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    Re: Tycho Brahe Mars oppositions
    From: Michael Dorl
    Date: 2004 Dec 1, 07:08 -0600

    At 07:18 PM 11/30/04 +0000, George wrote...
    >Michael Dorl offered his own calculations of when the Right-Ascensions of
    >Sun and Mars differed by 180 degrees, about 400 years ago.
    >In another message, he asked me about the table of Mars oppositions, of the
    >same era, that I had quoted extracts from, in Meeus' "Astronomical Tables"-
    >"Do you now how these times were calculated or how opposition is defined
    >Meeus defines his values as "the instant when the true heliocentric
    >longitudes of the Earth and Mars, referred to the mean equinox of the date,
    >are equal."
    >I suggest that Michael, on one hand, and Meeus and Tycho, on the other
    >hand, are referring to rather different quantities.
    I was aware that opposition is defined in terms of ecliptic coordinates but
    a first glance, I though I didn't have the requisite data so I used RA. I
    also had no idea what Brahe might have been thinking. On closer
    examination, I see that Mosier's routines do produce ecliptic coordinates
    so I modified my almanac to show difference in ecliptic longitude between a
    reference object and a target object.  So, I get a time of 11:44:00 TDT dT
    = 95.4 for the 11/18/1580 opposition TDT JDate 2298474.98889.  George's
    earlier message gave a time of 11:41.
    I still don't know exactly what I have since the routines produce something
    called 'ecliptic longitude' for all bodies and something called 'apparent
    ecliptic longitiude' for only the Sun.  The Astronomical Almanac says
    opposition is defined in terms of apparent ecliptic longitude. At the
    instant in question, the ecliptic longitude is about 9 seconds of arc
    larger than the apparent ecliptic longitude; I suspect the difference is
    annual aberration.  I'll examine the code and correspond with Mosier to see
    if I can figure out what is and isn't included.  At this particular time
    the difference in ecliptic longitude is changing by about 1.25 arc seconds
    for each minute of time.

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