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You wrote:
"Mr. Reed, I believe that civil discourse requires a bit of formality, 
particularly due to some of the invective found in the archives.  Topics that 
involve intellectual discourse can become testy, so for now, I will stick to 
the nee-plus-ultra formality.  "

Sure, Brad. Whatever floats your boat is fine with me! :-)

And you added:
"I have been considering the statement by Mr. Reed that the changes in 
elevation at the moon's limb may result in "seconds" of variation with 
respect to the time of an event"

I do have one request: please do not refer to me in the third person. I 
PERSONALLY consider that impolite. Ok? :-)

You calculated the Moon's distance as:
"356,043 km = 14959871 km * 0.00238"

That's a bit low. The Moon is about 240,000 miles or 385,000 km away. Since 
the orbital eccentricity is around 0.055, the apogee and perigee distances 
are about 5.5% greater or less than this (somewhat variable because the 
Moon's motion is very far from a simple Keplerian ellipse).

You wrote:
"16.775 arc-minutes = DEGREES(arctangent (1737.4 km / 356043 km))* 60"

Just FYI, you don't need to dig out trig functions when you're calculating 
small angles unless you need an extraordinarily exact value. For small angles 
just take the distance across and divide by the distance out. Then multiply 
by 3438. That gives you the result in minutes of arc. It's convenient and 
quick, and you don't need a calculator. It's also very useful in marine 
navigation.

And you wrote:
"The angular rate of the moon is given in the Nautical Almanac,  in the 
increments section, as 14 degrees 19 minutes per hour (examine the increment 
for 59 minutes and 60 seconds)."

Now here you have made a mistake. That number you've taken from the almanac is 
the base rate at which the Moon changes its GHA (the total rate, on average, 
is about 10 minutes of arc per hour faster since you have to add "v"). But we 
don't want the rate of change of GHA. We need to know the rate of change of 
the Moon's position relative to the stars or in other words its rate of 
change of SHA. That is a MUCH small number. Subtract the Moon's average rate 
of 14.5 deg per hour from 15 degrees per hour... The rate of change of the 
Moon's position relative to Antares or any other star is around 0.5 degrees 
per hour, or dividing both by 3600, around 0.5 seconds of arc per second of 
time (the actual rate varies somewhat both because of the Moon's varying 
orbital speed and also because of changing parallax during an observation).

You wrote:
"Next we should find the highest mountains on the moon."

Actually what you need are the differences in altitude between the highland 
features near the Moon's limb and the lowland plains. The lowland plains are 
places like Mare Smythii and Mare Orientale. The highlands aren't usually 
named but there are some very high areas both north and south of Mare 
Orientale. The difference in altitude between the plains and highlands is 
about 10km. So the mountain heights you found should be doubled to get a real 
sense of the extremes of topography near the limb. Also note that the "limb" 
is a bit of a "moving target" because of lunar librations.

And you wrote:
"Time, seconds = Angle Subtended * Moons Angular rate
        Mons Huygens        0.222 seconds
        Mons Hadley         0.186 seconds
        Mons Bradley        0.169 seconds"

Again, because of the mistake I noted above, you need to multiply these 
numbers by about 30. You can easily get a difference in occultation timings 
of three seconds due to limb features.

And:
"In short, the tallest mountains on the moon, even if on the limb, fall far 
short of "seconds" of time."

As I hope you can see now, several seconds would not be an unusual timing 
difference due to limb features. For occultations, there's also another 
factor. Imagine a case where Antares is just barely occulted. That would 
happen when the Moon's center passes, for example, 15 minutes of arc just 
north or south of the star. The star will be seen to approach the limb at a 
shallow angle. In that case, a small difference in angular height of limb 
features can have an even larger impact on the timing of occultations. If the 
occultation is "grazing", a star can disappear and then briefly re-appear as 
it lines up with a deep valley near one of the Moon's poles.

And you concluded:
"From a different standpoint, lunar calculation for longitude could not have 
been successful had the limb provided such variation in precision as seconds 
of time.  Observers, of necessity, bring the object to the moon at different 
limb locations as a function of the close proximity of the moon to the earth. 
If seconds of variation existed, then the longitude could not have been 
determined with the degree of accuracy necessary."

Not true. At best, observers in the late 18th/early 19th centuries expected to 
determine GMT using lunar distances within 15 or 20 seconds, and even 30 or 
60 seconds of time was considered acceptable error. The few seconds, plus or 
minus, caused by the variations along the lunar limb did not matter to them. 
Whether it matters to modern lunar distance enthusiasts is an open 
question...

-FER




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