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> *From: *Jim Hickey
> *Date: *2025 Sep 12, 07:28 -0700
>
> The equation for JD works but the result given in the worked example
> does not agree with what I get when I put the equation in Excel.

> 


I ran a Monte Carlo test (several hundred random epochs in the 21st
century) on the Julian date formula in that file. All results were
correct. However, I too find discrepancies, up to about 3°, in the GHA.
Declination looks OK.

One problem I see is step 11:

GHA = MOD(GMST - λ, 360)

Greenwich mean sidereal time is an angle in the plane of the equator,
while apparent longitude (λ) is in the plane of the ecliptic. The
formula should use RA instead of longitude. For RA, Meeus says:

RA = atan2(cos ε sin λ, cos λ)

The PDF is a curious document. "Excel Algorithm for Sun’s GHA and
Declination" occurs twice. Both have 11 steps. I don't know if they're
identical. The second set credits Meeus, the first doesn't.

--
Paul Hirose
sofajpl.com

   

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