# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Lunar trouble, need help
From: Kent Nordstr�m
Date: 2008 Jul 5, 13:19 +0200

```Georeg wrote [5635]: The next point of issue is the Moon parallax. Kent
writes "It is unclear how
George measured his local parallax"

It's simple enough. See navlist [5530]. We agree precisely on the figure for
Moon HP, quoted by Kent to be 56m 36.5s, and by me, from Skymap, to be
.9435�, which works out as 56.61', or 56m 36.6. Can't expect much better
than that!

Yes, I have taken the moon's HP from Umland. But it might be a little
confusion here so let me try to explain how I calculate the moon's parallax.
Firstly, George is right about the value. The error in calculation is on me
(very embarassing) but the good news is that the model seems to calculate
correct.
I used 61d 41m 4,19s as (wrong) input data which gave 26m 50.39s. The input
should have been 60d 41m 04,19s.  When using this the parallax will be 26m
42,3s (George 26m 44s). So it seems that we don't have a disagrement here.

What my model does is as per below. As can be seen the calculation includes
two corrections for earth flatness (maybe a better English term is
oblateness?):
- find the azimuth to the moon
- find the difference between the geographic and geocentric latitude
- multiply  this difference with cosine for the azimuth
The azimuth is approx. 111d and the diff. between the latitudes is 5m 45s.
The product is +2m 6,46s, which gives a "local altitide" of  60d 38m 57,73s
+ 2m 6,46s =  60d 41m 04,19s to be used for parallax calculation. Due to the
earth oblateness the value is added to the true local altitude if the
azimuth is greater than 90d (the moon is pointing away from the pole),
otherwise the value is negative.

Next is a small correction to the moon's HP with the arguments latitude and
HP. This gives a "HP" of 56m 36s - correction 0,78s = 56m 35,22s.

Now the parallax is calculated as arcsine (sine "HP" x cosine "local
altitide") = arcsine ( sine 56m 35,22s x cosine 60d 41m 04,19s ) = 27m 42,3s
(George 27m 44s).

Geroge wrote:  Kent has ignored the augmentation factor, which allows for
the fact that an
observer is significantly closer to the Moon, when it's high in the sky,
than when its near the horizon. Indeed, he has taken "augmentation of Moon's
semidiameter" into account, in making an exact calculation of Moon's
altitude corrections (but when that has little or no influence on the final
lunar distance) but neglected to do so in correcting the lunar distance for
semidiameters (when it's crucial).

I am not sure I understand this comment. So again let me try to explain what
my model does for the moon.

The measured altitude is corrected for dip and the moon's semi-diameter:
61d 05m 16,4s - dip 10m 10,9s - SD 15m 25s = 60d 39m 40,5 s.
To this two corrections are done:
- augmentation of -13,3 s. The minus sign depends on the measurement of the
UL.
- refraction correction of + 0,34s (diff .in refraction form UL to
geocentre).

For finding the apparent distance (what I believe George defines as d) my
model does the following:
Obs. distance + corr. for index error +/- SD for the moon +/-SD for the sun
(if used) +/- corr. for augmentation of the moon +/- refraction correction
for the moon +/- refraction correction for the sun (if used). The correction
for augmentation is based on the arguments moon's semi-diameter and apparent
altitude. Is this what George means... "but neglected to do so in correcting
the lunar distance for semidiameters (when it's crucial)."??? Is the
"augmentation factor "someting else?

Georeg wrote: Kent doesn't hasn't yet told us what actual values he puts in
for his Sun
and Moon refraction, or his Sun parallax, and we need to know these for a
comparison (or at least, know how they are somehow to be included into the
lunar distance calculation.).

My input data were:
- moon's refraction -29,82s
- sun's refraction -1m 21s
- sun parallax 7,3s

Kent N

----- Original Message -----
From: "George Huxtable"
To:
Sent: Wednesday, July 02, 2008 10:49 PM
Subject: [NavList 5635] Re: Lunar trouble, need help

I can see why the Kent's correction to the lunar distance for semidiameters
differs, by a fraction of an arc-minute, from my own.

We agree about Sun semidiameter, but differ, a bit, about the Moon's.

Kent used-

Sun SD: 15m 45s
Moon SD: 15m 25s

whereas mine were (translated into the same units)-

Sun SD. 15m45s
Moon SD (as seen from Earth's centre) 15m 25s
Moon SD (augmented, to allow for altitude of 61 and-a-bit degrees) 15m 39s.

Kent has ignored the augmentation factor, which allows for the fact that an
observer is significantly closer to the Moon, when it's high in the sky,
than when its near the horizon. Indeed, he has taken "augmentation of Moon's
semidiameter" into account, in making an exact calculation of Moon's
altitude corrections (but when that has little or no influence on the final
lunar distance) but neglected to do so in correcting the lunar distance for
semidiameters (when it's crucial).

Kent has simply taken the semidiameters from Henning Umland's website, but
as Umland doesn't know the altitude at which the Moon was being measured
(because it depends on where the measurement is being made from), that
correction has be applied next, by him.

If Kent recalculates, taking augmentation into account, I suggest that he
will find perfect agreement between us, at least as far as the lunar
distance corrected for semidiameters.

Perhaps we can draw a line under that one, and go on to the next discrepancy
between us.

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

The next point of issue is the Moon parallax. Kent writes "It is unclear how
George measured his local parallax"

It's simple enough. See navlist [5530]. We agree precisely on the figure for
Moon HP, quoted by Kent to be 56m 36.5s, and by me, from Skymap, to be
.9435�, which works out as 56.61', or 56m 36.6. Can't expect much better
than that!

Now, if we're bothered to, we can make the correction for the reduction in
the Moon's HP on account of the spheroidal shape of the Earth, described by
Kent as "Earth flattening". At such a low latitude of 15�, this amounts to
only .01' (taken from a table in a modern Norie's), so we end up with a
corrected HP of 56.60'

Then multiply that by cos alt, to get the actual parallax at that altitude.
True altitude of the Moon's centre, after allowing for dip and semidiameter,
I get to be 60.6523�, or 60� 39' 08' in Kent's notation. This gives me Moon
parallax of 27.74', or 27' 44". That has to be compared with the figure Kent
quotes of 26m 50.39s. There's a significant difference here, of getting on
for a whole minute, so my next question is : exactly how did Kent arrive at
a Moon parallax of 26m 50.39, starting from an HP of 56m 36.5s?

Kent doesn't hasn't yet told us what actual values he puts in for his Sun
and Moon refraction, or his Sun parallax, and we need to know these for a
comparison (or at least, know how they are somehow to be included into the
lunar distance calculation.). Did Kent's final figure, for cleared lunar
distance, come from some tables, or from a log-trig calculation, or a
computer / calculator program, or what? Details would be of interest.

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.

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