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I verified Frank's formulas. They are indeed correct,
and I have a rigorous proof of this.
(Assuming no refraction).
Another way to write them is this:

ErDist(MA)=P.cot(dist).cos(MoonAlt).ErMoonAlt,

where ErDist(MA) is the error in the cleared distance due
to the moon altitude error, and P the numerical value
of maximal parallax that is P=0.016; the ratio of the Earth
radius to the distance to the Moon. Its reciprocal value
is the factor 6' in Frank's formulas.

ErDist(SA)=P.csc(dist).cos(StarAlt).ErStarAlt,

where ErDist(SA) is the error in the cleared distance due
to the star (or Sun) altitude error, and P is the same as
before. (csc is cosecant, reciprocal to sine).

So indeed everything deteriorates when the distance becomes
small; but when the distance is near 90 deg, Moon's
alt becomes irrelevant. Furthermore, when the altitude
of the Moon or of the star is close to 90 d, this altitude
becomes irrelevant:-)

Nice formulas, indeed!

Alex.

On Sun, 31 Oct 2004, Frank Reed wrote:

> I general, good (slightly approximate) expressions for the required accuracy
> of the altitudes are:
> AccuracyBody = 6' * sin(Distance) / cos(BodyAltitude)
> AccuracyMoon = 6' * tan(Distance) / cos(MoonAltitude).
> I have never seen these expressions in print anywhere.

   

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