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Michael Dorl wrote-

>...to wonder
>about lunar distance measurements using venus. I've never tried to measure
>any lunar distances but I went ahead anyway.  My results were consistently
>about 5 to 7 minutes lower than predicted by a program I wrote that uses
>the Mosier JPL AA routines.  I wonder if this is some fault in my measurements,
>calculations, or the AA routines.
>
>I'd really appreciate it if someone could independently work out the moon
>venus distance for
>
>89.50 west 42.85 north
>altitude 290 meters
>temperature 5 degrees C
>tick.usno.navy.mil time 6-13-06 CDT 11-13-06 Greenwich
>
>I assumed a 15 minute moon semi-diameter.

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

I've compared it with my own pocket-calculator program, which predicts the
actual angle you would expect to observe (i.e. "cleared", in the opposite
direction from usual) between the centre of Venus, and both near and far
limbs of the Moon.  Presumably, at that time of the morning, it was the
Eastern side of the Moon that was lit, and presumably Venus was slightly
West of (and well below) the Moon, so it was a lunar distance measured
across the Moon to its far limb. I ask Michael to confirm whether these
assumptions were correct.

My predictions are-

Venus to near limb 16d 5.1', Venus to far limb 16d 35.6'

These are the lunar distances you would expect to measure, refraction and
parallax having been allowed for in a reverse "clearing" process.

These correspond to a geocentric distance between the centres of Venus and
the Moon (such as you would read off a table of lunar distances in an
almanac) of 17d 0.7'

And these correspond to positions for-

Venus dec 09d 40.1' GHA 27d 59.9' distance 1.09726 AU, alt 27d 19.5' Az
102d 47.7
Moon  dec 19d 29.0' GHA 42d 22.7' distance 0.002647AU, alt 44d 11.8' Az
105d 30.7

note that in the 2 lines above, no refraction, parallax, or dip corrections
have been made

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

The above predictions are based on the formulae and data given in Meeus'
paperback of 1982, "Astronomical Formulae for Calculators", which is
somewhat simpler, and somewhat less precise, than in his "Astronomical
Algorithms" of 1998.

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

Michael has presented us with an unusual problem, in asking us to predict
the distance he observed. The usual way of working a lunar is to take the
observed distance (with observed altitudes), "clear" it of the effects of
parallax and refraction, then compare that with the predicted geocentric
distance. Michael asks for the opposite approach. It so happens that I have
a routine in my calculator that does exactly what he needs.

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

Michael's choice of that morning to measure Moon-Venus distance was a bad
one. It was taken shortly before the Moon was due to pass Venus, well to
the North of the planet. So the Moon's path was well clear of Venus, and
the line between Moon and Venus would be way out of line with the direction
of the Moon through the sky, which is nearly at right angles to a line
joining the Moon's cusps (horns). This misalignment reduces significantly
the rate of change of lunar distance, and so reduces the precision of lunar
distance as a measure of time.

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

Alex Eremenko added-

"In general, the lunar distances method gives you
an error which is about 30 times your measurement error.
So if you measure the distance with 12"=0.2' error,
the error in your result (longitude) will be 6'."

I think this is the result of a misunderstanding. It seems to me that
Michael was complaining that his lunar distance were 5-7 arc-minute less
than he had calculated. I hope he will confirm whether the 5-7 minutes
applies to lunar distance, not to longitude. In which case any longitude
deduced from those observations would be out by a factor of about 30x
greater, so about 3d of longitude. Alex is applying the factor of 30x at
the wrong point, it seems to me.

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

Alex continued-

But few days earlier, in the discussion on this list,
the general agreement was that you cannot do better with a modern
sextant:-)

(I am accumulating evidence that they could do better in early
XIX century when Lunars were indeed important for practical
navigators).

Certainly, lunars could give more precise results from an on-land
determination averaging many observations over a prolonged campaign, such
as Cook (for example) undertook.

Alex adds-

"Besides, Venus was "not recommended for Lunar distances"
by one of our experts on the Lunars (I think this was Frank Reed)."

Planets weren't even included in the earliest lunar-distance tables.

There are two problems about working with the near planets, Venus and Mars.

First, they can come quite near to Earth, so their horizontal parallax,
which varies considerably, needs to be considered. This can be taken from
the "additional correction" entry for the planet in the "stars and planets"
correction table in the almanac, for 0d altitude.

Second, planets have a finite size in the sextant's telescope, not a
point-source like a star. For Jupiter and Saturn, we always see them
full-face, or nearly so, so their centre-of-brightness is effectively the
same as the centre of the planet. Venus and Mars show crescent phases in
their illumination, rather like the Moon's. So the centre-of light can
differ from the planets centre-position by a large fraction of a
semidiameter. Usually, the observer will try to superimpose the
centre-of-light, not the centre, on to the Moon's limb. I understand that
predictions for Venus and Mars, in modern almanacs, do something to allow
for this effect.

My own predictions, above, do NOT allow for this crescent effect for Venus
and Mars.

George.

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

   

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