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Here's my shot at the Sun's GHA at noon UT1, May 4, using ICE. First
compute the "right answer" with the USNO MICA 2.0 program.

1. Examine IERS Bulletin A at the USNO Web site. For 2010 May 4 it says
TT-UTC = 66.184 s (that value will remain constant until the next leap
second) and UT1-UTC is predicted to be -0.02524 s. So delta T = 66.184 -
(-0.02524) = 66.2 s to sufficient accuracy.

2. Get Greenwich apparent sidereal time from MICA. It's a function of
UT1 only, so an error in delta T has no effect. (This is not absolutely
true, but practically so.) Enter 12:00:00 UT1, read GAST = 2h 49m 04.5706s.

3. Get the apparent true right ascension of the Sun. This is a function
of TT only. Noon UT1 = 12:01:06.2 TT, at which time the Sun's apparent
RA = 2h 45m 50.974s.

3. Since GHA = GAST - RA, the value from the foregoing figures is 3m
13.6s, or 48'24" GHA.

4. Turning to ICE, it says 2h 49m 04.5706s is the Greenwich apparent
sidereal time at 12:00:00 UT. (According to the documentation, the input
time is assumed to be UT1 for sidereal time and navigation computations,
TT in all other cases.)

5. At 12:01:06 TT (= noon UT1), ICE says the Sun's apparent RA = 2h 45m
50.973s.

6. GAST - RA = 3m 13.6s = 48'24" GHA, same as MICA. The only difference
between the programs was .001 s in RA.

Both programs have inadequate time input functions. MICA allows only .1
s precision, while in ICE it's one second. This prevents you from
utilizing all of the available accuracy and display precision.

Given ICE's coarse time steps, I was lucky to do as well as I did. It
would have been less trouble to use the Navigation function. Simply
enter 12:00:00 and request the Sun position. You get a direct readout of
48.4' GHA, which agrees with the values above and the USNO online sight
reduction tool.

In theory there is a problem because ICE's delta T is 72.3 s, about 6 s
too great. That means the Sun's RA is computed for 12:00:06, not noon.
But the Sun moves only 1 degree per day, or .04" per second of time, so
the delta T error is insignificant.

It's helpful to remember that delta T affects sight reduction via the
hour angle, which is the difference between apparent sidereal time and
the right ascension of the body. Sidereal time changes 30 times faster
than RA for the Moon, 360 times faster for the Sun, even more so for
other bodies. So, if you're forced to choose one or the other, it's
best to throw any time scale error into the RA computation.

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