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This relates to a posting, back in July, by Jeremy, in which he recalled his 
first lunar, which was taken somewhere, only vaguely specified, in the 
Caribbean.

Frank Reed proposed that it could be resolved, by trial and error, from his 
lunar calculator, at http://www.clockwk.com/lunars/lunars_v4.html . And 
indeed it could, as he demonstrated. But that calculator is by no means 
user-friendly for that purpose, being intended for a rather different job, 
that of finding the angular error in a measured lunar distance, taken from a 
known position.

I have used that lunar calculator several times, for various purposes, and 
found it to be useful and accurate.

I will discuss here the difficulties that use of the calculator presents, in 
obtaining longitude, and how it might be improved to serve that purpose 
better.

Frank provided these parameters as the solution to Jeremy's observations, 
without explaining the trial-and-error process he had used to get there. I 
will list these numbers in the order they are to be entered into his 
calculator.

DR Lat 14�  31'  N
DR Lon 61� 38.1' W
Body - Jupiter
January 26 1999
22 19 30 GMT
Distance 68� 19.4'  near.

When you press "calculate", the program comes up with-

Error in lunar 0'
Approximate error in longitude 0� 00.8'

So that DR longitude of 61� 38.1' is confirmed by the lunar observation, to 
good accuracy.

What if we happened to start with a different value of DR longitude?

Say, instead, we chose a longitude 1 degree further West, at 62� 38.1' W, 
keeping all the other parameters unchanged. The lunar calculator tells us-

Error in lunar -0.9'
Approximate error in longitude 0� 25.9'

and if we chose a longitude 1 degree further East, at 60� 38.1, the 
calculator gives-

Error in lunar 0.9'
Approximate error in longitude 0� 27.7'

====================

There are a few things to notice about these results.

First, differing directions of error in the DR longitude, East or West of 
the correct value, result in different signs of the error in the lunar 
distance, just as they should. But they don't provide different directions 
for the derived "approximate error in longitude". Just the magnitude of that 
error is supplied, its direction has been suppressed. So it isn't obvious 
which way the user should adjust his DR value to home in on a better answer. 
It's quite a complicated business, applying pure logic to work that out, 
because it depends on which side, East or West, of the Moon the other-body 
is, and therefore, whether the lunar distance should increase or decrease 
with time. The user has to make a trial change, to discover which way the 
error moves. Quite possible, but awkward and unnecessary.

Second, the amount of the error is way out from what one would expect; less 
than half of it. If a change in DR longitude of 1 degree is made from the 
correct value, one would hope the lunar observation to result in a perceived 
error of 1 degree, approximately so at least, and not a value that's less 
than half a degree.

If a user has started with a DR of 62� 38.1' W, and obtained that calculated 
error of 25.9', what will he do as a result? He will apply that as a 
correction to his initial value, once he has discovered which direction to 
apply it, so will subtract it from his initial DR, to give a new DR of 62� 
12.2' W, and then repeat the calculation, to give-.
Error in lunar -0.5'
Approximate error in longitude 0� 14.4.

So he has halved the error, and by continuing to reiterate in this way, the 
resulting error will halve each time round. It works, but it's an awkward 
way to do that job, when it could be done in a single step.

The reason for this behaviour relates to the simplified calculation of 
longitude error from lunar-distance error, which is presumably why the word 
"approximate" has been attached to it. Frank has told us that longitude 
errors are taken, always, to be 30x the lunar distance errors, which is only 
approximately true under certain circumstances. The Moon's angular speed 
through the stars changes; the lunar distance target body may misalign with 
the direction of the Moon's motion; and particularly, "parallactic 
retardation" may play a big part. It seems that this example may be a bad 
case, where lunar distance is particularly insensitive as a measure of 
longitude. Perhaps a factor of more than 60x is appropriate in this case, 
rather than the 30x that has been assumed. I am rather surprised that such 
large discrepancies occur.

So it seems to me that there would be real value in calculating a realistic 
factor for the sensitivity of a lunar, rathan then simply using an adopted 
value. That probably involves doung the calculation twice, for two 
slightly-different times, to determine that sensitivity factor. In a 
previous message, Frank has accepted that such a change would do some good, 
and has considered putting it into effect. I would encourage him to do so.

Then knowing that sensitivity, the error in lunar distance, and the correct 
sign of the necessary adjustment, his lunar calculator could, in one go, 
take the DR longitude and correct it by the right amount, to provide a new 
corrected longitude in one go. That may be so close to the truth as to 
obviate any need for further iteration. All the information is there to do 
it.

Perhaps Frank will explain the trial and error process he adopted, to home 
in on the solution he arrived at.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

==============================================

----- Original Message ----- 
From: 
To: 
Sent: Wednesday, July 16, 2008 3:03 AM
Subject: [NavList 5852] Re: My first Lunar


|
| Jeremy, you wrote:
| "Well I found my first lunar, and it will be tricky.  Here's the data that 
I
| have.
|
| GMT Date is 26 January 1999.  GMT of the sight was about 2220.  Dip
| correction is -7.7' of arc.  The lunar was at evening twilight and a near
| limb observation between Jupiter and the Moon was taken.  The sextant LD 
is
| 68deg 19.4'  IC is 0.0'.  An upper limb altitude of the moon was taken HS 
is
| 66 deg 09.3'  The Hs of Jupiter is 45 deg 22.3.
|
| Here's the rub:  I have no idea where I was other then to say I was 
probably
| somewhere in the Eastern Caribbean.  Best guess is about 20 deg North
| Latitude and 70 degrees West Longitude."
|
| Having a good DR position is convenient but not necessary when it comes to
| clearing a lunar. Of course if you want to assess the accuracy of the 
sight,
| then you want the actual position and correct GMT as nearly as possible. 
You
| can figure out where you are, more or less, by trial and error from your
| sight data. Go to the calculator on my web site, set the GMT of the sight 
to
| 22:19:30 and set your DR Lat to 14d 31'N and your DR Lon to 61d 38.1W. 
That
| nearly matches your sights, lunar and altitudes, too. So assuming your
| observations were good (and I would bet they were) you were probably about
| 30 miles west of Martinique. Does that fit your recollection?
|
| Now as it happens, this is yet another one of this miraculous lunar sights
| where you can do the clearing without using any spherical trig. If we take
| the pre-cleared altitudes and distance (the altitudes of the objects'
| centers and the center-to-center lunar distance) and add them up, we get
| nearly 180 degrees. So adjust the Moon's altitude higher by about 24 
minutes
| of arc and then work it AS IF they were exactly opposite each other in the
| sky.
|
| -FER
|
|
|
| |
|
|
| No virus found in this incoming message.
| Checked by AVG - http://www.avg.com
| Version: 8.0.138 / Virus Database: 270.4.11/1553 - Release Date: 7/15/2008 
5:48 AM
|
|
| 


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