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Re: Graphs of Lunar Distances.
From: Douglas Denny
Date: 2010 Oct 6, 17:09 -0700

Dear Frank,

Now having had a bit of time to look through the HP50 calculator programme for Lunar Distances and found teh slight error, I have re-calculated the results for Lunar distances on Saturday 25th Sept, and here are my corrected results as found for time measured by L.Dist for Jupiter; Capella and Vega against a known exact GMT.

All results are between plus one minute and two minutes in time of absolute, which suggests a systematic error of around one minute of time found which is within about half a minute of arc measurement absolute. Perhaps I am measuring Lunar distance angles with a sextant far better than I think I am capable of after all!

The programming error was, as you said would most likely be, a very simple and small slip... Very annoying once found; it took some considerable time to discover, as one keeps looking at it without seeing it.

It was with the built-in correction for refraction, which uses Bennett's formula, and which of course is in minutes of arc thus needs division by 60 before subtracting from the altitude in degrees. I had done this for the star altitude correction, but missed dividing by 60 in the refraction correction for the Moon's altitude (along with Par-in Alt). It has not made a huge difference to my previous results for LD converted to time as the altitudes are not so sensitive to slight variation either way for the end result of Lunar distance clearing.
What is more significant to me is they are now much closer together with all of them - remarkably so in fact, showing a better consistency in measuring than I thought possible.
---------

Results:-

MOON/JUPITER.

Moon/Jupiter. From Graph:
Observed distance to limb at 22HR-30'-00" was 34deg-12'.50
minus SD 14'.95 = 33deg-57'.55 observed LD.

Cleared LD = 33deg-53'.75
equiv = 22Hr-31'-47".7

An error of + 1min-47".7
----------------------------

MOON / JUPITER -
same measurements but using averages (arithmetic mean)

Observed distance to limb at 22Hr-29'-11" was 34deg-11'.96
minus SD 14.95 = observed LD of 33deg-57'.01

Cleared LD = 33deg-53'.19
equiv = 22Hr-30'-40".4

An error of 1min -29".4
-----------------------------

MOON / CAPELLA
from graph:

Using 23HR-00'-00" = Observed lunar distance to limb = 52deg-02'.0
plus SD 14'.95 gives Observed LD = 52deg-16'.95

Cleared LD = 52deg-07'.99
equiv = 23Hr-01'-01".97

An error of 1min-1".97
-----------------------------

MOON/VEGA (Vega to far limb)

23Hr-40'-00" Obs LD to limb = 94deg-23'.25 minus SD 14'.95
gives LD = 94deg-08'.3

Cleared LD = 93deg-33'.66
equiv = 23Hr-41'-12".5

An error of 1min-12"
-----------------------------

If these results are correct; and if they are accurate measurements; it seems I am measuring consistently to within a half a minute of arc (could just be the residual index error of the sextant?) and not what I expected to find (!). Also the averaged results for Moon/Jupiter were better (closer to correct absolute time) than my graphing method, which is definitely not what I expected.

There is nothing quite like actual scientific experiment to demolish the sacred cows of prejudiced views.

Douglas Denny.
Chichester. England.

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