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Peter, you wrote:
"I assume that this difference in GHA is inherited from the star's SHA, since 
GHA Aries is relatively straightforward to calculate."

I would say that it's the other way around. The SHA's of the stars have been 
measured to amazing levels of accuracy, first by ground-based astrometry, 
which was already orders of magnitude beyond the needs of navigators, and 
more recently by the HIPPARCOS satellite mission which nearly made all 
previous astrometric work obsolete. Given an accurate position in SHA/RA and 
Dec and accurate measurements of parallax and proper motion, the positions of 
the stars can be predicted to a fraction of an arcsecond for centuries to 
come (proper motion is the biggest uncertainty in long-term positions). 
Likewise, the positions of Solar System objects are known to a fraction of an 
arcsecond from the numerical integrations done primarily by the folks at JPL. 
So we've got the positions on the celestial sphere. They can be considered 
"known quantities". 

Now consider GHA of Aries or equivalently Sidereal Time. These depend on the 
the exact fine details of the rotation of the Earth which are instrinsically 
unpredictable. We codify this in astronomical calculations through delta-T. 
Any error in delta-T corresponds directly to an error in the expected 
longitudes of the GPs of celestial bodies using the usual "four seconds to 
one mile" rule. If there is an error of 0.4 seconds in the estimated value of 
delta-T, then there would be an error of 0.1 minutes of arc in the GHAs of 
all celestial objects. While the angles among objects on the celestial 
sphere, like a star-star angle, e.g., can be calculated to a fraction of a 
second of arc fifty years in the future, the GHAs that far ahead could easily 
be wrong by dozens of seconds of arc. Similarly, for any dates before about 
1750, there are uncertainties in delta-T of some seconds increasing rapidly 
in earlier eras. In the extreme case, when considering astronomical events 
visible at the dawn of civilization, while we know where all of the celestial 
bodies were located in the sky relative to each other at any minute of any 
day five thousand years ago, we don't know which way the Earth was pointing 
(in longitude) to better than thirty degrees or so. We can't correlate our 
clocks with theirs.

-FER




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