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    Re: Moon Occultation of Jupiter
    From: George Huxtable
    Date: 2004 Dec 3, 00:30 +0000

    This is an attempt to sweep up some of the debris from recent disagreements
    between Frank Reed and me.
    
    He wrote-
    >Did you know there was a Jupiter occultation  last
    >month, too? Many people in the eastern US observed it... in broad daylight.
    >Unfortunately, it was cloudy here.
    
    Not observable here, unfortunately. Actually, it was the first in a series
    of 11 Jupiter occultations, at roughly monthly intervals, until August
    2005. None will be visible to me, but the next, on the morning of Dec 7th,
    will be visible from the US.
    
    Frank said-
    >By the way, I think you doubled the apparent diameter of Jupiter somewhere
    >along the way... It's about 0.6 arcminutes.
    
    Yes, I did. Thanks for the correction. It makes the changes I was referring
    to twice as fast as I made them out to be.
    
    ====================
    
    I think Frank and I agree about the difficulty of calculating the moment of
    Jupiter's extinction. To reinforce that message, Meeus' account of how to
    do it occupies several pages, in the "Occultations" chapter of his
    "Astronomical Tables". He even offers a BASIC program to do it, occupying 3
    pages of small print.
    
    ====================
    
    Frank quoted me-
    >"The end result is that Jupiter has only about a fifth of the
    >surface  brightness of the Moon."
    
    and replied-
    >Not really. When the Moon is past last-quarter, phase effects diminish its
    >surface brightness considerably. Jupiter and the Moon will have very nearly
    >equal average surface brightness for this occultation. In astronomers' units,
    >the surface brightness of both will be about -3.2 magnitudes per square
    >arcminute.
    
    Yes, that's true, my model was too simplistic and omitted the effect of the
    direction of incident light at the Moon's limb. But I am not sure what
    Frank is referring to when he speaks of the Moon's "average surface
    brightness".
    
    I was trying to deduce the surface brightness of Jupiter compared with that
    of the nearby Moon limb, from which it has to be distinguished. Let's
    repeat that calculation, but include the the incident-light angle this
    time.
    
    First, Jupiter is a factor of about 5.2 further from the Sun than the Moon
    is, which means that the Sunlight at the Moon is brighter by 5.2 squared,
    or 27. But Jupiter reflects 43% of the incident light, whereas the Moon
    reflects only 7%, so seen face on it would be brighter than Jupiter by a
    factor of 27 x .07 / .43, or about 4.4 times brighter. But now we have to
    look at the angle at which the sunlight strikes the Moon's surface, at the
    near limb to Jupiter (the bit I omitted before). At last-quarter, the Sun
    was directly above that limb, so the brightness ratio would be 4.4, as
    before.
    
    But the recent Jupiter occultation of November 9th, which Frank was
    presumably taking as his example, occurred 5.5 days after Moon's last
    quarter, which was on Nov 5th. The Moon must have appeared as a faint thin
    crescent. By that time the Moon's phase had changed through 70 degrees, and
    the direction of sunlight falling on the limb had changed by the same
    amount; so the resulting brightness at the Moon's surface would then be 4.4
    cos 70, or about 1.5 times as bright as the surface brightness of Jupiter.
    Jupiter is, of course, always seen and illuminated nearly face-on.
    
    So there's now much less difference between my estimate and Frank's, who
    expects the two brightnesses to be the same. It's interesting that there's
    any difference between us at all, though. Are we calculating different
    quantities?
    
    The December 7 Jupiter occultation will occur much nearer the last quarter,
    so the Moon's limb will then be MUCH brighter than Jupiter, about 4 times
    as bright.
    
    =============
    To my question-
    
    >"If Frank can make out a Jupiter DISC under those circumstances, against  the
    >glare from the Moon, he's a much better observer than I am (which may  well
    >be the case)"
    
    Frank replied-
    
    >This is, of course, very closely related to the issue of lunars accuracy.
    >Can you make out a tenth of a minute of arc when you look through a
    >sextant? How
    > about two-tenths? If you believe that most observers can do this, then it
    >is also possible to see the disk of Jupiter (and yes, I can see it clearly at
    >7x  and better at 10x). The disk of Jupiter is about 0.6 minutes of arc across
    >right  now. I agree that *some* people can't see that small an angle through a
    > telescope at these magnifications, but I think most people can and  most
    >people with sextant experience routinely do so. And if you  *don't* agree that
    >most people can see the disk of Jupiter, then you would have  to conclude that
    >lunars would have to have been much less accurate historically  then people
    >have supposed.
    
    I wasn't doubting that with a good telescope to your sextant, against a
    dark sky background, a good observer can make out the disc of Jupiter.
    
    What I was questioning was whether, nestling against the bright limb of the
    Moon, the disc of Jupiter could then be made out, with sufficient accuracy
    for timing the inner and outer contacts. American observers should have the
    chance to check this on December 7th, but not me.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george---.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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