wiki.tfes.org/Sea_Travel_in_the_SouthSea Travel in the South2020-05-21T17:42:34Z<p>Tom Bishop: </p>
<hr />
<div>It appears that sea navigation in the South has historically been a difficult endeavor. While ship logs from the southern seas are difficult to find online, prior investigation into this subject has produced information of interest.<br />
<br />
==Zetetic Cosmogony==<br />
<br />
On [https://archive.org/details/ZeteticCosmogony/page/n43 p.30] of ''Zetetic Cosmogony'' by Thomas Winship we read:<br />
<br />
{{cite|Sir Robert Ball, in his Story of the Heavens,” page 163, informs the reader that; <br />
<br />
:"The dimensions of the earth are known with a high degree of accuracy"<br />
<br />
This writer is recognised as an able exponent of globular hypotheses, and it is generally conceded that what he says may be regarded as correct. Let us now enquire with what high degree of accuracy the dimensions of the earth are known. If the earth be the globe it is generally said to be, it is evident that the further we go south from the equator, the smaller will the circles be, and no circle south of the equator could be equal to that at the equator. <br />
<br />
The SS Nithsdale , of Glasgow, Captain Hadden, sailed from Hamelin Bay, in Western Australia, on 8th January, 1898, arriving at Port Natal on 1st February, 1898, having steamed 4,519 nautical miles. Her log, of which the chief officer, Mr. Boyle (also a passed Master), kindly gave me a copy, shows that she did not make quite a rhomb line track.<br />
<br />
Hamelin Bay is in latitude 34° south and longitude 115° 5' east. Port Natal is situate in latitude 29 0 53' south and 31° 4' east longitude. The difference of latitude being so small, we shall not get far out if we take the middle latitude, viz,: 32° south. The difference of longitude is 84° 1' or 4.28 of the complete circle of 360° round the world. Something must be added to the ship's log so as to bring the distance up to the rhomb line track, say 100 miles; therefore, to find the distance round the world at 32° south it is only necessary to solve the following problem: <br />
<br />
:As 84° 1' : 360° : : 4,619 nautical or 5,390 statute miles, <br />
:&#58; X. Answer &#61; 23,000 miles, nearly. <br />
<br />
This is several thousand miles in excess of what the distance would or could be on a globe. And further south on a globe, the distance would be less.}}<br />
<br />
{{cite|Lieutenant Wilkes says that in less than 18 hours he was 20 miles to the east of his reckoning, in latitude 54 0 20' South.}}<br />
<br />
===H.M.S. Challenger===<br />
<br />
{{cite|In the southern hemisphere, navigators to India have often fancied themselves east of the Cape when still west, and have been driven ashore on the African coast, which, according to their reckoning, lay behind them. This misfortune happened to a fine frigate, the Challenger, in 1845. How came Her Majesty’s Ship Conqueror, to be lost? How have so many other noble vessels, perfectly sound, perfectly manned, perfectly navigated, been wrecked in calm weather, not only in dark night, or in a fog, but in broad daylight and sunshine from being out of reckoning?}}<br />
<br />
{{cite|In the “Cruise of H.M.S. Challenger" by W. J, J. Spry, the distance made good from the Cape of Good Hope to Melbourne is stated to be 7,637 miles. The Cape is in latitude 34° 21' south and Melbourne in latitude 37° south, the longitude of the Cape being 18° 30' east and Melbourne 145° east. The middle latitude is 35 1/2°. Difference of longitude 126 1/2°, which makes the distance round the world at that latitude (35 1/2°) to be over 25,000 statute miles and as great as the equator is said to be. Thus we see on reliable evidence that the further we go south the greater is the distance round the world. This latter distance is many thousand miles more than the purely theoretical measurement of the world at that latitude south. From the same work, we find the distance from Sydney to Wellington to be 1,432 miles. The middle latitude is 374°, and the difference of longitude 23° 36', which gives as the distance round the world at latitude 37 1/2° south, 25,500 satute miles! This distance is again greater than the greatest distance round the "globe" is said to be and many thousands of miles greater than could be the case on a globe. Thus, on purely practical data, apart from any theory, the world is proved to ''diverge'' as the south is approached and not to ''converge'', as it would do on a globe.}}<br />
<br />
===South Sea Voyages===<br />
<br />
{{cite|In "South Sea Voyages:" by Sir James C. Ross, Vol. 1, page 96 states: <br />
<br />
:"We found ourselves every day from 12 to 18 miles by observation in ''advance'' of our reckoning"<br />
<br />
Page 27: <br />
<br />
:"By our observations at noon we found ourselves 58 miles to the eastward of our reckoning in two days"}}<br />
<br />
===Voyages Towards the South Pole===<br />
<br />
{{cite|"Voyage towards the South Pole," by Captain Jas, Weddell, states: <br />
<br />
:"Feb. 11th. at noon, in lat. 65° 53' South, our chronometers gave 44 miles more ''Westing'' than the log in three days"}}<br />
<br />
===Anston's Voyage Round The World===<br />
<br />
{{cite|In "Anson’s Voyage round the World," by R. Walter, page 76, the following statement is made: <br />
<br />
:"It was indeed, most wonderful that the currents should have driven us to the eastward with such strength; for the whole squadron esteemed themselves upwards of 10 degrees more westerly than this land (Straits of Magellan); so that in running down, by our account, about 19 degrees of longitude, we had not really advanced half that distance"}}<br />
<br />
==Alexander Gleason==<br />
<br />
On [https://archive.org/details/AlexGleasonIsTheBibleFromHeaven/page/n396 pg. 396] of Alexander Gleason's book ''Is the Bible from Heaven? Is the Earth a Globe?'', its author relays the following:<br />
<br />
{{cite|We are now ready to offer our final evidence for the consideration of all parties. <br />
<br />
Following is the coast tracing of the west coast of South Africa, also eastern coast of South America, each bearing its relative position to each other in both latitude and longitude, and relative' positions on the Equator. We style the illustration fig. 42. We will further state that this tracing is from a small-sized globe map, which we preferred for convenience, but it will be found to agree very closely, so far as relative coast-lines, latitude, longitude and distances are concerned, with the best maps known.}}<br />
<br />
[[File:Gleason Fig42.png|700px]]<br />
<br />
{{cite|We have made a scale of degrees of longitude from Washington east to the meridian of 105° on the continent of Africa. Now, if we take the extreme distance on the Equator between Africa and South America, we find it to be 56° of longitude, and these equal 3,360 miles from A to A on the scale, but if we allow the globe theorists all they claim for curvature, it would be about sixty miles more, and thus it stands on the scale, 3,420 miles. Now, if we measure the distance between Cape of Good Hope on the scale and Cape Horn, we will find the two distances to very closely agree. Now, if one inch represents one thousand miles on the Equator, on water, it certainly represents one thousand miles in every other place on the same globe scale. We next take the distance from Cape of Good Hope to Buenos Ayres, which is 60° or 3,600 miles, according to the same scale or any other globe scale in the land made by “scientific and educated men.” So much for authentic theory, and we will next see what the authentic, practical, and experienced navigator says in regard to these distances and the ''very shortest time'' ever made between these places by the best class of steamships, built by the best builders that Europe affords, and at the expense of the East India Government. <br />
<br />
In order to procure these facts it has taken considerable time, and no expense has deterred us from securing facts which is now a great relief and pleasure to give to the world. We trust the reader will bear patiently with us while we give the demonstrated facts in the case. <br />
<br />
About the middle of November, 1891, I put the following notice in the New York World: <br />
<br />
::''Wanted'' — The address of an unlimited number of navigators or sea-faring persons who have made the voyage or voyages between the following places, and can give the distances in knots, and approximate time in days, of making the several voyages: No. 1 —Cape Town, Africa, to Buenos Ayres or Montevideo. No. 2—Cape Town, Africa, to Cape Horn, etc.; others of which we will not take time to mention, of which we have time, measurements, etc.<br />
<br />
From the most experienced, or he who furnished the best references, we selected the information; no one knowing for what purpose we wanted the desired knowledge, or anything in regard to our views. The following became my informant in regard to the desired information: <br />
<br />
53 Woodward Ave., South Norwalk, Ct.<br />
November 23, 1891.<br />
<br />
::''Alex. Gleason, Esq.:'' <br />
<br />
::Dear Sir — Seeing the enclosed [which he cut from the paper advertisement ] I wish to say that I can give you the required information, having served in the Cape Horn, west coast of South America, and Australian trade for several years, as second officer of steamer Lochinvar, Abbey Town and Palgrave. Awaiting further information concerning your terms, believe me <br />
<br />
::Respectfully yours, <br />
::Charles B, Browne. <br />
<br />
[reply to my second letter.] <br />
<br />
::Dear Sir — In reply to your letter received today, I wish to state to you how far I can meet your requirements. First, to satisfy you that ''I am what l claim to be,'' and qualified to give you all the information required, the number of my certificate is 014358, licensed on June 4, 1884, in London, England, by the Lords of Privy Council for trade. Second, certificates of discharge: No. 1, four mast - steamship Palgrave; No. 2, steamship Compta; No. 3, ship Huron, put back disabled; No. 4, transferred to Abbey Town, bound to South America and N. S. W., and Chili, South America. Served on this voyage from October 6, 1886 to October 7, 1887. This is the date of my last official discharge. The above certificates are now in my possession. <br />
<br />
::From charts used during my service in the ships named, I can give you all the information required; but cannot from ship’s log book....At the same time, I can and will gladly, give you all the information you want from my charts.... <br />
<br />
::Thanking you for enclosed, believe me, <br />
<br />
::Yours respectfully, <br />
::Charles B. Browne. <br />
<br />
::P. S. — I have also letters for service and ability, signed by Captains Dunn, Tullis, Thomas and Andrus, and Chief Officer Adams. C. B. B. <br />
<br />
[Third Letter, December 10 1891]<br />
<br />
::''Alex. Gleason, Esq.:'' <br />
<br />
::Dear Sir....The courses and distances are all taken from charts used in steamships Lochinvar, Abbey Town, Compta and Palgrave. I would state that the distances are in all cases worked to geographical or nautical miles, sixty of which are equal to sixty-nine and one-fourth English miles. You are, no doubt, aware that there is 6070 feet to the nautical mile; this is often the cause of dispute with regard to the distance from port to port, many people not being aware of the difference between a nautical and statute mile. Distances, course and time are as follows: <br />
<br />
::First — Cape Town to B. Ayres ; course, west by 6° south; distance, 4560 miles. ''Best time'' record known, steamship Lochinvar, Capt. Shelly* 13 days, 13 hours, 45 minutes. <br />
<br />
::Second — Cape Town to Cape Horn; course, west by 24° south; distance. 5700 miles. ''Best time'' on record, Abbey Town, Capt. Tullis, 13 days and 23 hours. <br />
<br />
::Yours respectfully, <br />
::Charles B. Browne. <br />
<br />
It would be useless to weary the patient reader with all the details of voyages, distance and time that this navigator has given to Aukland, N. Z., Sydney, Australia, etc. But it is well worth while to now consider the above carefully. <br />
<br />
''First'' — If we take any globe map of the world and measure the distance from the Cape of Good Hope to Buenos Ayres, we will find it from 180 to 200 miles further than it is from Cape of Good Hope to Cape Horn. Bear this in mind. The navigator says that from Cape Good Hope to Cape Horn is 5700 miles, and he gives the course. This would throw Cape of Good Hope, South Africa, back to B and South America back to C, and make that distance, which theory shows to be the least by about 200 miles, the greatest by 1,140 miles. <br />
<br />
''Second'' — We will notice that at A A is represented a pin head on the Equator and on the coast lines of the two continents; this would hold the two coast lines in position on the Equator, which is an undisputed point. But if we take these continents and open their southern points to B. C. it will give the degrees of longitude that divergency required on the principle of the earth a plane, and Capt. Browne would be all right with his Mercator charts. But what has become of our New York friend’s requirements in regard to the degrees of longitude? This we will see further on as we examine the ship’s time record. <br />
<br />
To the above fact I wrote Captain Browne, calling his attention to this discrepancy of distance, and after waiting until a reply was past due, I wrote a second letter, stating that perhaps there was some mistake in the figures, thinking they had got them transposed by some means in giving the numerous calculations. I stated to him that I had measured the distance on several globe maps with a fine steel line and they all told the same story. Further, I did not wish to publish a mistake of this kind, if such it was. To this last, and the first, I received the following pert reply: <br />
<br />
::February 14, 1892. <br />
::''Alex. Gleason, Esq.:'' <br />
<br />
::Dear Sir — I have received both your letters. But having been away from home in my steamer, and when at home, very busy, I have been unable to attend to your request before this. In reply, would say that I don’t pretend to know anything about working nautical questions with a tape-line. Furthermore, am very much surprised to learn from you that Cape Horn is 200 miles nearer Cape Town than Buenos Ayres. I don’t take nearest points when working these questions, but degree of latitude and longitude. And if the following latitudes and longitudes are wrong, then the Admirality Charts in my possession are wrong: <br />
<br />
::Lat. of Cape Town..34 0 24' S. Long, of Cape Town..18°32' E. <br />
::Lat. of B. Ayres...34 0 30' S. Long, of B. Ayres...58°00' W. <br />
::Lat. of Cape Horn..55 0 59' S. Long, of Cape Horn..67°12' W. <br />
<br />
::If you can make Buenos Ayres 200 miles nearer Cape Town from these figures, there is no need for me to work any questions for you. Please take notice that the questions worked for you were done so by Mercator’s Sailing Chart, which is our usual way of finding course and distance from point to point. Allow me to say that Cape Horn is nothing more than a rock, so whatever point you take don’t amount to a ''row of pins.'' <br />
<br />
::Yours respectfully, <br />
::Charles B. Browne. <br />
<br />
It was my interrogatory letter that has called forth these statements from Captain Browne, which to his mind did not amount to a “row of pins,” and perhaps had he previously known my purpose in calling forth these responses, the value of what I would have gotten from that source would have been less than the estimate that he has put upon it. Nevertheless, Captain Browne is all right with his charts, his degrees, his latitudes and longitudes, also the time record’s which we next notice. <br />
<br />
Before going too far with the considerations of the relative or comparative time, mentioned by our challenger in the forepart of this article, under the indicator C, it will be necessary to notice the very best time ever made by the best crafts that float the northern seas, and perhaps the medium, also. We have entered no confederacy with steamship lines, but have procured some catalogues from which we have clipped two leaves for the benefit and interest of those who wish to be informed on these matters. First, we give one abstract of log, '‘Norddeutscher,” Lloyd’s Steamship Line, Captain H. Hellmers, from Southampton to New York.}} <br />
<br />
[[File:Gleason-Log.png|600px]]<br />
<br />
{{cite|We give the above log, that the readers may see and be able to judge, in regard to variations of the vessel’s course from point to point or port to port. <br />
<br />
The following is a copy ''verbatim'' from the Hamburg-American Packet Company's catalogue, J. W. Klauck, agent, 70 Exchange street, Buffalo, N. Y.: <br />
<br />
::"Speed —These steamers have at once stepped to the front rank among ocean greyhounds, and must be counted among the fastest ships afloat. The best time accomplished was six days and twelve hours from New York to Southampton, being the fastest trip ever made between these two ports. This is equal to a trip of five days and twenty-one hours from New York to Queenstown, Southampton being about 300 miles east from Queenstown. The time by rail from Southampton to London is; two hours. The landing arrangements at Southampton are considered superior to those of any port in England, the trains, starting from the docks and the Hamburg-American Packet Company’s special trains awaiting the passengers there. During the past three years steamers have maintained a regular fast weekly express service between New York, Southampton and Hamburg, taking passengers to ''London within seven days, and to Hamburg within eight days,'' while the actual average ocean passage is reduced to a little more than six days. This line, according to the annual report of the United States Superintendent of Foreign Mails, takes the first place over all others in the conveyance of the mails between New York and London. Their great regularity is indicated by the fact that almost all trips were made within a margin of a few hours. The arrival at New York, Southampton or Hamburg can therefore be easily forecast."<br />
<br />
Passengers leaving New York on Thursday are landed in Southampton on the following Thursday, reaching London on the same day, thus bringing them from New York to London in less than a week (it has been done in six days and 16 hours, a feat not equaled by any other line.) This shows the wonderful convenience which these steamers offer to the traveling public. <br />
<br />
The fastest runs were about twenty and three-fourths knots per hour, which is equal to 23 7/8 English miles, and exceed the speed of transcontinental trains. <br />
<br />
::TIME RECORDS<br />
::SPECIMEN RUNS — FROM NEW YORK <br />
<br />
::Furst Bismarck, June 18, ’91.........6d. 12h. 58m. <br />
::Columbia, Oct. 9, ’90................6d. 15h. 0m. <br />
::Normannia, Nov. 20, ’90..............6d. 17h. 03m. <br />
::Augusta-Victoria, Sept. 18, ’90......6d. 22h. 32m. <br />
<br />
::FROM SOUTHAMPTON. <br />
<br />
::Furst Bismarck, May 9, ’91...........6d. 14h. 15m. <br />
::Columbia, June 27, ’91...............6d. 15h. 58m. <br />
::Normannia, May 21, ’91...............6d. 16h. 45m. <br />
::Augusta-Victoria, Oct. 2, ’90........6d. 22h. 30m. <br />
<br />
We will consider first,the build of these South-sea steamers as compared with those of our latest pattern. We are informed by the agent, Mr. J. W. Klauck, and others tell us that these South-sea steamers are all built by the same class of builders, or same building company, on the Clyde in Europe. The steamship Abbey Town, we were informed by Capt. Browne, was built by the East India government for this special southern trade, and it is this that gives the best time on record in the southern seas. Between New York and Hamburg, and Cape Town and Cape Horn, there is but about 1° 30' difference, or say 100 miles, according to the globe measurement; that is, if we measure the difference from Hamburg to New York on a globe map with dividers, then place them on Cape Town and they will only lack about one degree and a half of reaching Cape Horn. Now, so far as danger or contingencies are concerned in making the voyages in a given equal time, the one preferred to the other, the South Sea has the advantage. This is shown on the navigator’s charts, both in currents, rocks, shoals, islands, etc. This can be seen on the ordinary Mercator map of the world. <br />
<br />
The question now resolves itself to this: On the globe principle, Cape Town to Cape Horn 3,600 miles; best time ''ever made'' 10 3/4 miles per hour, 335 hours &#61; 3,601 miles. If the above be true, the Cape Horn steamer was ''six days'' making up that existing difference of one hundred miles in distance, under the most favorable circumstances, and this the ''very best time ever known!'' <br />
<br />
We will now look at the matter from another standpoint. We will allow the northern navigators all they claim for distance and time. We now ask that the southern navigators and nautical inspectors be allowed their 1 moderate'claims for both time and distance, namely: Cape Town to Cape Horn, 5,700 miles. Time: 13 days 23 hours &#61; 335 hours at 17 miles per hour, 5,695 miles. Is it not as possible for the South Sea vessel to make seventeen or eighteen miles per hour in an extreme case, as it is for the northern to make twenty or twenty-one miles per hour ? We leave this for you to answer. <br />
<br />
Inasmuch as we believe that we have, not only in this article, but previous ones, given sufficient evidence to more than overbalance every reasonable objection to our position, we will only ask of him who is still skeptical, the same that has been asked of me. “Just stop and consider it, I say, for a short time and see if all these matters do not harmonize perfectly with philosophical and astronomical, and also with the experience of men who navigate the seas, especially those south of the Equator.”}}<br />
<br />
==See Also==<br />
<br />
:*Diverging lines of longitude in the South are also discussed in the chapter [https://www.sacred-texts.com/earth/za/za42.htm "Degrees of Longitude" in ''Earth Not a Globe'']<br />
<br />
[[Category:Form and Magnitude]] [[Category:Maps and Models]]</div>Tom Bishophttps://wiki.tfes.org/Issues_in_Flight_AnalysisIssues in Flight Analysis2020-05-01T22:36:59Z<p>Tom Bishop: </p>
<hr />
<div>'''Issues in Flight Analysis''' refers to the issues in using flight information as a scientific tool for determining the layout or dimensions of the Earth. It is often asked whether it is possible to use flights to determine geographical information about the Flat Earth models under investigation (Ie. The [[Bi-Polar Model]] or other possible models).<br />
<br />
There are many factors to consider other than geography, such as jet streams and trade winds. Non-stop flights are not necessarily always non-stop for various reasons. It is found that planes can and do travel at supersonic speeds (groundspeed) on a regular basis. Investigators have also found that listed flight times are purposely skewed by large amounts. The wind anomalies and conditions may exist differently over different parts of the Earth. Based on these complications, it is difficult to utilize the flights in any certain way in investigation of the Flat Earth geographic models in discussion. <br />
<br />
==Listed Flight Times Skewed==<br />
<br />
===Why Flights Take Longer===<br />
<br />
http://www.travelandleisure.com/travel-tips/airlines-airports/why-flights-take-longer ([https://web.archive.org/web/20200501222318/https://www.travelandleisure.com/airlines-airports/why-flights-take-longer Archive])<br />
<br />
{{cite|Did you know that a flight from New York City to Houston, Texas is over an hour longer today than if you took the same flight in 1973? Now it takes about three hours and 50 minutes, but 43 years ago it would have taken 2 hours and 37 minutes. What gives?<br />
<br />
~<br />
<br />
Surprisingly, flight time is calculated from when the aircraft releases the parking brake (on push back) to when it sets the brake on arrival to the gate,” commercial pilot Chris Cooke told Travel + Leisure. “All that waiting in line during taxi and takeoff counts toward flight time.<br />
<br />
Not surprisingly, saving money is another reason flights take longer today. “Airlines are able to save millions per year by flying slower," reveals a video from Business Insider.}}<br />
<br />
===Are You Being Told the Truth about Flight Times?===<br />
<br />
A study which says airlines are skewing flight times:<br />
<br />
https://www.telegraph.co.uk/travel/travel-truths/Are-airlines-exaggerating-flight-times-so-theyre-never-late/ ([https://web.archive.org/web/20200428145735/https://www.telegraph.co.uk/travel/travel-truths/Are-airlines-exaggerating-flight-times-so-theyre-never-late/ Archive])<br />
<br />
''Are you being told the truth about flight times?''<br />
<br />
{{cite|Passenger jets have never been more advanced. With Boeing’s 787 Dreamliner, introduced in 2011, leading the charge, and new models like the 737 MAX and the Airbus A320neo following in its wake, the aircraft on which we travel are safer, smoother, quieter and more fuel efficient than ever.<br />
<br />
They also appear perfectly capable of flying faster than their predecessors. Just last month the low-cost carrier Norwegian issued a celebratory press release after one of its 787 Dreamliners whizzed from John F. Kennedy International Airport in New York to London Gatwick in five hours and 13 minutes, setting a new transatlantic record for a subsonic plane. That’s three minutes quicker than the previous best time set by British Airways in January 2015.<br />
<br />
So why, record-breaking feats notwithstanding, are airlines claiming it takes longer and longer to fly from A to B?<br />
<br />
That’s according to research by OAG, the aviation analyst, carried out for Telegraph Travel. '''It found that over the last couple of decades, despite new technology, scheduled flight times - ie. how long an airline estimates it will take to complete a journey - have actually increased by as much as 50 per cent.'''<br />
<br />
Looking at Europe’s busiest international route, for example - Heathrow to Dublin - it found that in 1996 the vast majority of airlines published a scheduled flight time of between 60 and 74 minutes. Fast forward 22 years and almost all claim the journey takes between 75 and 89 minutes, while a handful bank on 90 minutes or more.}}<br />
<br />
==Jetstreams Enable Routine Supersonic Flight (Groundspeed)==<br />
<br />
[https://www.wired.com/story/norwegian-air-transatlantic-speed-record/ Riding a Wild Wind, Transatlantic Jets Fly Faster Than Ever] ([https://web.archive.org/web/20180513163657/https://www.wired.com/story/norwegian-air-transatlantic-speed-record/ Archive])<br />
<br />
''A 200-mph jet stream has sent several passenger jets to nearly 800 mph and helped break a (subsonic) speed record.''<br />
<br />
{{cite|OK, about that "subsonic" bit. You might know that the speed of sound at an altitude of 30,000 to 40,000 feet is roughly 670 mph. But Norwegian’s planes didn't break the sound barrier. Those near-800-mph figures represent ground speed—how fast the aircraft is moving over land. Their air speed, which factors out the 200-mph wind boost, was closer to the 787's standard Mach 0.85. (The older Boeing 747 can cruise at Mach 0.86, but is less efficient than its younger stablemate.) When talking supersonic, and breaking sound barriers, it's all about the speed of the air passing over the wings, which in this case was more like 570 mph.}}<br />
<br />
==Anomalous Winds over the Southern Oceans==<br />
<br />
Winds over the Southern Oceans are reputed to be of an anomalous nature, as compared to winds in the North.<br />
<br />
===Australian Antarctic Division===<br />
<br />
http://www.antarctica.gov.au/magazine/2001-2005/issue-4-spring-2002/feature2/what-is-the-southern-ocean ([https://web.archive.org/web/20200501222510/http://www.antarctica.gov.au/magazine/2001-2005/issue-4-spring-2002/feature2/what-is-the-southern-ocean Archive])<br />
<br />
{{cite|The Southern Ocean is notorious for having some of the strongest winds and largest waves on the planet.}}<br />
<br />
===BBC Earth===<br />
<br />
http://www.bbc.com/earth/story/20151009-where-is-the-windiest-place-on-earth ([https://web.archive.org/save/http://www.bbc.com/earth/story/20151009-where-is-the-windiest-place-on-earth Archive])<br />
<br />
{{cite|There are huge belts of wind caused by the uneven way the Sun heats the Earth's surface. 30° north and south of the equator, the trade winds blow steadily. At 40° lie the prevailing westerlies, and the polar easterlies begin at around 60°.<br />
<br />
Ask any round-the-world sailor and they will quickly tell you the stormiest seas, stirred by the strongest winds, are found in the Southern Ocean. These infamously rough latitudes are labelled the "roaring 40s", "furious 50s" and "screaming 60s".}}<br />
<br />
===Journal of Geophysical Research===<br />
<br />
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2003JD004179 ([https://web.archive.org/web/20200501222619/https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2003JD004179 Archive])<br />
<br />
{{cite|The Southern Ocean is a vital element in the global climate. Its circumpolar current plays a crucial role in the global transport of mass, heat, momentum, and climate signals from one ocean basin to another. Moreover, the Southern Ocean hosts the strongest surface winds of any open ocean area, fostering strong heat, moisture, and momentum exchanges between the ocean and atmosphere. However, the Southern Ocean is tremendously undersurveyed by traditional observation methods because of the remoteness of the area and rough environment, causing the largest data gap of global oceans.}}<br />
<br />
==Easterly and Westerly Wind Directions==<br />
<br />
===Prevailing Winds===<br />
<br />
[https://en.wikipedia.org/wiki/Trade_winds Maps of the Trade-winds] show that winds can travel in both Easterly and Westerly directions in the Northern and Southern Hemispheres:<br />
<br />
[[File:Map_prevailing_winds_on_earth.png|670px]]<br />
<br />
===Ocean Currents===<br />
<br />
The winds also cause the direction of the ocean gyes, which [https://books.google.com/books?id=bOg0EqqrDRgC&lpg=PA133&pg=PA153#v=onepage&q&f=false in turn show both Easterly and Westerly directions] in the Northern and Southern Hemispheres.<br />
<br />
[[File:Ocean Gyres.png|670px]]<br />
<br />
Note: The seen clockwise and counter-clockwise prevailing wind and ocean currents runs contradictory to the Coriolis Effect. See '''[[Coriolis Effect (Weather)]]'''<br />
<br />
==Non-Stop Flights==<br />
<br />
Reported issues with Non-Stop flights may suggest that the existing flights depend on a balance of physical phenomena.<br />
<br />
===Annoyed by a fuel stop on your direct flight?===<br />
<br />
https://www.cbc.ca/news/canada/north/airline-fuel-stops-divert-1.4495744 ([https://web.archive.org/web/20200501204953/https://www.cbc.ca/news/canada/north/airline-fuel-stops-divert-1.4495744 Archive])<br />
<br />
''Annoyed by a fuel stop on your direct flight? Why airlines can't always plan ahead''<br />
<br />
{{cite|Travel delays. We've all been there.<br />
<br />
But there's something about fuel stops that particularly irritates travellers. Why didn't the airline plan ahead? How could it not know the aircraft would need more fuel?<br />
<br />
In November Chad Hinchey was on a direct WestJet flight from Edmonton to Yellowknife when he says the pilot announced they were going to have to divert to Fort McMurray, Alta., because of bad weather.<br />
<br />
Passengers were told that the plane didn't have enough fuel to attempt a landing in Yellowknife and fly to an alternate airport if it had to.}}<br />
<br />
===Flights Stop for Fuel===<br />
<br />
[https://web.archive.org/web/20161026015807/http://www.wsj.com/articles/SB10001424052970203436904577152974098241982Nonstop Flights Stop for Fuel]<br />
<br />
By SUSAN CAREY And ANDY PASZTOR<br />
<br />
January 11, 2012<br />
<br />
{{cite|Dozens of Continental Airlines flights to the East Coast from Europe have been forced to make unexpected stops in Canada and elsewhere to take on fuel after running into unusually strong headwinds over the Atlantic Ocean.<br />
<br />
The stops, which have caused delays and inconvenience for thousands of passengers in recent weeks, are partly the result of a decision by United Continental Holdings Inc., the world's largest airline, to use smaller jets on a growing number of long, trans-Atlantic routes.}}<br />
<br />
===So-called nonstop flights now stop for fuel===<br />
<br />
[https://www.mainlinemedianews.com/mainlinetimes/news/air-travel-so-called-nonstop-flights-now-stop-for-fuel/article_353ddf8a-b55f-5b3b-a171-9f0fba573886.html Air travel: So-called nonstop flights now stop for fuel]<br />
<br />
{{cite|In winter, to lower the odds of getting snowed in by an ice storm, a good idea is to choose warm weather for your connection, even if it seems a slightly longer trip. In summer, fogs and thunderstorms can also wreak havoc with airline schedules. Obviously, buying your tickets far in advance, there is no way to avoid these situations. But if you’re buying your ticket at the last minute, check a source like the Weather Channel before nailing down your final arrangements.<br />
<br />
If the jet-setters of the 1960s had climbed aboard a plane designed 40 years before, they would have been getting into something with wooden wings. In some ways the world changed more rapidly and dramatically in your grandfather’s day than your own.<br />
<br />
Accept the reality that most of the stress in travel by plane is out of your control. As you will quickly see, you have much less control of things in general than you might like to believe.<br />
<br />
Be aware that so-called nonstop flights now stop for fuel. Flights to the East Coast from Europe are being forced to make dozens of totally unexpected stops in Canada and elsewhere to take on fuel after running into unusually strong head winds over the Atlantic Ocean. According to The Wall Street Journal and other sources, these stops, which have caused dramatic delays and inconvenience for thousands of passengers in recent weeks, are the results of a decision by United Continental, the world’s largest airline, to utilize a smaller jet on a growing number of long transatlantic routes.<br />
<br />
The strategy works when the winds are calm. It allows the airline to operate less expensive aircraft. And with fewer cabin-crew members to an array of European cities that would not generate enough traffic to justify larger planes. But according to Susan Carey and Andy Pasztor, by pushing its 757s to nearly the limit of their roughly 4,000-nautical-mile range, United is leaving little room for error, especially when stiff winds increase the amount of fuel the planes’ twin engines burn.}}</div>Tom Bishophttps://wiki.tfes.org/Lunar_Eclipse_due_to_Shadow_ObjectLunar Eclipse due to Shadow Object2020-04-09T16:50:44Z<p>Tom Bishop: Separating out the two different explanations for the Lunar Eclipse</p>
<hr />
<div>A '''Lunar Eclipse''' occurs about twice a year when a satellite of the sun passes between the sun and moon.<br />
<br />
This satellite is called the Shadow Object or Antimoon. Its orbital plane is tilted at an angle to the sun's orbital plane, making eclipses possible only when the three bodies (Sun, Object, and Moon) are aligned. Within a given year a maximum of three lunar eclipses can occur. Despite the fact that there are more solar than lunar eclipses each year, over time many more lunar eclipses are seen at any single location on earth than solar eclipses. This occurs because a lunar eclipse can be seen from the entire half of the earth beneath the moon at that time, while a solar eclipse is visible only along a narrow path on the earth's surface.<br />
<br />
Total lunar eclipses come in clusters. There can be two or three during a period of a year or a year and a half, followed by a lull of two or three years before another round begins. When you add partial eclipses there can be three in a calendar year and again, it's quite possible to have none at all.<br />
<br />
The shadow object is never seen in the sky because it orbits the sun on the ''day'' side of the earth, in the large vicinity where celestial bodies are invisible. As the sun's powerful vertical rays hit the atmosphere during the day they will scatter and blot out nearly every single star and celestial body in the daytime sky. We are never given a glimpse of the celestial bodies which appear near the sun during the day - they are completely washed out by the sun's light. In fact, when the daytime Moon gets too close to the sun's vicinity it will completely disappear from sight. Except for during the time of Solar Eclipse, the Moon is only seen during the day at a far opposite side of the sky from the sun.<br />
<br />
Dr. [[Samuel Birley Rowbotham]] has provided equations for finding the time, magnitude, and duration of a Lunar Eclipse at the end of [http://www.sacred-texts.com/earth/za/za29.htm Chapter 11] of [[Earth Not a Globe]].<br />
<br />
There is also a possibility that the Shadow Object is a ''known'' celestial body which orbits the sun, and which projects its shadow upon the moon; but more study would be needed to track the positions of Mercury, Venus and the sun's asteroid satellites and correlate them with the equations for the lunar eclipse before any conclusion could be drawn.<br />
<br />
==Celestial Bodies Not Visible==<br />
<br />
During the day the celestial bodies near the sun are invisible. An example of this is seen in the appearance of the Moon during the Solar Eclipse. The Moon seems to appear out of nowhere to intersect the Sun.<br />
<br />
[[File:Partial-solar-eclipse.gif]]<br />
<br />
Another example of the sky-colored moon is seen in the [https://www.timeanddate.com/eclipse/solar/2017-august-21 timeanddate.com Solar Eclipse simulations].<br />
<br />
==Ancient and Modern Astronomers==<br />
<br />
The reason the ancient societies such as the Greeks and Babylonians were able to predict the Lunar Eclipses was because the predictions are based on recurring charts and tables of past eclipses. Modern Astronomers still use the same pattern prediction methods. It had nothing to do with the shape of the earth or the actual geometry of the system. The Lunar Eclipse is a phenomenon which comes in patterns. By studying these patterns it is possible to predict when the next transit or eclipse will occur. The astronomer can use historic charts and tables with a few equations to predict the time, magnitude, and duration of a future eclipse.<br />
<br />
This does not apply only to the eclipse, either: All recurring phenomena such as the transits of planets, occultations of bodies, and precision of paths across the sky are predicable only because they are phenomena which come in patterns. Astronomers predict celestial events by studying the patterns and predicting when the next occurrence will occur.<br />
<br />
See: [[Astronomical Prediction Based on Patterns]]<br />
<br />
==Modern Eclipse Models==<br />
<br />
'''Q'''. But what about NASA's yearly lunar eclipse predictions? They must be based on a geometric model, and not simply cycles in the sky, surely?<br />
<br />
'''A'''. NASA freely admits that they use ancient cycle charts for their eclipse predictions. The Saros Cycle and those cobby old ancient methods which simply look at past patterns in the sky to predict the next one is precisely how &quot;modern theorists&quot; predict the lunar eclipse today.<br />
<br />
See: [[Astronomical_Prediction_Based_on_Patterns#The_Eclipses|Astronomical Prediction Based on Patterns - The Eclipses]]<br />
<br />
==Why the Lunar Eclipse is Red==<br />
<br />
One explanation is that the Lunar Eclipse is red because the light of the sun is shining through the body of the Shadow Object which passes between the Sun and Moon during a Lunar Eclipse. The red tint occurs because the Shadow Object is not sufficiently dense. The Sun's light is powerful enough to shine through the Shadow Object, just as a flashlight is powerful enough to shine through your hand when you put it right up against your palm.<br />
<br />
[[File:2007-03-03 - Lunar Eclipse small-43img.gif|350x]]<br />
<br />
=External links=<br />
*[http://books.google.com/books?id=GzkKAAAAIAAJ&amp;pg=PA#PPA74,M1 Zetetic Cosmogony chapter on the Lunar Eclipse]<br />
*[http://www.personalityresearch.org/metatheory/flatearth.html Why the Earth may really be flat]<br />
<br />
[[Category:Cosmos]]<br />
[[Category:Moon]]</div>Tom Bishophttps://wiki.tfes.org/Symplectic_IntegratorsSymplectic Integrators2020-03-06T18:12:28Z<p>Tom Bishop: /* Solar System Integrator Comparison */</p>
<hr />
<div>As result of issues with the [[Three Body Problem]] mathematicians have opted to create special algorithms for use in multi-body problems as a method of keeping the system stable. Usually associated with the Hamiltonian and KAM theories, '''Symplectic Integrators''' are special geometric integrators which preserve the geometry of an orbiting system.<br />
<br />
Wikipedia defines Symplectic Integrators as:<br />
<br />
{{cite|In mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations.}} <br />
<br />
==Integrator Comparison==<br />
<br />
===Sun-Earth-Moon System===<br />
<br />
'''[https://publications.mfo.de/handle/mfo/1355 Computing the long term evolution of the solar system with geometric numerical integrators]''' ([https://web.archive.org/web/20200303022220/https://publications.mfo.de/bitstream/handle/mfo/1355/snapshots-2017-009.pdf?sequence=1&isAllowed=y Archive])<br><br />
By mathematicians Shaula Fiorelli Vilmart ([http://www.unige.ch/~fiorelli/ bio]) and Gilles Vilmart ([https://web.archive.org/web/20200517202052/https://www.unige.ch/~vilmart/cv_vilmart_2020.pdf bio])<br />
<br />
:''Abstract''<br />
<br />
:{{cite|Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the same initial data yields the correct behavior. We explain the main ideas of how the evolution of the solar system can be computed over long times by taking advantage of so-called geometric numerical methods. Short sample codes are provided for the Sun–Earth–Moon system.'''}}<br />
<br />
The standard algorithms produce 'wrong solution' because the Moon is ejected from its orbit. A different algorithm is necessary to keep it together, and produces the 'correct' behavior.<br />
<br />
Figure 7 from the paper shows a comparison between a non-symplectic and symplectic integrator:<br />
<br />
:'''''The Sun-Earth-Moon System'''''<br />
<br />
:[[File:Sun-Earth-Moon-Integrators.png|800px]]<br />
<br />
:{{cite|'''Figure 7''': Comparison of the explicit Euler method (left) and the symplectic Euler method (right) for the Sun-Earth-Moon system simulated over one year. The distance between the Moon (blue trajectory) and the Earth (black trajectory) is scaled by a factor of 100 in the plots, to better distinguish the Earth and the Moon.}}<br />
<br />
The paper describes that the algorithm which keeps it together is the ''symplectic integrator.''<br />
<br />
:{{cite|The symplectic method, an integrator that preserves the energy well over long times.}}<br />
<br />
:''Initial Data''<br />
<br />
:{{cite|In Table 1 we provide masses, positions, and initial velocities of the Sun, the Earth, and the Moon at a given date (here 1st of January 2016), and a value for the gravitational constant G<br />
<br />
:[[File:Earth-Moon-Sun-Table1.png|450px]]<br />
<br />
:''Table 1: Initial data from <sup>[8]</sup> for Sun, Earth, Moon on 01/01/2016 at 0h00. Masses are given relative to the Sun mass M''<sub>☉</sub>.<br />
<br />
:The Sun is chosen as reference and located at the origin (0, 0, 0). Distances are expressed in astronomical units ua, a quantity based on the Earth–Sun distance (1 ua is about 150 million kilometers), and the time is in Earth days}}<br />
<br />
:''References''<br />
<br />
:<sup>[8]</sup>Observatoire virtuel de l’IMCCE, Portail système solaire, Miriade ephemeris generator, Observatoire de Paris & CNRS (2016), http://vo.imcce.fr/webservices/miriade.<br />
<br />
A history of the n-body problem is given:<br />
<br />
:''History - Is the Solar System Stable?''<br />
<br />
:{{cite|A question closely related to the topic of this snapshot is the issue of the stability of the solar system. Soon after Newton proposed his universal law of gravitation, many researchers, including, amongst others, Pierre-Simon Laplace (1749–1827), Joseph-Louis Lagrange (1736–1813), and Siméon Denis Poisson (1781–1840), were studying the question whether the regular trajectories of the planets will continue nicely until the end of times, or if collisions or ejections will occur.<br />
<br />
:In 1885, King Oscar II of Sweden sponsored a competition about this question. The prize was awarded to Henri Poincaré (1854–1912), ''although he did not really solve the problem.'' His contribution, however, is at the origin of the theory of dynamical systems. It also led to important developments in “Hamiltonian perturbation theory” and gave rise to the so-called Kolmogorov–Arnold–Moser (KAM) theory, which deals with the persistence of quasi-periodic motions under small perturbations, see the survey [7]. '''Unfortunately, this beautiful theory does not apply to realistic solar system models.'''}}<br />
<br />
:''Conclusion''<br />
<br />
:{{cite|We have seen that the energy, a key invariant of all mechanical systems, is well preserved by the symplectic Euler method. In contrast, the explicit Euler method, and more generally any standard explicit Runge–Kutta methods, do not preserve it and are thus not suitable for integration over long time intervals. A mathematical theory called “backward error analysis” permits to demonstrate that symplectic integrators have a good energy conservation for such mechanical systems.}}<br />
<br />
A special integrator, called ''symplectic integrators'', which preserves the energy and prevents the body from escaping is used, and is therefore 'more suitable'. Does this sound like a full clean simulation of gravity?<br />
<br />
:''Source Code''<br />
<br />
The above paper includes the source code for the above Sun-Earth-Moon System, for use with the free open source software [https://www.scilab.org/ Scilab], where the integrators can be tested.<br />
<br />
:[[File:Sun-Earth-Moon.gif|400px]]<br />
<br />
===Sun-Jupiter-Saturn System===<br />
<br />
[https://web.archive.org/web/20200413182206/http://www.cmap.polytechnique.fr/~massot/MAP551_web_20182019/Notes/MAP551_PC9_3A_MassotSeries_2018_2019.pdf Another paper] states the same for the Sun-Jupiter-Saturn system:<br />
<br />
{{cite|Following [8, 7], let us consider the Sun-Jupiter-Saturn system, where for simplicity we neglect the<br />
other bodies and influences in the solar system. Surprisingly, applying a standard numerical method<br />
yields a dramatically wrong solution, where one of the planets is ejected from its orbit. In contrast,<br />
a well chosen symplectic integrator with the same initial data yields the correct behavior.}}<br />
<br />
''Initial Data''<br />
<br />
[[File:Jupiter-Saturn-Table1.png|450px]]<br />
<br />
{{cite|We provide in Table 1 the positions and initial velocities for the Sun, Jupiter and Saturn at a given date (here September 5th 1994), expressed in astronomical units, based on the Earth-Sun distance (1 A.U. is about 150 million kilometers), and the time is in earth days.''}}<br />
<br />
==Always Returns Stable Conditions==<br />
<br />
The following is a paper which looks at symplectic and non-symplectic simulations and says that symplectic integrators always give stable conditions regardless of the perturbations which affects the body:<br />
<br />
'''[https://www.researchgate.net/publication/281108779_Numerical_Integration_Techniques_in_Orbital_Mechanics_Applications Numerical Integration Techniques in Orbital Mechanics Applications]''' ([https://web.archive.org/web/20200303190457/https://www.researchgate.net/profile/Patrick_Chai/publication/281108779_Numerical_Integration_Techniques_in_Orbital_Mechanics_Applications/links/55d5e3c008ae9d659489d4fc/Numerical-Integration-Techniques-in-Orbital-Mechanics-Applications.pdf Archive])<br />
<br />
:{{cite|Revisiting Table I, the ''non-symplectic integrators'' do not give a stable solution even at time step of 1e-4. The solutions from these integrators are chaotic and shoot off to infinity.<br />
<br />
:~<br />
<br />
:The ''symplectic integrators'' are very good at keeping the orbit stable for even long period integrations. For all the integrators that provide stable solution at time step of 1e-3, increasing the integration time to six orbital period yields the same result. Symplectic integrators are particularly good at this since it can keep the errors bounded.<br />
<br />
:~<br />
<br />
:From the two problems analyzed in this paper, one can clearly see the advantages of the symplectic integrator over the non-symplectic integrators. The symplectic integrators produce consistently better results with higher accuracy and slightly less run time. The fourth order symplectic integrators in particular are extremely successful in propagating both the restricted three body problem and the simple two body problem. As discussed earlier, the symplectic integrator is able to achieve stable solutions at lower integration tolerance and run time. For long duration integration, which is often the case for most orbital mechanics applications, the error on the non-symplectic integrators are unbounded and can grow. On the other hand, the symplectic integrator, by keeping the Hamiltonian constant, is able to bound the error and prevent it from growing substantially, '''always able to return to stable condition after perturbations.'''}}<br />
<br />
We read that the non-sympletic integrators do not give stable solutions, while symplectic integrators are "always able to return to stable conditions after perturbations".<br />
<br />
Does an algorithm which always returns a system to stable conditions regardless of perturbations sound like a legitimate reflection of bodies operating under Newton's laws?<br />
<br />
==Description==<br />
<br />
The purpose of the symplectic integrator is to preserve the area or geometry of the phase space.<br />
<br />
'''University of Rochester'''<br><br />
'''[http://astro.pas.rochester.edu/~aquillen/phy411/lecture7.pdf PHY411 Lecture notes Part 7 – Integrators]''' ([https://web.archive.org/web/20200303190758/http://astro.pas.rochester.edu/~aquillen/phy411/lecture7.pdf Archive])<br />
<br />
Figure 4 shows different trajectories:<br />
<br />
:[[File:Orbit Trajectories.png|650px]]<br />
<br />
Further down in the document:<br />
<br />
:[[File:Symplectic Description.png|650px]]<br />
<br />
:...<br />
<br />
:[[File:Symplectic Description 2.png|650px]]<br />
<br />
We read above that symplectic integrators are designed to preserve the geometry of phase space.<br />
<br />
==Phase Space vs. Position Space==<br />
<br />
It has been argued that these definitions apply only to "Phase Space," and that Phase Space is entirely different than the normal Position Space that we know which uses the x, y, and z coordinates. It has been argued that Phase Space does not contain the Position Space coordinates.<br />
<br />
In truth, Phase Space is merely Position Space with additional dimensions. We read a definition from '''''[https://books.google.com/books?id=tKcrDAAAQBAJ&newbks=1&newbks_redir=0&lpg=PA397&pg=PA397#v=onepage&q&f=false Physics for Degree Students B.Sc Second Year]''''' ([https://web.archive.org/web/20200305233656/https://books.google.com/books?id=tKcrDAAAQBAJ&newbks=1&newbks_redir=0&lpg=PA397&pg=PA397#v=onepage&q&f=false Archive]):<br />
<br />
:''10.4 Phase Space''<br />
<br />
:{{cite|'''A combination of the position space and momentum space is known as phase space.''' Thus phase space has six dimensions. A point in phase space is, therefore, completely specified by six coordinates x, y, z, p<sub>x</sub>, p<sub>y</sub>, p<sub>z</sub>. Complete information about any particle in a dynamic system can be obtained from a knowledge of these six co-ordinates which completely determine its position as well as momentum. As there are ''n'' particles a knowledge of 6''n'' co-ordinates gives complete information regarding position and momentum of all then particles in the phase space for a dynamic system. The concept of phase space is very useful while dealing with dynamical systems actually existing in nature.}}<br />
<br />
Scrolling up to section 10.2 we read the definitions of Position Space, verifying that it is the normal x, y, z position coordinates:<br />
<br />
:''10.2 Position Space''<br />
<br />
{{cite|The three dimensional space in which the location of a particle is completely given by the three position coordinates, is known as position space.}}<br />
<br />
Thus, if the geometry of ''Phase Space'' is preserved with a Symplectic Integrator, the geometry of ''Position Space'' is also preserved.<br />
<br />
===Figure Eight Example===<br />
<br />
Compare this figure eight three body problem in Phase Space and Position Space:<br />
<br />
https://demonstrations.wolfram.com/PlanarThreeBodyProblemInPhaseSpace/ ([http://archive.ph/POucx Archive])<br />
<br />
:[[File:Three Body Phase Space.png|600px]]<br />
<br />
Compare the above to the Figure Eight Three Body Problem solution in Position Space, plotted on the x and y.<br />
<br />
https://www.researchgate.net/publication/253681041_Dynamics_and_stability_of_multiple_stars ([https://web.archive.org/web/20200303192856/https://www.researchgate.net/profile/V_Orlov/publication/253681041_Dynamics_and_stability_of_multiple_stars/links/5432aa320cf22395f29c3164/Dynamics-and-stability-of-multiple-stars.pdf Archive])<br />
<br />
:[[File:Three Body Real Space.png|600px]]<br />
<br />
Plotted on the x and y, and looks surprisingly like the Phase Space version.<br />
<br />
It looks the same because it is the same. Phase Space is merely Position Space with detail in additional dimensions which represents momentum. The shape of an orbit represents geometry, as well as energy loss/gain.<br />
<br />
==Usage==<br />
<br />
'''[https://lss.fnal.gov/archive/other/cita-95-3.pdf Is the solar system stable?]''' ([https://web.archive.org/web/20200306233257/https://lss.fnal.gov/archive/other/cita-95-3.pdf Archive])<br><br />
Scott Tremaine<br><br />
University of Toronto and Institute of Astronomy, Cambridge<br />
<br />
In the above paper Scott Tremaine performs an analysis of the Solar System, concluding that the Solar System will be stable for millions of years. It is seen that this analysis uses Symplectic Integration techniques:<br />
<br />
:[[File:Tremaine-Symplectic.png|700px]]<br />
<br />
''Related Examples''<br />
<br />
:*[http://adsabs.harvard.edu/full/1992AJ....104.1633S Symplectic Integrators For Solar System Dynamics] by Scott Tremaine<br />
:*[https://link.springer.com/article/10.1007/s10569-013-9479-6 High precision symplectic integrators for the Solar System] by Jacques Laskar, et all.<br />
:*[https://dspace.mit.edu/bitstream/handle/1721.1/54394/31053409-MIT.pdf;sequence=2 Symplectic Maps for the N-body Problem with Applications to Solar System Dynamics] by Matthew Jon Holman<br />
<br />
==New Scientist - The World of Symplectic Space==<br />
<br />
A New Scientist article titled '''''[https://www.massey.ac.nz/~rmclachl/newscientist1994.pdf The World of Symplectic Space]''''' ([https://web.archive.org/web/20200306235233/https://www.massey.ac.nz/~rmclachl/newscientist1994.pdf Archive]) by Robert McLachlan, Ph.D. ([https://web.archive.org/web/20200307011302/https://www.massey.ac.nz/~rmclachl/SciRevMcL.html bio]), provides a background and history of this subject, admitting that Newton's Laws of Motion cannot simulate the Solar System or the n-Body problems. It is necessary to use a workaround using Symplectic integration, which preserves area and geometry.<br />
<br />
:''Conventional calculations of the future of the Solar System quickly degenerate into disarray as computer errors build up. Symplectic integration could save the day''<br />
<br />
:{{cite|WHAT will the Solar System be like in the distant future? Will Pluto and Neptune collide? Will the Earth be thrown into a different orbit by the combined gravitational pull from all the other planets? You might think that the answers are easily calculated. Just program a computer with Newton’s laws of motion, tell it the positions of the planets now, and wait while it grinds out the future of the Solar System for the next billion years. Right?<br />
<br />
:Wrong. With a calculation as complicated as this, the computer is almost certain to come up with the wrong answer. It is not that the computer, or even that the person programming it, makes mistakes. The problem arises because computer replaces real time with a series of snapshots. Consequently, the calculations a computer makes are not absolutely precise, so it can only provide us with an approximate picture of what will happen in the real world. Normally the errors are so small that they go unnoticed, but when computers are set to work on the enormously long string of calculations needed to simulate the movement of the planets round the Sun, tiny errors in each step can build up to make the final result wildly inaccurate.<br />
<br />
:''Confusion reigns''<br />
<br />
:The errors are inevitable because the equations describing the Solar System are so complicated that precise solutions cannot even be attempted. Problems arise when errors build up systematically or, worse, when the errors become chaotic. If this happens, the error in the calculated result will not only be large, but unpredictable too. They can lead to results that defy the laws of physics—in an extreme case the planets could spiral into the Sun, for example, or gain energy from nowhere and spin off into space.<br />
<br />
:These errors affect every computer model although their effects go unnoticed because calculations usually run for a short time preventing wild variations from building up. Even a simple pendulum could start swinging like a propeller if the simulation were left to run for long enough.<br />
<br />
:'''Mathematicians have discovered they can get around these problems if the computer model is built not on the laws of motion that apply in our familiar three-dimensional space, but on the geometrical laws of a much larger mathematical world called symplectic space.''' What we understand as movement in our space can be represented as pure geometry in the very different world of symplectic space. This geometry provides a much more efficient way of representing movement mathematically: while it cannot prevent the computer from introducing errors, it ensures that, whatever the errors, the outcome is a physically reasonable one.<br />
<br />
:The laws of geometry in symplectic space are applied through mathematical tools known as symplectic integrators: simple formulae that a computer can use to create reliable simulations of chaotic and complex aspects of real systems. Symplectic integration is already helping scientists to model the forces between tens of thousands of atoms in a crystal lattice—a system far too complex for conventional methods to handle reliably—and successfully predict properties of the material such as its strength or the way it vibrates.<br />
<br />
:Not every system in our Universe is symplectic, however. Dissipative forces such as friction or viscosity do not obey geometric laws and cannot be simulated using symplectic integration. Applying the method to weather forecasting is complicated, for example, because air resistance is a dissipative force and has to be ignored.<br />
<br />
:One example where symplectic simulations can help is in designing circular particle accelerators. The Main Ring accelerator at Fermilab in Illinois, which was built in 1972 before symplectic motion was understood, cannot store particles for long because small variations in their paths rapidly build up into uncontrollably large deviations. Physicists now realise that with the new symplectic methods they would have been able to simulate these effects, and design the machine to cope.<br />
<br />
:Conventional computer models use position and time to deduce velocity, but position and velocity are treated on an equal footing in symplectic space. For instance, in a model of the Solar System each planet is defined by six dimensions—three for its velocity in each direction and three for its position. The dimensions are coupled by special kinds of angles known as symplectic angles. These angles cannot be measured with a protractor: two lines superimposed on each other, for example, have a normal angle between them of 0° but a symplectic angle of 90°.<br />
<br />
:The special features of this weird space are its laws of geometry. That space and geometry are closely linked can be seen by looking at the properties of a triangle in two different types of space. We are taught at school that the angles of a triangle add up to 180°, but this is not always true if the triangle is not on a flat plane. For example, imagine a triangle on the surface of the globe, which has one corner at the North Pole and the other two on the equator. No matter What the angle at the pole, both the angles at the equator will be exactly 90°, so the three angles are bound to add up to more than 180°. By choosing the space carefully, mathematicians can arrange for certain geometric laws to hold true. In the example of the triangle, the angles add up to 180° only if the space is flat.<br />
<br />
:If the space is complex, then the geometric laws can be complex too. As the planets move in symplectic space according to the symplectic laws of geometry, so they move in three-dimensional space according to Newton’s laws of motion. Symplectic geometry ensures that symplectic angles remain the same as the planets move. This geometry can describe all the complicated motion of the Solar System.<br />
<br />
:Symplectic space has been hard to explore because its geometry is so unlike that of three-dimensional space (the name comes from the Greek word symplegma, meaning tangled or plaited). After many decades of study, the breakthrough came during the 1950s when the Russian mathematician Vladimir Arnol’d at the Moscow State University, along with Andrei Kolmogorov and Jiirgen Moser, proved a theorem that explains some of the implications that these hidden geometrical laws hold for real motion.<br />
<br />
:In the case of a single planet in a circular orbit around the Sun, the motion is nonchaotic and well understood. But one problem that could not be by conventional means is what happens when there is a second planet exerting a small gravitational pull on the first. Does the circular orbit merely become slightly elliptical? Does it develop a chaotic wobble? Or will the first planet wander off entirely? The Kolmogorov-Arnol’d-Moser (KAM) team proved that all three are possible. Given certain initial conditions, the orbit can still be regular. But if the starting conditions are slightly different, it could be chaotic. Once in a chaotic state, the orbit might even “leak out” in a process known as Arnol’d diffusion, which causes the planet to wander away from its circular orbit.<br />
<br />
:''Alternative orbits''<br />
<br />
:The problem lies in determining which type of orbit a system will adopt. The KAM theorem shows that chaos and order are infinitely mixed. Between any two regular orbits lie chaotic ones, and the planet could adopt any one of an infinite number of each type of orbit. But a planet that behaves nonchaotically can never become chaotic.<br />
<br />
:Traditional computer models of planetary orbits produce outrageous results because the build-up of errors in the calculation leads to results that run counter to the laws of motion on which the model is based. Symplectic integration avoids these pitfalls by modelling not just the forces and accelerations as happens in conventional computer simulations, but by also keeping symplectic angles fixed in symplectic space. While the computation will still, inevitably, accumulate errors, the KAM theorem guarantees that they will ''not nudge a planet into an impossible orbit''. The result does not predict the exact motion of our Solar System, but it does provide useful information about it. For example, ''astronomers can work out Pluto’s distance from the Sun in a billion years’ time, but not which side of the Sun it will then be on.''<br />
<br />
:Although scientists have started to use symplectic integration only recently, it is not a new idea. In the 1950s René de Vogalaére, a mathematician then at the University of Notre Dame in Indiana, suggested rewriting formulae to preserve symplectic angles at each step. But his paper was rejected by a mathematical journal and the idea was forgotten. In 1983, it was rediscovered independently by Ronald Ruth at Lawrence Livermore National laboratory in California and Feng Kang at the Chinese Academy of Sciences in Peking. Since then, the study of symplectic integration has gone from strength to strength and the technique is giving scientists new insights into the workings of the Solar System. That chaotic motion exists in the Solar System was first suggested in 1988 by conventional computer calculations. But these were painfully and unnecessarily slow, and symplectic integrations can be carried out in a fraction of the time to simulate this chaos far into the future. Scientists now model the entire lifespan of the Solar System, thought to be about 10 billion years, and know that the model is reliable because it obeys the laws of symplectic geometry.}}<br />
<br />
==Solar System Integrator Comparison==<br />
<br />
Andrew Winter provides a simulation of the outer planets of the Solar System, showcasing the Forward Euler method versus the Symplectic Euler method.<br />
<br />
:{{#ev:youtube|https://www.youtube.com/watch?v=ewor7sRfS6w}}<br />
:(Archive [https://wiki.tfes.org/File:Numerical_Integration_of_the_Solar_System_2.mp4 1] [https://web.archive.org/watch?v=ewor7sRfS6w 2])<br />
<br />
:Description: {{cite|On the left the solar system is evolved forward in time using the Forward Euler method while on the right the Symplectic Euler method is used. Both schemes may be evaluated explicitly; however, it should be noted that the Symplectic Euler method is defined implicitly and is only made explicit due to the form of the Hamiltonian being separable into functions of purely the positions and momenta. The Forward Euler scheme does not preserve any properties of the system and is only 1st order accurate. The Symplectic Euler scheme is also only 1st order accurate, but it preserves the structure of the elliptical orbits and Hamiltonian providing the time step is reasonably small. Both methods used the same time step of 200 days with the rest of the parameters being drawn from Hairer, Lubich, and Wanner's text on geometric integration as in my [https://www.youtube.com/watch?v&#61;b3J3lDYQRAs previous video]}}<br />
<br />
We see in the above video that with the Euler Forward method that Jupiter is ejected from the Solar System after a single orbit around the Sun. Saturn is thrown beyond Neptune, &c., as the Solar System quickly degenerates.<br />
<br />
===Forward Euler Descriptions===<br />
<br />
[https://en.wikipedia.org/wiki/Euler_method Wikipedia states] that the 'Forward Euler method' is also known as the 'Euler method':<br />
<br />
:{{cite|In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.}}<br />
<br />
Descriptions [https://web.archive.org/web/20200413202055/https://www.sciencedirect.com/topics/engineering/forward-euler from Science Direct sources state:]<br />
<br />
:{{cite|Forward Euler is the simplest numerical integrator.}}<br />
<br />
===Source Files===<br />
<br />
The author provides steps for reproducing his plots with MATLAB in the description of his [https://www.youtube.com/watch?v=b3J3lDYQRAs linked associated video], which shows a successful Störmer–Verlet simulation of the Solar System:<br />
<br />
::''This is a demonstration of the Stormer-Verlet method applied to the outer solar system consisting of Jupiter through Pluto. The computation was carried out in Matlab with a time step of 200 days, a final time of 200,000 days, distances in astronomical units (AU), and masses normalized by the Sun's mass. The masses of Mercury through Mars were lumped together with the Sun. The initial conditions for position and velocity along with the scaled masses were obtained from pg. 13-14 of the 2nd Ed. of "Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations" by Hairer, Lubich, and Wanner.<br />
<br />
::''To reproduce this plot, download the main script and functions linked below and run the main script with the functions either in the same folder as the main script or somewhere else in Matlab's search path (for Windows users C:\Users\YourUserName\Documents\MATLAB). The only variable that needs editing in the script is "method = methods{index}", where "index" should be the number corresponding to the numerical method you want to use from the list given below.''<br />
<br />
::''The numerical methods provided include:''<br />
::''1) Forward Euler''<br />
::''2) Runge-Kutta 23''<br />
::''3) Runge-Kutta 45''<br />
::''4) Symplectic Forward Euler''<br />
::''5) Stormer-Verlet''<br />
<br />
::''Main script:''<br />
::[https://web.archive.org/web/20200413202553/https://drive.google.com/file/d/15hzHrNtRuSudn8t2B_yyBobFYzexAWY4/view Solar_System_Example.m]<br />
<br />
::''Functions:''<br />
::[https://web.archive.org/web/20200413202857/https://drive.google.com/file/d/1ycdie6XUNQdq1otkDvRYH0ctPX6yfQ3y/view solarSysDiffEQ.m]<br />
::[https://web.archive.org/web/20200413202853/https://drive.google.com/file/d/1Mo_6XRmO_CO34-HmkNZjtC99dbqhd3Zk/view solarSysHam.m]<br />
<br />
===Störmer–Verlet is Symplectic===<br />
<br />
It is seen that the Störmer–Verlet is a symplectic method.<br />
<br />
Paper: ''[https://aip.scitation.org/doi/abs/10.1063/1.468951?journalCode=jcp Qualitative study of the symplectic Störmer–Verlet integrator]''<br />
<br />
Abstract: {{cite|'''''Symplectic numerical integrators''''', such as the '''''Störmer–Verlet''''' method, are useful in preserving properties that are not preserved by conventional numerical integrators.}}<br />
<br />
==Quotes==<br />
<br />
Symplectic integrators are used in other areas in science. From the [https://accelconf.web.cern.ch/IPAC2015/papers/mopma030.pdf abstract of a particle physics paper] we read:<br />
<br />
{{cite|It has been long understood that long time single particle tracking requires symplectic integrators to keep the simulations stable}}<br />
<br />
==Addendum==<br />
<br />
As explicitly admitted, Newton's Laws ''cannot'' simulate the Solar System. Exotic methods are required to preserve the area and geometry of an orbiting system.<br />
<br />
On KAM theory New Scientist states "While the computation will still, inevitably, accumulate errors, the KAM theorem guarantees that they will not nudge a planet into an impossible orbit.", while another researcher remarks regarding KAM theory - "Unfortunately, this beautiful theory does not apply to realistic solar system models" <sup>[https://wiki.tfes.org/Symplectic_Integrators#Integrator_Comparison]</sup>. One paper concludes that "the symplectic integrator, by keeping the Hamiltonian constant, is able to bound the error and prevent it from growing substantially, always able to return to stable conditions after perturbations." <sup>[https://wiki.tfes.org/Symplectic_Integrators#Always_Returns_Stable_Conditions]</sup><br />
<br />
New Scientist tells us that that the simulations are not built on the laws of motion that apply in our familiar three-dimensional space <sup>[https://wiki.tfes.org/Symplectic_Integrators#New_Scientist_Article]</sup>, that those models tend to fall apart quickly, and that these alternative geometric methods discussed cannot be used for prediction of the positions of bodies: "The result does not predict the exact motion of our Solar System, but it does provide useful information about it. For example, astronomers can work out Pluto’s distance from the Sun in a billion years’ time, but not which side of the Sun it will then be on." <sup>[https://wiki.tfes.org/Symplectic_Integrators#New_Scientist_Article]</sup> Which is interesting since any direct and real simulation ''of motion'' would inherently know that Pluto makes an orbit every 248 years around the Sun, regardless of the author's downplay of 'a billion years'. This is also a contradiction of the popular claims that the Solar System can be truly simulated with Newton's laws out to millions or billions of years, or even for a shorter period of time barring the special geometry preserving methods which keeps it together.<br />
<br />
All of this tells us that these methods are not realistic models of orbiting systems which can be used for prediction, and are really niche academic frivolities — the end result of a submission to the [[Three Body Problem]] and science's desperate attempt to get invalid laws and an unworkable system to work.<br />
<br />
Instead of a working model we are presented with a system based on "geometric laws". The truth is that if Newton's laws worked to describe the Solar System he would have done it himself in the 1700's, rather than concluding that divine intervention keeps the Solar System together <sup>[https://wiki.tfes.org/Three_Body_Problem#Newton.27s_Solution]</sup>, and which this geometric approach is the ultimate manifestation of. Newton's own conclusion that the Solar System is unworkable under his laws was true then and remains true today. We are once again faced with the reality that the accepted laws of gravity and motion are not, and cannot, be used to simulate the Sun-Earth-Moon system or the Solar System.<br />
<br />
==See Also==<br />
<br />
*'''[[Three Body Problem]]''' - The heliocentric Sun-Earth-Moon system cannot be simulated<br />
:*'''[https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns Perturbation Methods]''' - Epicycles are still used for astronomical prediction<br />
:*'''[https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#The_Eclipses Eclipse Prediction]''' - The eclipses are predicted with cycles and patterns<br />
:*'''[[Symplectic Integrators]]''' - A special method of orbital simulation which preserves geometry and forces stability<br />
<br />
[[Category:Cosmos]]<br />
[[Category:Gravity]]<br />
[[Category:Celestial Mechanics]]</div>Tom Bishop