A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Longitude via lunar altitudes, simplified
From: Gary LaPook
Date: 2007 Feb 02, 17:09 -0800
From: Gary LaPook
Date: 2007 Feb 02, 17:09 -0800
Well, what a disappointment because I thought that I was the first one to think of this method, I have been playing with it for years. I conceptualized itthis way. Any two or three star fix will be fixed at the correct latitude and at the correct SHA and can be plotted on a chart labeled with SHA as opposed to longitude. This fix rotates around the world every 23 hours 56 minutes and 3.9 seconds always maintaining the correct latitude and a constant SHA. What then ties this fix in SHA to longitude is GHA aries which varies with time. Since the moon marches to the beat of a different drummer its position does not move in conjunction with the fix SHA when you vary your assumed time. So by iterating time you move the moon line till in coincides with the stellar fix and so determine the time and by that the GHA aries and so the longitude. The Starpath example used two planets but using stars is better because the moon moves slightly more rapidly in relationship to the stars than it does in relationship to the planets so you have a larger difference to work with. BTW this is the way GPS works. The onboard clock is not accurate enough to determine the time accurately enough to determine the orbital positions of the satellites which is necessary to determine the propagation delay of the GPS signal from the satellite to the observer. This is why you need a minimum of three satellites in view for the GPS to work. The system uses the same methodology, it adjusts the time base in steps until the third gps position line coincides with the two LOP fix derived from the other two satellites. On Jan 30, 6:46 pm, "Peter Fogg"
wrote: > Francis Chichester described a method of finding longitude and watch > correction from lunar altitudes ("Longitude Without Time"; *Journal of the > Institute of Navigation *, Vol. 19, 1966) that he apparently devised > independently, although it is said to have been earlier described by John > Letcher, best known for his work on self-steering systems. > > This method: longitude via lunar altitudes, has been discussed at least a > couple of times on this and/or the earlier Nav List. It tends to be less > accurate than the conventional method of lunar distances but has the > advantage of using familiar sight reduction methods. It requires the moon's > azimuth to be near to due east or west. > > The Starpath site: > > http://www.starpath.com/catalog/accessories/starpilot/lun_alt.htm > > describes the method, with an example, using the StarPilot calculator (based > on a Texas Instruments TI-86) and successive reiterations to achieve a > result. > > George Bennett has devised what he claims to be: "a simple method of ... > calculating longitude from lunar altitudes that does not require a > succession of approximations". > > This proposed method, with a worked example, has been published as: > "Longitude from Lunar Altitudes Simplified" in the *Journal of the Institute > of Navigation *, Vol. 53, No. 2, 2006. > > This article can be accessed by going to: > > http://gbennett.customer.netspace.net.au/ > > and then choosing the last option on the left: > > *Longitude from Lunar Altitudes Simplified* > > ** > > The following example of finding longitude and watch correction from lunar > altitudes contrasts the methods used by the Starpath site and that proposed > by Bennett. The symbols and sign conventions are Bennett's; the time, DR and > bodies used come from the Starpath example. > > Date 19th January 2000: DR position N47� 45�, W123� 05� > > Time Zone 8h W: Height of Eye 9 ft: Sextant Index Correction 0 > ** > *Observations and Calculations* > > * * > > Body Watch Time Obsd. Alt. Azimuth Int. > > Mars 17h 50 m 00 s 25� 04.9� 223.5� T18.2 > > Saturn 17 50 00 52 37.5 154.5 A3.3 > > Fix at 17h 50 m N47� 39.0�, W123� 35.1� > > Moon (LL) Observation at 17h 50 m 00 s Altitude 19� 30.2� > > *Moon Observation and Intercept Calculations * > > at 17 50m 00.0s, Latitude N47� 39.0�, > > Sextant Altitude 19� 30.2�. > > Watch Correction Longitude Intercept > Slow (+)10m(WS) W126� 05.1�(LS) T6.3(IS) > 0 (WF) W123 35.1(L0) T2.1(IF) > > Note: 10m = 2� 30� > > Azimuth of the Moon not required > > LS = W123� 35.1�+ 2� 30� = W126� 05.1� > > IS 6.3 > > F = --- = -- > > IS - IF 4.2 > > WS - WF = 10m LS - LF = 2� 30� > > *Required Watch Correction* > > ** > > WP = 10m - F x 10m = *- 5m 00s (Fast)* > > *Required Longitude* > > ** > > LP = W126� 05.1� - F x 2� 30� = *W122� 20�* > > * * > > Check: When the above watch correction and longitude is used with the > original data the intercept should be zero. ** > > *Starpath Values* > > ** > > *- 5m 12s (Fast) and W122� 17�* > > * * > > In the context of lunar observations these differences are of no > significance. > > The Starpath values, while similar, involve five pages of graphics.* * > > ** --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@googlegroups.com To unsubscribe, send email to NavListfirstname.lastname@example.org -~----------~----~----~----~------~----~------~--~---