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Re: one second of time
From: George Huxtable
Date: 2008 May 18, 22:32 +0100
From: George Huxtable
Date: 2008 May 18, 22:32 +0100
Coralline Algae asked- | Using sidereal time, meridian transit of a star. | | I am going to investigate this method as it intrigues | me as a solution for a totally non electric culture, | Although they would have to be able to make | mechanical clocks. | With a telescope having crosshairs in the eyepiece, to | what accuracy can the meridian transit timing be made? | Assuming accuracy of a few seconds, then I would | guess that next requirement would be tables converting | sidereal time to mean solar time for each day of the year? | After which the primary clock could be adjusted based | on a timer which started running at the transit. | If I am missing something here I would appreciate | clarification. ============== I'll say a bit about how timing was worked at Greenwich Observatory, some of which is based on surmise rather than knowledge. In 1676, only 20 years after Huyghens invented the pendulum clock, the two Great Clocks were installed in the Octagon Room at Greenwich, by the famous maker Thomas Tompion, for Flamsteed. For a precise pendulum clock, it helps to have a long pendulum, a slow beat, and a small arc of oscillation. The ticks were two seconds apart, half the speed of a grandfather clock, and the pendulum was 13 feet, so four times longer than a grandfather. One clock was set to keep Greenwich Mean Time, and the other to run slightly faster, to keep Sidereal Time. With a telescope clamped in place to show the meridian passage of Sirius, in daylight or darkness, then Sirius should pass the crosswires at the same sidereal time each day, corresponding to its Right Ascension. There was a small correction to make, of a few seconds over the year, to adjust for Sirius' known slow change in RA, as a result of precession. It was a simple matter to note the time of the sidereal clock, when Sirius crossed the middle wire. For best accuracy, the observer needed to estimate an interpolated time, between ticks, to a fraction of a second. I presume that the resolution of the telescope would be good enough that the star-crossing itself could be observed to a small fraction of a second. In which case, the main error would be in interpolating between the clock beats. I doubt whether the observer at the telescope was in a position to hear the ticks of the sidereal clock himself, and to be sure which tick came from which clock. Instead, he would have to call the moment of crossing, for an assistant to estimate the clock-time. There would be no attempt to reset the clock or to readjust its rate, just to note its deviation each day. My guess is that it could be done to a quarter of a second, or so. Once you have a clock reading sidereal time, with a known error, it becomes a simple matter to then set the other clock to tick off mean time, knowing the simple relation between the mean day and the sidereal day. That's just a matter of arithmetic. There may indeed have existed a table to convert one to the other, as Coralline suggests, but if so it was very simple. And the cross-checking didn't call for another timer, as Coralline suggests, but just of reading one clock against another. Once there's a clock keeping accurate mean time, that can be used to time Sun meridian passages, at Greenwich Apparent Noon, to establish the Equation of Time precisely, an early Greenwich task. One of Flamsteed's first tasks, once he had his clocks working, was to establish whether the Earth really turned at a steady speed, so that each (sidereal) day was the same length as any other. That had been no more than an assumption before, but Flamsteed was able to establish its truth, within the accuracy of his clocks. Of course, we know better now, that the Earth's rotation speed is gradually slowing, to an extent far less than Flamsteed had any hope of measuring. Both of Tompion's clocks survive, but the two that a modern visitor can see, slowly ticking away behind the wainscot in the Octagon Room, are replicas. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---