>predicting where the moon will be at a given time, and vice versa >Question: is there an easy way to understand AND remember how the moon moves >throughout the month?
The moon's motions have been predictable since at least the 1700s, when 'lunars' were used to navigate. 'Understanding & remembering' are not my bailiwick. You can remember that the moon follows the sun but is 51 minutes later each day (that is an average figure -- I _think_ it is true at any latitude.....) Or, instead of remembering, you could just get a moondial. There have been some good posts on this subject over time; I've been off the sundial list for a year but have the earlier posts --Peter ----------------- Date: Sun, 18 Jan 1998 21:21:36 +0100 From: "fer j. de vries" <[EMAIL PROTECTED]> > I tried to design a sundial for the moonlight - moon dial. But I got more problems than solutions. Maybe somebody can help me? http://www.hs-bremen.de/planetarium and AKTUELL What accuracy do you want? If you want to convert "moontime" into "watchtime" there are to many parameters. But if the main goal is just to find the time roughly there are many solutions. The main part is a table with average values for the hourangle between the moon and the sun in realtion to the age of the moon. Roughly there are 30 days in one period from new moon to new moon. Each day the hourangle between the moon and the sun changes about 24 * 60 / 30 = 48 minutes. One solution is to use an equatorial sundial and rotate the dial's plate with n * 48 minutes in which n is the age of the moon in days from new moon. Or make on a normal sundial a number of scales for the age of the moon and on each scale hourpoints with an offset of n * 48 minutes. Connect all the hourpoints and you get a moondial as in the attached figure. In that figure the scales for the age of the moon are circles, but that isn't necessary. Also the pattern of the normal sundial can be removed. In the bulletins of the Dutch (92.5), Spanish and British (92.1) Sundial Societies some about moondials is written. In the book Orologi Solari by Girolamo Fantoni, Italy, you find a capital about moondials. The picture in this mail is scanned from that book. moondial.jpg Fer de Vries. ---- a photograph of a Chinese moondial, probably a few centuries old, was included by Joseph Needham in Volume III of _Science & Civilisation in China_ (Cambridge: Cambridge University Press, 1959), in Plate XLII, opposite page 309. The briefest of references to this instrument appears on page 311. =============== Date: Mon, 9 Nov 1998 18:57:45 -0500 Reply-To: History of Astronomy Discussion Group <HASTRO- From: Fred Sawyer <[EMAIL PROTECTED]> Subject: Re: moondials You can try the following web site: www.quns.cam.ac.uk/Queens/misc/Dial.html You might find the following article on Moon Dialing interesting - I wrote it for The Compendium : Journal of the North American Sundial Society. I have not included the graphics or computer program here, but the discussion and example may prove useful. Moon Dialing Fred Sawyer Digital COMPENDIUM 1(2) May 1994 One of the more interesting passages attempting to explain or shed light on the fascination the dialist has with the sundial can be found in Frank Cousins' introduction to his book Sundials: "The sundial still remains, despite all advances in the art of time measurement, the one philosophical tool which combines the two poles of the human condition most faithfully: transience and arrogance - transience in the ephemeral nature of the shadow cast and arrogance in the use of the gyrations of the Earth about its stupendous luminary delicately to define the successive quanta of human existence." - Frank W. Cousins 1969 Sundials Transience and arrogance. Indeed, the image of the fleeting shadow has often been invoked to suggest the transience of our existence and of our works; the image has a certain natural appeal. However, the arrogance we show by directly using the sun to clock our daily lives is alluded to far less often. Perhaps we should make an effort to raise our consciousness and seek ways to curb our arrogance. I submit that a first step in this direction would be to consider stepping our arrogance down a notch by using the moon rather than the sun as our source of light and shadow. Surely, the moon is a less stupendous luminary - if indeed it even qualifies as a luminary, offering as it does only the reflection of sunlight. A moondial would clearly offer us all a lesson in humility and at the same time provide an answer to the frequent refrain: "What do you do to tell time when the sun goes down?" Of course, this revelation is not new, and moondials, though rare, have existed for at least the last three centuries. A moondial is simply a sundial together with some mechanism to correct for the difference between solar and lunar hour angles. This mechanism may take many forms: 1) A simple graph or correction table, such as may be seen here or, in a slightly different form, on the famous Queen's College sundial in Cambridge England. 2) A mechanism for rotating the dial to give a direct reading, based on the current phase of the moon, such as may be seen in Nicholas Bion's well-known 18th century work, The Construction and Principal Uses of Mathematical Instruments. 3) A set of spiralling hour-lines designed to replace the usual lines and to function correctly only in response to illumination by the moon, such as the arrangement developed by Girolamo Fantoni (Bulletin of the British Sundial Society 92(1):11-15, February 1992). My goal in the present article is to provide a simple (but computer-aided) foundation on which the insomniac dialist can begin to retrieve the moondial from its relative obscurity and dismissal as an inaccurate curiosity. Even those few writers who have dealt with the moondial have tended to give it short shrift. Mayall suggests that one is lucky to come within 30 minutes of the correct time; and he is correct for most earlier treatments of the subject. As we will see, the formulas produced here and implemented on computer will virtually eliminate that error. Basic Theory How, then, do we adapt a standard sundial for use as a moondial? The basic theory was outlined by Nicholas Bion in 1723 as follows: "...the Moon by her proper Motion recedes Eastwards from the Sun every Day about 48 Minutes of an Hour, that is, if the Moon is in Conjunction with the Sun on any Day upon the Meridian, the next Day she will cross the Meridian about three quarters of an Hour and some Minutes later than the Sun: and this is the Reason that the Lunar Days are longer than the Solar ones; a Lunar Day being that Space of Time elapsed between her Passage over the Meridian, and her next Passage over the same; and these Days are very unequal on account of the irregularities of the Moon's Motion." "Now when the Moon is come to be in Opposition to the Sun, she will again be found in the same Hour-Circle as the Sun is; so that if, for example, the Sun should be then in the Meridian of our Antipodes, the Moon would be in our Meridian, and consequently would shew the same Hour on our Sun-Dials as the Sun would, if it was above the Horizon. But this Conformity would be of small duration, because of the Moon's retardation of about two Minutes every Hour. If moreover the Sun, at the Time of the Opposition, be just setting above our Horizon, the Moon being diametrically opposite to it will be just rising, &c...." "[To make] the Table...used for finding the Hour of the Night by the Shadow of the Moon upon an ordinary Dial..., draw 4 Parallel right Lines or Curves of any length, and divide the [Center] Space...into twelve equal Parts for 12 Hours, and the two other Spaces into 15, for the 30 Lunar Days." "First observe what Hour the Shadow of the Moon shews upon a Sun-Dial; then find the Moon's Age, and seek the Hour correspondent thereto in the Table, and add the Hour shewn by the Sun-Dial thereto; then their Sum, if it be less than 12, or else it's excess above 12, will be the true Hour of the Night. For example; Suppose the Hour shewn upon the Sun-Dial by the Moon, be the 6th, and her Age be 5 or 20 Days, against either of these Numbers in the Table you will find 4, which added to 6 makes 10, and so the Hour of the Night will be 10. Again, Suppose the Moon shews the Hour of 9 upon the Sun-Dial, when she is 10 or 25 Days old, against 10 and 25 in the Table you will find 8, which added to 9, makes 17, from which 12 being taken, the Remainder 5 will be the true Hour sought. And so of the others." - From Edmund Stone's 1758 translation of Nicholas Bion's The Construction and Principal Uses of Mathematical Instruments, Book VIII, Chapter 6. Note that this passage is abbreviated because the actual instrument Bion described to implement this design breaks the cardinal rule requiring that the gnomon always be parallel to the celestial axis. His use of the instrument rotates the gnomon out of the north-south plane. A Different Approach Given the traditional reliance on knowing the current lunar age (phase) to use a moondial, it would be natural to think that the key to a more accurate reading is a more precise determination of the moon's phases. However, more precision here actually would be of little utility. The traditional calculation only uses the phase to determine the point of entry in what is itself a very approximate table of data, assuming an average 48 minutes/day additional elongation from the sun's position. For more precision, we need to return to the fundamentals. Begin by selecting an hour of day to use as a reference time. For convenience, we use midnight Standard Time - the time when the (fictional) mean sun crosses the longitude line half-way around the world from the longitude line at the center of our own time zone. Thus, the reference time for May 1 in the Eastern Time zone is 2400 EST May 1 (or equivalently, 0500 GMT May 2). Next, determine the lunar and solar apparent right ascensions for the reference times. These values can be found from an ephemeris or from the astronomical software available on many electronic bulletin boards. Although the solar right ascension does not change significantly from hour to hour, there is a fairly large variation in the lunar value - whence the need for selecting a reference time. Now note that at any moment, the difference between the sun's and moon's hour-angles equals the difference between the moon's and sun's apparent right ascensions: HA sun - HA moon = RA moon - RA sun Thus, by calculating this difference between the apparent right ascensions, we obtain a preliminary value for the lunar equation of time. When this value is added to the moon's hour-angle, which is obtained by reading the shadow on the moondial, we have the solar hour-angle, i.e. local apparent time. Now modify this initial value for the equation to account for the usual solar equation of time with which all dialists are familiar, and for the difference in longitude between the dial's location and the central meridian of the time zone. These are both normal adjustments which convert any traditional sundial reading from local apparent time first to local mean time and then to standard time. Finally, for convenience, add (or subtract) 12 hours to (from) the equation as it now stands. This modification allows us, for example, to interpret what is normally the 10am line on the sundial as 10pm, and the noon line thus becomes the hour-line for midnight. We now have a lunar equation of time calculated for the moment of midnight standard time in the dial's time zone. This value should work very well close to midnight; however, the never very well-behaved moon rapidly introduces errors. To improve accuracy at other times of night, make an additional adjustment, after the lunar equation has been applied to the reading, by subtracting 2 minutes for each hour that the result falls before midnight and adding 2 minutes for each hour after midnight. This adjustment, which works well enough over short periods, is based on the traditional rule of thumb which forms the basis for older moondial treatments: the moon's elongation from the sun increases on average by 48 minutes in each 24 hour period. All of these adjustments are incorporated into the executable program included with this issue of the Digital COMPENDIUM. A listing of the QuickBASIC source code for the program is also included. The program produces a monthly table for the lunar equation of time and displays a worked example of its use. With this equation and final adjustment, the dialist should be able to get much improved accuracy from a moondial on any bright moon-lit night. Of course, for about half the nights in any given month, before and after the new moon, there will not be enough light from the moon even to take a reading (these nights are roughly those shown in red on the digital moondial chart). But for those nights when a near full moon shining brightly through the window wakes you from a sound sleep, you can now use your favorite dial to tell you how many hours you have before the alarm goes off and the 20th century intrudes again on your dialing reverie. Closing Reflection Having now finished presenting the intended material for this article, I feel compelled to make a confession to the reader: Midway through the preparation it occurred to me that a good case could be made for the charge that contriving a celestial billiard game, banking rays of light off the moon and down to a dial - all in order to keep track of our night hours, may yet be a step up in arrogance. Perhaps there is no escaping our baser nature! ---------------------------------- As an example, suppose on the night of June 21, 1994 we have a moondial reading of 11:35 a.m. at longitude 72 degrees in the Eastern time zone. Recall that what would be an a.m. reading on a sundial becomes p.m. on the moondial. The digital moon chart lists an equation for this date and location of -1:24, thus correcting the original reading to 10:11 p.m. This adjustment includes allowance for the solar equation and for the 3 degree (i.e. 12 minute) difference between the dial's longitude and the central meridian (75 degrees) of the time zone. Making a final adjustment of -4 minutes (since the first result is approximately 2 hours before midnight) yields a time of 10:07 p.m. Eastern Standard Time. Reading 11:35 (a.m. converted to p.m.) Equation -1:24 ________ First Result 10:11 p.m. Adjustment -0:04 ________ 10:07 p.m. Eastern Standard Time Thus, a total correction of -1:28 is applied to the 11:35 reading to obtain the time 10:07 p.m. In order to see how close this result is to a precisely calculated value, we can refer to an ephemeris, first, to find that at 10:07 p.m. on that date the apparent right ascensions are as follows: Moon 16:42:57 Sun 06:02:08 ________ Diff. 10:40:49 =====>> -1:19:11 (by subtracting 12 hours) Also, at this date, time and longitude, the local apparent time (corresponding to the sun's hour angle) is found by subtracting from Eastern Standard Time 1 minute 50 seconds for the solar equation of time and adding 12 minutes for the longitude difference, to obtain the result 10:17:10 p.m. Now subtracting the difference between the right ascensions yields an hour angle for the moon corresponding to 11:36:21, very close to the 11:35 reading with which this example began. Thus, in this case, the procedure produces a value with an error of less than 1.5 minutes. ====== Date: Thu, 14 Jan 1999 18:28:42 -0500 From: Patrick Powers <[EMAIL PROTECTED]> ...there are a few examples of moon dials - the most famous in the UK is the one at Queens College Cambridge (though I believe the Nuremburg Diptych dials carry them too). On the Queens College dial there is a table of 'hours correction' versus 'age of the moon, in days'. This is simply applied to the observed reading to convert moon time to apparent solar time. One then applies the EoT to get clock time. This process is not at all accurate and, except perhaps at the moment of full moon, is not likely to be something on which you would like to depend for an appointment! An interesting point is that the Queens College table is designed so that the correction is always added whereas I believe that on other moon dials may have to be added or subtracted. There is an interesting article in the BSS Bulletin (No.97.1 January 1997, p37) by Ing JTRC Schepman of the Netherlands entitled "How to determine time by Moonlight". In this article the author discusses these correction tables but also describes a simple analogue instrument to convert lunar indication to apparent solar time - it consists of concentric disks - and you may wish to refer to that article. Also, if you are able to get to Cambridge or can write to the Head Porter to buy a copy, you might wish to read the blurb in the Queens College leaflet on the dial - that too describes the way in which the simple table works. This dial was also discussed (albeit rather derogatorily I thought!) by the late Charles Aked in the BSS Bulletin 94.3 October 1994. There was another article in a BSS Bulletin (I think - though it may have been in the NASS Compendium, my memory is not clear! - about the ease (or otherwise!) by which a 'moon EoT' might be derived but I cannot find that at the moment. I suspect that these ideas only work on dials that use hour angle or azimuth. Patrick _______________________________________ Peter Abrahams [EMAIL PROTECTED] The history of the telescope & the binocular: http://www.europa.com/~telscope/binotele.htm
