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From: Ken Muldrew (no email)
Date: Mon May 03 2004 - 21:53:10 EDT
Frank Reed wrote:
> procedures that would work throughout the Solar System. This would
> require an almanac with heliocentric coordinates for all of the
> planets, but that's no problem (the Nautical Almanac from the 1780s
> included heliocentric latitudes and longitudes, for some odd reason,
> but not distances).
I think the longitudes and latitudes were to calculate the lunar distances
using the approximate formula:
D = arcos((cos(long1 - long2)) + (cos(lat1 - lat2)))
for the sun and applying the correction:
10^((5.3144 + log sin(moon's lat) + log sin(star's lat) + log versin(long1 -
long2) + log csc(D))-40)
for a star (with this correction in seconds). If the latitudes of the the moon
and star are of the same denomination then the correction is subtracted,
otherwise it is added. The "-40" is to take out the index from the logs.
Even with the moon at 5° off the ecliptic and the star at 15° off the
ecliptic, this rule gives the distance within 10"; the error is reduced in half
when the star is within 10°.
From Maskelyne's article in the Phil. Trans Roy. Soc. of 1764, p.263-276
(an approximate method for clearing the distance is also given.
Ken Muldrew.
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