At 08:24 AM 1/13/99 -0700, Philip P. Pappas, II wrote: >Dear Roger Baily, Arthur Carlson and Fred Sawyer, > >I am still in doubt whether to use the E.O.T. Would you please reconsider >your answers knowing that I'm trying to keep it simple for my sundial customers? > >Thanks again, > >John Carmichael > Dear John,
I think I found a way to tame the moon monsters. The solution is in the "Astronomy Lab" program and may be in Tide Tables! I was experimenting with the shareware program "Astronomy Lab". One calculation that this program plots is the "Moon Angular Speed" in degrees per day. This is the lunar equation of time we have been looking for. In minutes rather than degrees, the variation is up to 14 minutes on top of the 48 minute average daily correction that we have been quoting. The moon's equation of time is the variation on that average angular speed. The graph shows this well as the sum of two periodic cycles. The major cycle is the monthly lunar cycle. The moon speeds up when it is closest to the earth (perigee) and slows down when it is most distant (apogee). The cycle ranges from about 11.8 degrees (47 min) to 14.2 degrees (57 min). A yearly cycle is added to that giving maximum peaks of 15.4 degrees (61min) when the full or new moon (lunation) is in phase with the lunar orbital cycle. Arthur C. noted the connection between the lunar and solar (year) cycles. I am sorry for trying to describe this dual frequency harmonic sinusoidal curve in words but the graph could not be printed or saved in the trial version of the program I have. You will have to download the program to see for yourself. The graph would be a useful addition to your operating manual. The problem that you will still have is knowing when to start the correction cycle. Arthur C. and I both mentioned the error due to the timing of the full or new moon. The start of the equation of time cycle is different point. To start this cycle you need to know when the moon is at perigee or apogee. This is not an easy problem but there is another solution. Tide Tables. Tides are caused by the same lunar and solar cycles. The same harmonic in phase and out of phase phenomenon that causes neap and spring tides apply to the time correction. The height of the high, high tide will correspond to the high high equation of time. Some really smart person could automate this. Mount the moon dial on a well connected to the sea. The height of water in the well would vary with the tides. This could be used to drive a mechanism to shift the dial to correct for the lunar equation of time. Do I have an invention here? Rube Goldberg probably beat me to the patent office. Roger Bailey Walking Shadow Designs N 51 W115 and 1000 km from tide water.
