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Last week, Frank Reed offered the following challenge-

>So does your calculator prediction of GHA and Dec for
>Regulus (e.g.) on December 3, 1803 agree with the position in my online
>almanac?
>At 9 hours GMT, I've got GHA=56? 45' 6" and Dec=N 12? 55' 10".

He also offered corresponding predictions at 9h Greenwich Apparent Time,
but I will stick with the GMT version because that's the time-argument my
program uses.

My pocket calculator gives for Regulus at 9h GMT 0n 3 Dec 1803-

GHA = 56deg 45' 7.0" (an internal result: it actually rounds off before
displaying, to 56deg 45.1')

Dec = +12deg 55' 12.2" internally (display is rounded to +12deg 55.2')

so I can agree that Frank's program is providing pretty good results.

The accuracy that my program aims for is limited by the number of decimal
places to which the star coordinates have been stored internally. The dec
and RA are each held, in degrees, to the nearest whole millidegree (i.e.
?0.5 mdeg). The proper motions are held to the nearest whole millidegree
per century, (i.e. to ?0.5 mdeg/century).

The year 1803 is 1.8 centuries away from the epoch of the chosen star
catalogue, which was for 1984.5, from the 1984 Astronomical Ephemeris (my
program's 20 years old). The resulting error in star positions due to
proper motion in the intervening 1.8 centuries can than be 1.8 x ? 0.5 or
say ?1 millidegree. This combines with with the possible error in initial
star positions to give ?1.5 millidegree. Roughly speaking, that's ?5
arc-sec, which is compatible with my chosen rounding-off of display to 0.1
arc-min. So I don't claim any higher accuracy than that rounding.

There are additional errors due to some simplifications. For example, I
consider only the 18.6 year term in the nutation correction and ignore the
rest. But that contribution to error is expected to be small.

George

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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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