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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Longitude via lunar altitudes, simplified
From: Dave Walden
Date: 2007 Feb 13, 06:51 -0800
From: Dave Walden
Date: 2007 Feb 13, 06:51 -0800
I would suggest Letcher's Feb 1964 article in Yachting is the earliest "modern" rediscovery of the longitude by lunar altitude methods. As Frank points out, such methods were well known more than a hundred of years ago. The Ashe discussion is from: Monthly Notices of the Royal Asronomical Society, Vol XII, nov 1851-june 1852, page 179. (Available from Google books.) Many of the astronomy and navigation texts from the 1800's (and there are quite a large number on google books) have references to longitude by lunar altitudes. Since this was before LOP, most discuss only longitude assuming latitude by one of a number of other methods. See for example, New Methods of finding the Longitude at sea or on shore, by Yarrow and Lynn, 1826, also on google books. Below is an example using one of these methods with the data from Bennett's recent "Longitude from Lunar Altitudes Simplified". Outline: Find local hour angle of star given altitude, latitude, and declination of star. Find local sidereal time given LHA (sometimes t when measured +/-) and RA for star. Extend LST to time and place of lunar observation. Find LHA of moon given altitude, latitude, and declination of moon. Interpolate into RA of moon as a function of time to find time of RA that gives correct LST when combined with LHA. HAMEL@ 6 54 23 h L d 17.440000 41.258333 23.491667 fm sextant known lat alm dec cos t= 0.053432 calc fm h L d t(deg)= 86.937139 calc fm cos t t(hr)= 5.795809 calc fm t(deg) RA(hr)= 2.125222 fm almanac@6 54 23 lst(hr)=7.921031 55.261890 15.713400 min sec time dif st 2.246049 MOON@ 9 7 55 h L d 37.608333 41.401667 28.538333 fm sextant known lat alm dec cos t= 0.446633 calc fm h L d t= 63.472146 calc fm cos t t(hr)= 4.231476 13.888584 53.315014 lst(hr)=10.167081 10.024851 1.491079 required ra(hr)= 5.935604 56.136268 8.176065 required RA@9 0 0 89.008333 5.933889 56.033333 2.000000 RA@10 0 0 89.598333 5.973222 58.393333 23.600000 new time= 9.043616 2.616977 37.018614 delta time= -0.088328 -5.299690 -17.981386 Final answer, 5 min 18 sec vs published 5 min 47sec. As close as might be expected for the accuracies involved. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---