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    Re: GMT from Jupiter's moons
    From: George Huxtable
    Date: 2004 Jul 14, 18:16 +0100

    Fred Habard asked-
    >This is more of a surveying problem rather than a marine navigation
    >problem, and primarily of historical interest, but....
    >All the ephemerides I have seen for occultations of Jupiter's moons are
    >timed to the minute.  I have not seen tables for occultation of stars
    >by the moon.  Was one minute the limit of resolution for determining
    >GMT in the old days or could averaging of numerous observations give a
    >more accurate determination of Greenwich time?
    From George-
    It was an important matter, in the early days of longitude, to discover and
    record in almanacs the longitudes of various headlands and islands that
    vessels were likely to pass, so that they could reset their reckoning when
    they did so. The most accurate way of doing so in those days from on land
    was by timing of immersions and emersions of the two inner satellites of
    Jupiter, Io and Europa, as they passed into and out of the shadow of their
    planet. So then, the method had great significance for navigation.
    Similarly, it was used to establish the longitude of Barbados when testing
    the fourth Harrison chronometer.
    The trouble is that these are not instantaneous events. If you watch Io
    (for example) extinguish, it doesn't pop off like a switched-off light.
    Because of its finite size, it takes over 3 minutes to move through a
    distance equal to its diameter. And the shadow-edge of Jupiter shows a
    penumbra, because of the finite semidiameter of the Sun seen from that
    distance, which makes the switch-off more indefinite still.
    Starting with the Paris Observatory, who have been custodians of the
    World's precise timing ever since, from the 17th century astronomers have
    recorded times of these events, an important purpose being to support
    land-surveyors, who would note their local time of the same event.
    Astronomer and surveyor would both note the time of the last (or first)
    twinkle of light they could see in their telescopes. This would come from
    the last (or first) sliver of the satellite to see any of the Sun, at the
    moment when that patch of the satellite could still see just a sliver of
    the Sun as it was becoming completely eclipsed by Jupiter. You might guess
    that this timing depended on the quality and aperture of the telescope that
    was used at the observatory, and the timing of the same event by a surveyor
    would relate to when the last twinkle disappeared from his own view in an
    inferior field-telescope, which was likely to happen a few seconds earlier.
    They may have used some rule-of-thumb to adjust the time-difference to
    allow for this difference in telescope capabilities, but I have not managed
    to unearth it.
    The predicted times of these events were published, and even in the first
    Nautical Almanac in 1767, these times, for Io and Europa, were provided, to
    the nearest second of time. This was far more precise than can be found in
    recent almanacs, in which, as Fred notes, they are given only to the
    nearest minute. I doubt whether the accuracy of those early predictions
    quite matched the precision of the tabulation, however.
    Nowadays, precise timings, to the second, of the beginning and end of an
    immersion (etc) are available from only one source that I'm aware of. This
    is the special annual supplement for that purpose to the "Connaissance des
    Temps", which usefully carries text in both French and English. In other
    almanacs, predictions, to the nearest minute only, appear to relate to the
    moment when the mid-line of the planet's penumbra just bisects the disc of
    the satellite, and so the light from the satellite has dropped to just half
    its initial value. This might be a useful measure if one had a photometer
    and could plot the brightness curve as it fell, or rose, with time. But
    using the eye with a telescope, I suspect that a diminution of brightness
    to half would be only just noticeable, because of the rather logarithmic
    response of the eye. So I suspect that making one's best guess by eye at
    the moment of that last twinkle, and comparing with the timing of the end
    of an immersion in that special supplement, would give the best comparison
    of time, in spite of its imperfections.
    I append here a helpful email received on this subject 3 years ago from M
    William Thuillot of the Bureau des Longitudes, Paris, at thuillot@bdl.fr
    Two kinds
    of predictions are available.
    You may find standard predictions in the French ephemerides
    (Annuaire du Bureau des longitudes , Connaissance des Temps,
    our www site) where satellites are reduced to their centers,
    the umbra cone is pointed toward  the center of the Sun and
    is tangent to an ellipsoidal planet. Jupiter is assumed to be
    without any atmosphere. These predictions are generally
    provided to the nearest minute of time (to the tenth of minute
    for eclipses). They are sent to the Astronomical almanac and
    other foreign ephemerides services.
    These computed times of phenomena correspond to the mid event
    (when the brigthness of the eclipsed satellite is half fainter
    than the not eclipsed one, or when it is bissected during the
    transits, the umbra or the occultations). It appears to have
    been a very current method of observation in the past (see for
    example the Catalogue of eclipses of the Galilean satellites
    published by J.H. Lieske in Astronomy and Astrophysics in 1986).
    The eclipses were mainly observed in order to avoid the closeness
    to Jupiter, immersion and emersion observations (during occultations)
    are very rares in the archives. One of the advantages of the
    mid-event method  is that the bias due to the size of the instrument
    is "averaged" since the first specks and the last specks are
    affected by opposite time delays. I guess the accuracy may be
    around 10 seconds of time in observing an eclipse of Io.
    The second kind of predictions is only provided by the Supplement
    a la Connaissance des Temps. As explained in the first pages of
    the booklet, these predictions are made assuming spherical
    satellites, umbra cone both tangent to a spherical Sun and
    to an ellipsoidal planet, visibility cone pointing to the center
    of the Earth and tangent to the ellipspoidal planet.
    No effect of the Jovian atmosphere is taken into account.
    These assumptions allow us to get the time of the contacts with
    the umbra cone and the visibility cone corresponding to the
    theoretical first and last specks more accurately observable
    with telescopes and photometers (when possible).
    For me, this problem came up in 2001 when I was advising on a BBC series
    which tried to reenact some aspects of a leg of Cook's first
    circumnavigation, in the modern replica of "Endeavour". The BBC had
    selected a small onboard team of navigators to do things as Cook had to
    (that first voyage was before Cook had a chronometer). After major repairs,
    before departing from Endeavour River in (modern) Queensland for Batavia
    (modern Jakarta), Cook had taken the opportunity to deduce longitude by
    timing the disappearance of a Jupiter Moon, to back up his lunar distances.
    The reenactment navigators wished to do the same, and before departure from
    the UK had successfully observed such an event. As Jupiter was only just
    getting far enough from the Sun to be visible at all, suitable satellite
    events visible from Australia were rare. The team flew out a few days
    early, with a 4-inch reflector, to use the one event that was available, in
    a pre-dawn observation. The skies were nicely clear, and Io was beautifully
    visible. Except for the crucial few minutes around the immersion, when a
    cloud appeared in just the wrong place. Sod's Law strikes again!
    I thought the resulting TV series was abysmal...
    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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