----- Original Message ----- From: "Sean Barton" Sent: Wednesday, March 03, 2004 12:49 PM Subject: Re: Sunrise/Sunset Adjustment for Daylight Savings Time > Interpolate just means (for example) that if you know that it is 50 > Fahrenheit at 7 am and 60 Fahrenheit at 9 am then you can guess/interpolate > that the temperature at 8 am is 55 Fahrenheit. (Interpolate means that you > make a mathematical approximation using the information you have available). > > > ----- Original Message ----- > To: "Sean Barton" > Sent: Tuesday, March 02, 2004 11:20 PM > Subject: RE: Sunrise/Sunset Adjustment for Daylight Savings Time > > > What do you mean by 'interpolate the ecliptic longitude of the sun?' > ----- Original Message ----- From: "Sean Barton" Sent: Tuesday, March 16, 2004 11:59 AM Subject: Re: sunrise calculations > Ed, > > I imagine that the fractional difference between sunrise times of two days > > does not correspond percentage wise to the ecliptic longitude and that's why > > we need to do interpolating. Is this true? > This would actually give you a very good answer. What would be even better > (than doing the whole sunset calculation twice for neighboring days and > interpolating your final answer to be somewhere in between) is to instead > interpolate the mean ecliptic longitude of the sun. You can go ahead and do > this reasonably close without even doing the calculation the first time. > For example. If you want to do sunset on March 15 in the UT-6h time zone, > you can guess that sunset will be about 18:00 local time or 24:00 UT. So > the expected time of the event is %50 of the way from midday UT March 15 and > midday UT March 16. So in the table for ecliptic longitude of the sun, use > a value that is %50 of the way from March 15 to March 16. Once you have > done the whole calculation using this mean ecliptic longitude of the sun, > you may get a result of 17:25 local time or 23:25 UT. So instead of %50 > (the interpolating factor you used the first time) it would have been better > to use 685/1440 because 23:25 is 685/1440 of the way from midday March 15 to > midday March 16. > > ----- Original Message ----- > To: "Sean Barton" > Sent: Tuesday, March 16, 2004 9:45 AM > Subject: Re: sunrise calculations > > > After looking at your email and the website about a hundred times, I am > happy to tell you that I understand what you mean. What I don't know how > to > do is how to get the interpolating factor and to extract from that factor > the more accurate ecliptic longitude of the sun for the particular time of > day. I am new to this stuff and I even have the Astronomical Algorithms > book, but I'm real dizzy. > > I imagine that the fractional difference between sunrise times of two days > does not correspond percentage wise to the ecliptic longitude and that's > why > we need to do interpolating. Is this true? > > I really appreciate any assistance you can give me. > > ----- Original Message ----- > From: "Sean Barton" > Sent: Monday, March 15, 2004 5:11 PM > Subject: Re: sunrise calculations > > > This just means that you will need to intelligently "average" the values > for > the two closest days to come to a more exact value for the mean ecliptic > longitude of the sun for the particular time of day. (Remember mean > ecliptic longitude doesn't change suddenly from one day to the next but > is > gradually changing all the time.) When I can be of further assistance, > please let me know. > > > ----- Original Message ----- > Sent: Monday, March 15, 2004 9:34 AM > Subject: sunrise calculations > > > At the end of the calculations document you state the following: > > Now you should really interpolate the ecliptic longitude of the sun > and > do > the whole calculation again. > > Can you please email me how to do this. > > Thank you very much > > ----- Original Message ----- > Sent: Sunday, January 04, 2004 20:08 > Subject: Moonstick etc. > > > > Hello, > > > > I live at 42 degrees South, i.e. Hobart, Tasmania. I have been looking at > the Moonstick, Sunset dial, Lunawheel etc. and wondered if they are able to > be used in the Southern Hemisphere and, if not, do you have Southern > Hemisphere equivalents? > > > > Regards, ----- Original Message ----- From: "Sean Barton" Sent: Sunday, January 04, 2004 9:14 PM Subject: Re: Moonstick etc. > On the moonstick and lunawheel, moon phase symbols are the standard symbols > (e.g. first quarter lighted on the right). The symbols will predictably > match the appearance of the moon from the north pole of the Earth only. On > the equator, the symbol's right or left is often seen in the moon as either > up or down. In the southern hemisphere, it is more fully reversed. So the > only adaptation required the make the moonstick and lunawheel preferable to > the southern hemisphere instead of the northern is to reverse right and left > on the moon phase symbols. The sunsetwheel is completely universal and > works worldwide. When you have more questions, please let me know. > ----- Original Message ----- > Sent: Thursday, January 29, 2004 10:03 AM > Subject: Confused about February 2004 full Moon > > > > Hi Moonstick: > > I've confused myself trying to reconcile the USNO full Moon predition > (http://aa.usno.navy.mil/data/docs/MoonPhase.html#y2004) of 08:47 UTC on > February 6 2004 and the time I get from the LunaWheel. > > > > Are the day number labels at the 1200 UTC tick marks for each day? If so, > I read the time of the full Moon as 2100 UTC on the 5th. > > > > Thanks for your help! ----- Original Message ----- From: "Sean Barton" Sent: Thursday, January 29, 2004 12:00 PM Subject: Re: Confused about February 2004 full Moon > Hi Will, > > The lunawheel computes mean moon phase as defined in the specs of the > moonstick instructions > (http://www.moonstick.com/moonstick_instructions.pdf). Many almanacs report > moon phase based on apparent ecliptic longitude differences between the moon > and sun. The difference between the former and the latter can be compared > to the difference between clock time and sundial time (before the equation > of time correction is applied). It may be helpful to view the following > document. http://www.moonstick.com/MSSI.pdf Also, the attached (below) > answer to a question similar to yours may help further. When I can be of > further assistance, please let me know. Thank you for your continued > interest. > ----- Original Message ----- > From: "Sean Barton" > Sent: Saturday, October 28, 2000 11:22 AM > Subject: Fw: Moonsticks / Accuracy > > ... > > I'll draw and analogy from the equation of time, something you are probably > more familiar with. The equation of time basically comes from two > components. One having a frequency of six months. The other having a > frequency of slightly longer than one year. Actually, about 21000 cycles > makes 21001 years. The "six month" component comes from the tilt of the > Earth's axis and thus its synchronized with the seasons for all time. This > correction is approximately as follows. MLoS is mean longitude of sun. > 6MCoEoT is six month component of the equation of time. AD is approximate > date. > MLoS 6MCoEoT AD > 000° ±00m Mar 22 > 045° -10m May 7 > 090° ±00m Jun 21 > 135° +10m Aug 6 > 180° ±00m Sep 21 > 225° -10m Nov 5 > 270° ±00m Dec 21 > 315° +10m Feb 5 > 360° ±00m Mar 22 > > The "about one year" component is due to the ellipticity of the Earth's > orbit and thus follows Earth's perihelion as it moves through the seasons > over the course of about 21000 years. Last I checked, the perihelion was > about Jan 3. Over about 60 years, it will slowly advance to Jan 4 and then > Jan 5 and after about 21000 years, will get all the way around back to Jan > 3. Here is this correction tabulated approximately. > MAoS: mean anomaly of the sun > A1YCoEoT: about one year component of the equation of time > ADiY2K: approximate date in the year 2000 > MAoS A1YCoEoT ADiY2K > 000° ±00m Jan 3 > 045° +05m Feb 18 > 090° +08m Apr 4 > 135° +05m May 20 > 180° ±00m Jul 4 > 225° -05m Aug 19 > 270° -08m Oct 4 > 315° -05m Nov 18 > 360° ±00m Jan 3 > > So once you know the reading from the sundial and the equation of time, you > just add them together to get "watch time" or mean time. > > Sundial time can be thought of as "apparent time" while watch time can be > thought of as "mean time". To speak of "true time" is ambiguous. > > Now let me see if I can parallel all of this talk about time over to moon > phase. Analogously there would be two types of moon phase, "apparent moon > phase" and "mean moon phase". (Actually, what is commonly found tabulated > in almanacs is akin to the former, but technically is neither of these.) > You would define apparent moon phase as the time difference between transit > of the moon and sun. Same as the time difference of the sun shadow and moon > shadow on a sundial. So, for example, when the sun shadow reads 18h11m and > the moon shadow reads 12h11m you could say that the "apparent moon phase" is > exactly first quarter. ("Apparent moon phase" is based on right ascension > differences. Almanacs commonly tabulate based on ecliptic longitude > differences.) > "Mean moon phase", on the other hand, would be what you would achieve after > you applied the "equation of moon phase" to the "apparent moon phase". It > would agree exactly with the moon phase indicators found on wrist watches > (and the calculations of the moonstick). > > The appropriate "equation of moon phase" to be applied to the "almanac" moon > phase to achieve the "mean moon phase" is the negative of what you found > here, http://www.moonstick.com/MSSI.pdf. Like the equation of time, it also > has two components. The "about one year" component is actually the same one > that is found in the equation of time except that instead of having an > amplitude of about 8 minutes, it has an amplitude of about 4 hours (because > the month is about 30 times longer than the day). The other component has a > frequency of about one month and an amplitude of about 12 hours. It is due > to the ellipticity of the moon's orbit and thus follows the perigee of the > moon which does not stay fixed with the seasons but rather advances on the > seasons by about one cycle in 9 years. Consequently, the "equation of moon > phase" would be more difficult to compute on the fly. The main obstacle > being the determination of the location of the lunar perigee (which follows > an 8.8... year cycle). > > As you can see, the moonstick is inaccurate and the almanacs are correct > only in the sense that clocks and watches are inaccurate and sundials are > correct. > > ... > ----- Original Message ----- > Sent: Tuesday, April 06, 2004 10:23 AM > Subject: moonrise/moonset question > > > I recently was studying a farmers almanac, looking at the moonrise and > moonset times, and noticed that the difference day to day changed quite > significantly. From 83 minutes to 22 minutes. Thanks in part to one of your > pages, I now understand why. The moon has an elliptical orbit. > > My Question is this: I looked at both the moonrise and moon set times and > the time differences were out of sync. That is, when the moonrise varied 83 > minutes day to day the moonset varied only by 36 minutes. How can this be? ----- Original Message ----- From: "Sean Barton" Sent: Tuesday, April 06, 2004 12:51 PM Subject: Re: moonrise/moonset question > Hi, > As the moon's declination (north/south position or latitude) changes, the > number of hours between moonrise and moonset change. For example, here > where I am at, (at about 30 degrees north latitude,) when the moon is 23 > degrees north or the equator, it is up (between moonrise and moonset) for > about 14.5 hours at a time. When the moon is at 23 south. It is up about > 10.5 hours at a time. This is in direct analogy with the sun and the > seasons and the varying length of the day. In summary, the ellipticity of > the moon's orbit causes both moonrise and moonset to move in the same > direction (both later or both earlier). The inclination (tilt) of the > moon's orbit relative to the equator of the Earth causes moonrise and > moonset to vary in opposite direction (i.e. one gets later and the other > gets earlier). When I can be of further assistance, please let me know. ----- Original Message ----- Sent: Thursday, April 15, 2004 2:22 PM Subject: lunawheel, moonstick scale design > Concerning the date markings on both the lunawheel and the moonstick: In > checking events (lunar eclipse vs full moon, Oct. 2004) both devices give > the same result but I am confused by the day markings. Does a line labeled, > for example, the 15th of the month indicate noon the 15th with the long > index lines between the numbers indicating midnight OR does the numbered > line indicate midnight (15.0)?? Colored interval on the day scale of the > lunawheel seem to indicate numbered lines mark noon. Time of the event seem > to indicate numbered lines mark midnight at the beginning of the day (i.e., > 15 = 15.0 = midnight; and noon the 15th = 15.5). I have assumed all events > in UT on the devise with appropriate shifts for longitude needed to get > local times. ----- Original Message ----- From: "Sean Barton" Sent: Friday, April 16, 2004 9:28 AM Subject: Re: lunawheel, moonstick scale design > Hi, > The numbered lines are the centers of each day (noon). The long lines > represent midnight. ----- Original Message ----- Sent: Monday, April 19, 2004 2:13 PM Subject: moonrise, moonset calculation question > Can you please answer this question?: > How can the moonrise and moonset times be calculated by an exact formula,using the 5 basic types of lunar month?: > sidereal month: 27.321661547 + 0.000000001857*y days > tropical month: 27.321582241 + 0.000000001506*y days > anomalistic month: 27.554549878 - 0.000000010390*y days > draconic month: 27.212220817 + 0.000000003833*y days > synodic month: 29.530588853 + 0.000000002162*y days > > Regards, ----- Original Message ----- From: "Sean Barton" Sent: Monday, April 19, 2004 3:07 PM Subject: Re: moonrise, moonset calculation question > Hi, > The position in the tropical month will give you a first estimate of the > declination (latitude) of the moon. The position in the draconic month will > give you a further improvement on this first estimate (a correction of up to > 5 degrees). The position in the synodic month will give you a first > estimate of the hour angle (local time of meridian transit) of the moon. > The position in the anomalistic month will give you a further correction to > this first estimate (a correction of up to 6 degrees). The position in the > sidereal month gives you a first estimate of the "sidereal" hour angle or > right ascension of the moon and would be used for getting a first estimate > of the "sidereal" time of rise and set (something that you are probably not > interested in). The position in the sidereal month is useful for getting > sidereal time of rise and set but not for "regular" time. The basic idea is > that once you are reasonably sure where the moon is (declination and hour > angle) you need only determine when the rotation of the Earth brings you > within 90 degrees (geocentrically) of this location (this is when the moon > will rise). There is not a lot more detail I can give you here without > going to considerable effort. I might suggest that you get a copy of > http://www.amazon.com/exec/obidos/tg/detail/-/0160515106/ which is published > by the United States Naval Observatory. This includes detail far beyond the > patience of most people. It is highly numerical though and requires an > understanding of basic astronomy terminology. current through 2004-04-19 copyright (c) 2004 Sean Barton and respective question sources, all rights reserved