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Re: Easy Lunars in 1790
From: Ken Muldrew
Date: 2006 Apr 27, 13:38 -0600
From: Ken Muldrew
Date: 2006 Apr 27, 13:38 -0600
On 27 Apr 2006 at 11:34, Alexandre E Eremenko wrote: > Could you post the data of your lunars? > GMt, DR position, sextant reading, and IC > and the brand of sextant used? > > How your error in longitude compares with Thompson's? > Can you tell what part of the error comes from Thompson's > almanac and reduction and what part comes from observation? I don't have those particular calculations handy as they are at home (and I just did the clearing; I haven't compared Thompson's error with the almanac error for those sights). However, I pulled up one that I looked at last year from an excel file as it will provide an example of Thompson's errors. He used a Dolland brass sextant of 10" radius with a vernier divided to 15". His DR position can be back calculated using the almanac data below but I haven't done it for this case. From Thompson's notebook: Feb 17, 1801 - Aldebaran Sun RA 22?01'17" Moon RA 29?01'50" Dec 15?05'03"N SD 15'10" HP 56'10" Sun TA 51?56'10" Sun AA 51?56'10" Moon TA 33?56'48" Moon AA 33?11'26" D 35?53'06" Temperature -6?F Longitude 114?39'00"W Witchell's method corrections: Corect'n 1 -12" Corect'n 2 -51'42" Corect'n 3 12" time of sight moon FL to aldebaran hr| min| sec| deg | min| sec 7 | 35 | 25 | 37 | 03 | 00 ....36 | 25 |.......02 | 30 ....37 | 22 |.......01 | 25 ....38 | 16 |.......01 | 15 ....39 | 11 |..........| 45 ....40 | 12 |..........| 15 7 | 37 | 48 | 37 | 01 | 35 | avg ...-19 |-44 |....| -21 |-19 | watch & index errors 7 | 18 | 4 | 36 | 40 | 16 time of sight procyon hr| min| sec| deg | min| sec 7 | 45 | 01 | 75 | 08 | 15 ....46 | 06 |.......20 | 15 ....47 | 03 |.......31 | 15 7 | 46 | 04 | 75 | 19 | 55 | avg ...-19 |-44 |....| -21 |-19 | watch & index errors 7 | 26 | 20 | 74 | 58 | 36 The watch error is calculated from the time sight and then put back into the tabular results (so he calculates the local apparent time when the altitude of Procyon is 7?26'20", compares that to the watch time that he wrote down and then gets a correction). That correction is then put back into the lunar data to get the proper time for his lunar shot. d 36?24'55" at 7h18m04s LAT 1801 Almanac lunar distance (GAT) 12:00 37?22'31"....15:00 35?51'25" JPL lunar distance 12:00 37?23'19"....15:00 35?52'16" D 35?53'06" GAT from 1801 almanac: 14h56m40s GAT from JPL data: 14h58m21s LAT 7h18m04s Longitude from almanac: 114?39'06"W Longitude from JPL data: 115?04'17"W If we clear the distance using a calculator, then we get: D 35?53'16" resulting in: GAT from 1801 almanac: 14h56m18s GAT from JPL data: 14h57m59s LAT 7h18m04s Longitude from almanac: 114?33'44"W Longitude from JPL data: 114?58'54"W True longitude (modern survey): 114?58'50" So if Thompson had an almanac based on a better theory of the moon as well as a calculator to clear his lunar more precisely, his longitude would only have been off by 4" ;-) But seriously, when we looked at a bunch of Thompson's lunars last year (the posts are in the archives) we found that his standard deviation was 20' (in longitude) using the old almanacs and would have been 14' if he had the JPL data, so not bad but not great. But we do have to consider that he got this sextant in 1792 and there was much rough travel in the interim (perhaps 30,000 miles by canoe, horseback, dogsled, and foot). There are instances in his journals where his canoe is overturned in whitewater and the sextant has to be fished out downstream. Sometimes he has to rely on other fur traders to carry his sextant (a practice so abhorent that he notes it in his journals). He had no opportunity to have the instrument serviced so one has to be impressed with the performance he coaxed from the instrument. Note: I haven't corrected the data for temperature or pressure (his altitude above sea level was about 3250 ft.). Ken Muldrew.