A list member was kind enough to point out an embarrasing error in my message. The Moon's orbit is much closer to Earth's orbital plane than it is to Earth's equatorial plane. (5 degrees or so). I apologize. I had to leave immediately after sending the message, so I simply typed my thoughts as they came rather than verifying first.
The gist of the message remains the same. The Moon isn't equivalent to other celestial bodies in relation to EoT because it is the only heavenly body that is for all intents and purposes a part of Earth. (Earth and Moon both orbit the Sun revolving around a common point, to be precise.) A sundial on the Moon would have its own EoT that would be cousin to Earth's EoT, I'm thinking. Calculating variations in the Moon's apparent motions is a whole new ballgame.
The five degree tilt of the Moon's orbit is still an issue to consider, I think. If I remember correctly, the nodes of the Moon's orbit "slide" around Earth in an 18 year cycle, or something to that effect. The image in my mind is of a hula-hoop rotating around a beach ball. This may be one reason the Moon as a timekeeper provides notoriously vague results.
Again, I've been researching much of this online for a moon dial that I want to build, but I haven't actually built a moon dial yet and haven't come close to finalizing the moon dial specs yet, so please don't take my word for it. My intent was to point out some issues that I think should be considered when designing a moon dial. Better to consider the issues now, rather than after the dial is designed and built!
Feel free to correct any errors, or e-mail me directly.
Albert Franco
Albert Franco <[EMAIL PROTECTED]> wrote:
I've never built a Moon dial or even a sundial beyond "classroom project" phase, but I do have a well studied understanding of celestial motion and mathematics, so I'll go ahead and give my perspective. I have researched moon dialing, sun dialing and general celestial motions quite a bit in the past year.Earth's Elliptical OrbitBecause EoT is in part derived from the speed of Earth in orbit in relation to the Sun, I'm thinking that it couldn't be applied to Moon time. Although many of the same forces and effects will apply to Moon time, it won't be the same graph for the Moon as it will for other celestial bodies. Earth must rotate more than 360 degrees to see a celestial object in the same place in the sky approximately 24 hours later. Also, Earth's speed in orbit changes. These reasons explain the "left and right" changes in the figure eight analemma that graphically represents EoT. Because the Moon travels along with Earth, I don't think Earth's speed in orbit will have the same effect as it does in regards to all other celestial bodies. Because the Moon's orbit around Earth is more or less in Earth's equatorial plane, and not in the plane of Earth-Sun orbit, I don't think the effect of turning more than 360 degrees will have the same effect either.Tilt of Earth's AxisThe 23.45 degree tilt of Earth with respect to it's orbit (and thus with respect to the plane of the Sun/Earth orbit) also contributes to EoT. Again, this tilt is in relation to the Sun and all other celestial bodies as observed from Earth. But, the Moon orbits aruond Earth's equatorial plane (generally), and so the tilt of Earth doesn't have even close to the same effect on the Moon as it does on all other celestial bodies. In fact, I would go so far as to say that the Moon is really a part of Earth, from a celestial perspective, and from an EoT perspective.Analemma.com provides an explanation of EoT that clearly explains the two reasons for my perspective:Another source of info, including Keplarian Elements for the Moon, is the Links section at The Yahoo Group. (Before I knew about Sundial Mailing List I created the group, and now it is used as my "online Bookmarks" for all things related to dialing.) There are 10 or 12 Moon links there, and some will probably be useful for your project:Night Sky Celestial "Clock face"For information on a method of viewing the Big Dipper as an hour hand, you can visit my website linked below my name. It is two weeks old, and many design and content changes will occur in the next six months to a year. It also is primarily intended as an online starting place for myself, no matter where I am. So don't judge too harshly!Sunny skies,Albert Franco35.03 N95.53 Wheiner thiessen <[EMAIL PROTECTED]> wrote:Dear Louise,Yes , EoT applies to all dial readings, whetherby the Sun, the Moon or any stars or planets.EoT refers to the speed of the earth's rotation and sothe sky with all its heavenly objects tells you aboutlocal apparent time.But your 48 minute rule is very much 'rule of thumb'.If you wanted a dial for your latitudes that uses the night skyit would be much better to use the principle of hour angleson the equatorial plane for the moon, or even better the differencein hour angles between Sun and Moon or between Sun and anystars of your choice.I designed a celestial ring dial which was featured inthe BSS June 2003. It does not use the shadow ofthe Moon but its hour angle in the equatorial plane.Good luck.Heiner51N/ 1W----- Original Message -----From: Louise RigozziSent: Monday, November 03, 2003 9:24 PMSubject: Moon chart question from new memberDear Sundial Mailing List members,
I have just joined the list and have quite a tricky question to ask already! I am working with Tony from Lindisfarne Sundials in England to create a sundial at a very high latitude (78 degrees) and I am including a correction graph for reading from the moon's shadow. This is because for three to four months of the year there will be little or no sun. I have made the graph illustrate the principle that the moon is 48 minutes 'fast' each day before the full moon and 48 minutes 'slow' each day after it. The graph hopefully gives the idea that the more precise you can be with the number of days (and even half or quarter days) you are from the full moon, the more accurate your reading will be. If anyone is interested in seeing it, I can JPEG it to you. My main question is, after adding/subtracting the hours and minutes from the reading of the moon's shadow, whether you then need to add/subtract the minutes according to the Equation of Time (! ! ! which will also be shown on the dial face) for that day of the year. Thanks! Louise Rigozzi
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