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Frank Reed wrote-

"By the way, does anyone do oblateness the way Chauvenet
does? That's how my calculator does it."

And Michael Dorl wrote-

"As far as I can tell there is nothing in the routines to allow for
oblateness of the earth. One can specify a elevation. Looks like the earth
is assumed to have a radius of 6378137 Meters, same as equatorial radius in
my 1988 AA page K6.

If I include an elevation of -9600 meters, I get a ctr/ctr distance of
16d20'25.88". Taking off a  moon semi-diameter of 15'3.88" gives a ctr to
limb distance of 16d5'22" or 16d5.37' which is close to Frank's 16d5.5'. I
got the -9600 meters by considering the earth to be an oblate spheroid. I
think Mosier considers the earth to have an equatorial radius so setting
the elevation negative should compensate for the oblateness."

Michael's use of an adjusted altitude to allow for the Earth's oblateness
is new to me, and deserves a bit more thought before I comment on it.

I'm aware of two ways in which the oblateness of the Earth comes in.

1. It affects the apparent ALTITUDE of the Moon, by an amount which was
supplied in navigators' table for "Reduction of the Moon's horizontal
parallax", which effectively multiplies the HP by (1- ((sin lat)squared
/300)). This can change the Moon's altitude by up to 0.2', at the equator.
This may already be a "hidden" part of Michael's clearing process; it would
need to know the observer's latitude, very roughly.

2. It affects the AZIMUTH of the Moon, by a similar amount, of up to 0.2'.
For ordinary navigation using Moon altitudes above the horizon, parallax in
azimuth has no effect at all. Even for lunar distances, which ARE affected
by a displacement in azimuth of the Moon, there would be no parallax in
azimuth if the Earth was a sphere. It's the oblateness that gives rise to
the change in azimuth of up to 0.2', greatest at latitudes of 45d, greatest
for azimuth differences between Moon and body of ?90d. Some fraction of
this parallax in azimuth should be applied as a correction to the lunar
distance, depending on the angle the line between the Moon and the body
makes with the horizontal. This correction is mentioned in Meeus, but no
formula are given. Smart's Text-book on Spherical Astronomy, in para. 121,
shows how to derive the correction in azimuth. Chauvenet treats the matter
in some detail, and very thoroughly, as is his wont.

If Frank is allowing for that azimuth correction to lunar distance (and for
ultimate accuracy, that really should be done) then it's a step further
than most others have taken their clearing of lunar distances. In my own
clearing process, that term has been neglected, and it may explain at least
part of the small divergence between Frank's "clearing" results and my own.
Henning Umland has shown me his routine for making such a correction, which
may now be included in the lunars section of his website.

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

I suggested, about that divergence between Frank's lunar "clearing" and my own-

"It might be enlightening to track it down."

And Frank replied-

"Thanks for questioning this. It could easily be that I've got a sign wrong
somewhere or something like that. I'll see what I can find."

It's just as likely to be an error or approximation of my own, as one of
Frank's, but it would be good to get to the bottom of it.

What I suggest is that we take a simple situation that involves little or
no trig and see if we agree then. Perhaps an on-land lunar distance taken
between the Moon and Schedar, at a GMT of 19h 51m 35s on 29 Oct 2001, at
lat N 56d 32.9', long E 34d 03.3', somewhere near Moscow.

If I've made no error, then Schedar would be dead over the observer's head,
and the Moon would be exactly to his South. In which case, the lunar
triangle shrinks to a straight line, there's no correction for the star,
the true lunar distance between centres would depend only on the Moon's
dec., and the clearing process would be a matter of simply
adding/subtracting the Moon's parallax and refraction. In that case, by the
way, there would be no Moon azimuth correction.

Perhaps, if Frank would kindly check those initial assumptions, and if he
agrees they make for a suitable test, we might compare our results for
lunar distance between centres.

Whether it's best to take this comparison of fine-points off-list, or to
leave it on in case it interests others, is up to Frank; I have no strong
feelings either way.

George.


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