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Historical Lunars : take in account 'delta-T' or ignore it ?
From: Antoine Couëtte
Date: 2009 Dec 11, 06:37 -0800
From: Antoine Couëtte
Date: 2009 Dec 11, 06:37 -0800
Historical Lunars : take in account 'delta-T' or ignore it ? PRELIMINARY NOTE : I earlier recently started addressing the items here-under with Frank E. Reed (private communications). Frank indicated that these topics might better be covered on NavList. Therefore and after extensive and in-depth reprocessing I am submitting everything to all of us in NavList. ******* FOREWORD When re-processing "historical" Lunars (i.e. "real world" Lunars observed during the period @1700-@1900 A.D.) with to-day computational power, should we take in account "delta-T" or ignore it ? Although the effects of delta-T are (almost) negligible during this past 2 century period, - and accordingly the topic raised here might seem almost void or even useless - it seems interesting to agree on what should be the "best way" to-day to tackle historical Lunars for the sake of respecting good navigation principles. SECTION I Note : This introduction may be skipped by knowledgeable Readers who may directly proceed to SECTION II here-after. SECTION I only brings back to mind a somewhat "comprehensive big picture" regarding Lunars through recalling the following important points which need to be remembered. - 1 - For extended periods of time before accurate 'Chronometers / Timekeepers' could be manufactured - i.e. before the spectacular achievements by Harrison in the UK followed many years later by Le Roy and then Berthoud in France - Lunars were almost the only practicable method to reckon/reconstruct "astronomical time" by comparison between "Observed" and "Tabular" Lunar Distances, which in turn enabled to derive an Observer's Longitude, and - 2 - While the sun RA varies by some 2.5 arc minutes per hour of elapsed time, the Moon RA - and to a great extent the distance between the Moon and every 'usable' Body - varies about half a degree during the same elapsed hour. As a consequence, any angular error in measuring a lunar-body distance will translate into an Observer's Longitude error magnified some 30 times. In order to minimize such errors in Longitude, it has long been recognized that Lunar distances must be observed and recorded with the utmost achievable precision and care, and - 3 - Since Lunar distances themselves are almost non subject to the too often quite unpredictable effects of horizon dip, but only and to some limited extent to atmospheric refraction (including body shape distortion due to differential refraction), in the best cases Lunar Distances can be measured to a quite high "meaningful" accuracy. A Lunar Distance observational accuracy of 0.1 arcminute (6 arcseconds) can be assessed as the very best one a well trained observer can achieve with an excellent sextant. For the reason stated in �2 hereabove, it has been customary to attempt clearing Lunars to this level of accuracy. Given both the complexity of the relevant computations and the historical limitations of ephemeris accuracies - see �6 hereafter - such a 6 arc second intended computation accuracy level could not be consistently reached in the past. However - and in other words - there is no computational "overkill" when one attempts clearing Lunars to an accuracy of 0.1 arcminute, i.e. to +/- 12 seconds of elapsed time, which also translates into +/- 3 minutes of uncertainty in Longitude. Nowadays accurate lunar distances clearing computations have become fully and routinely achievable : see for example the GREAT on-line Lunar Computer by Frank E. Reed (http://www.historicalatlas.com/lunars/lunars_v4.html) Congratulations again Frank ! , and - 4 - Historically, the fact that UT is not a strictly "uniform" time-scale has been fully ascertained only as late as of the first quarter of the 20th century, although UT irregularities had been suspected for at least half a century before. This led to establishing the distinction between an almost 'perfectly smooth' Ephemeris Time (ET) time scale, while the UT time scale directly linked to the Earth irregular rotation was and has been recognized as being a quite 'irregular' time-scale. The difference between both Times scales is widely known as 'delta-T'. Given the rate of change of Lunar distances, certainly 'delta-T' values smaller than 12 seconds of time - equating to a change in the Moon RA inferior to 6 arc seconds, and a change in the Moon GHA inferior to 3 arc minutes - could be regarded as 'almost negligible', and - 5 - There still remains to-day some uncertainty on delta-T values in ancient times. Intensive research has been performed here since the 1980's and in particular by MM. Stephenson and Morrison. Their best current results have been summarized in http://eclipse.gsfc.nasa.gov/SEhelp/deltaT.html and in http://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html . Although there remain significant delta-T uncertainties before the first half of the 17 th century, starting from the 1620's and thereafter (i.e. during all the Lunars epoch) , our current knowledge of the delta-T is quite reliably accurate, and - 6 - For over 2 centuries, 'fairly good' lunar positions predictions were available to Navigators and in particular as soon as the 1730's. One and half century later greater accuracies were achieved with Hansen's Theory. However sooner or later - i.e. 10 to 20 years at the most after their first 'flashing and impressive' results - all these 'historical' theories started going off-track. They all needed additional 'observed corrective terms' required to bring predictions back into conformity with observations. Even the first version (completion date 1908) of Ernest William Brown's Lunar Theory - albeit extraordinary for its time - and subsequently published in 1919 under the form of its much celebrated Tables of the Motion of the Moon included in particular an 'empirical term' exceeding 10 arcseconds in Longitude to best reconcile predictions with observations. Only since the middle of the 20th century, have Lunar Movement theories been established which could and can reliably achieve accuracies consistently better than 0.1 arc minute. The second version of E.W. Brown's Lunar Theory, i.e. the Improved Lunar Ephemeris 'I.L.E.' by Brown and Eckert published shortly after 1950 was the first such Moon motion theory to consistently achieve accuracies better than 0.1 arc minute, including for computations related up to a couple of centuries in the past. This improvement was mainly the result of properly taking in account the time differences between the ET and UT Time scales (see � 4 hereabove). Subsequently there was no longer need for the 'empirical term' which was removed. In the 1980's the I.L.E. theory was then followed by the now 'deadly accurate' DE20x - DE40x Numerical Integrations from JPL altogether with the ELP 2000-xx Analytical Theories and the INPOP06 Numerical Integration from Bureau des Longitudes. When dealing with Lunars, we should keep in mind that we can consistently and accurately predict/compute the Moon Position with an accuracy equal or better than 6 arcseconds only since the middle of the 20th Century, and - 7 - When working with an accuracy of 6 arcseconds on celestial coordinates, we will assume that all the previously used time scales/variables - whether the 'Temps Uniforme' used by Urbain Le Verrier or the 'Ephemeris Time' used by Simon Newcomb are the same as the TDT time scale and the current TT time scale and that there has been no appreciable discontinuity between them. SECTION II With the perspective of the various points summarized hereabove, how should we best proceed if we are to reprocess / re-compute historical Lunars with to-day's computation tools? I would like to offer the following comments and will certainly be very glad to hear feed-back from the NavList community, especially if view points are different from the one I am detailing here-after. -*-*- First, we can state that, when they cleared their Lunars, the 18th, 19th and (if any) the early 20th centuries Navigators were not aware of the "necessity" of using 2 time scales. In other words - and unless they used data amended with 'observed corrective terms'(see �6 here-above) - they (unknowingly) cleared all their Lunars with the Value delta-T=0.0 seconds of time. This point has 2 different consequences if we are to compute again to-day their historical Lunars with our now much improved theories and much improved computational power : If we want with our current "computation tools" check the quality of their Lunars, we should put ourselves in their exact same environment, i.e. reprocess their Lunar computations with delta-T = 0, and If on the other hand we want to best derive their observed longitudes - and/or positions - we should certainly then take in account values of delta-T. -*-*- Second, I am submitting here-after a fictitious example of an upcoming Lunar which shows that - if we were to ignore to-day the effects of delta-T on Lunars - we would significantly increase our error in UT determination, and therefore our Longitude uncertainty. ••••••• 23 Dec 2009 Height of Eye = 17 ' T = 59�F , P = 29.92 ' Estimated UT / Position : 16h58m53.0s / N3707.1W01253.7 - All observations assumed to occur at the same time - Distance SUN-MOON = 77�53'7 , SUNL = 5�50'1 , MOONL = 50�05'0 . All sextant measures are corrected for Instrument error (and only instrument error), i.e. all other corrections (dip, refraction, SD, Parallax ... ) need to be performed from the "raw data" hereabove. *** If we compute observer's position from the observed heights : o With delta-T = 66.7 seconds (close to current value for Dec 23, 2009) : • Lunar Distance UT = 17h00m00.7s - i.e. TT = 17h01m07.4s - hence UT error = -1m07.7s, cleared distance = 78�34.00', and • We also get the following position at time of Lunar Distance : N3659.9W01300.3 (result of 2 body fix), and • Crosscheck with Frank's on-line computer (you need to enter both heights) : Error in Lunar : -0.1', approximate Error in Longitude 03.9', cleared distance = 78�33.9' o With delta-T = 0.0 second : • Lunar Distance UT = 17h01m07.4s - i.e. TT = 17h01m07.4s - hence UT error = -2m14.4s, cleared distance = 78�34.00', and • We also get the following position at time of Lunar Distance : N3659.9W01317.1 (result of 2 body fix), and • If it were possible to use Frank's on-line Lunar Clearing computer with delta-T=0.0 s for this example, this would offer additional independent cross-check of these results. Note : In either case (delta-T=0.0s or delta-T=66.7 s) and since we assume unchanged Latitude (using same both Heights), the recorded Lunar Distance 77�53'7 defines the very same Terrestrial Time TT = 17h01m07.4s. By comparison with the "delta-T=0.0 second" position, and since the Earth has "slowed down", the Observer's geographical position is shifted 66.7 seconds of time - or 16.6' - to the East. In either case we have here exactly the same Bodies configuration as seen from the Earth surface. Only the Observer's support - i.e. the Earth itself - has slowed down and accordingly the Observer's Terrestrial position has become shifted to the East. *** If we use and consider estimated position - i.e. N3707.1W01253.7 - as being the "true/exact Observer's position" : o With delta-T = 66.7 seconds (close to current value for Dec 23, 2009) : • Lunar Distance UT = 17h01m44.0s - i.e. TT = 17h02m50.7s - hence UT error = -2m51.0s, cleared distance = 78�34.79', and • Crosscheck with Frank's on-line computer (do not enter any heights) : Error in Lunar : -0.1', approximate Error in Longitude 03.1', cleared distance = 78�34.7' o With delta-T = 0.0 second : • Lunar Distance UT = 17h06m09.4s - i.e. TT = 17h06m09.4s - hence UT error = -7m16.4s, cleared distance = 78�36.32', and • If it were possible to use Frank's on-line Lunar Clearing computer with delta-T=0.0 s for this example, this would offer additional independent cross-check of these results. Note : It is interesting to remark here that neither bodies positions (whether celestial coordinates or heights) are the same because*** TT are different for each value of delta-T (*** BTW, why do we get different TT values ?... any takers here ?). Also, one can easily observe the effect of the apparent Sun starting "slowing down" due to the increasing refraction which becomes appreciable near the horizon. This explains why, for a delta-T value equal to 66.7 seconds, we have a difference of 3m18.7s between both TT values, hence cleared distances different by 1.53'. LAST NOTE : Finally I am also aware that some of the computation results given here-above in the previous example point our more directly towards "Time-keeper / Chronometer error" rather than towards "Longitude Errror" or "Lunar Distance Error"(these last 2 itemns being immediate results presented on Frank's Computer). Therefore, and although both concepts are very closely related, it might be interesting to cover this subject regarding "Lunars Philosophy" on NavList(under a separate file ?). Comments from our NavList Community are most welcome, so that we all benefit from each other's contributions. Thanks to all Antoine M. "Kermit" Couette -- NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To , email NavList+@fer3.com