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I wrote:
> Regarding ICE, the delta T of this old program has become excessive,
> with some impact on Moon coordinates.

The effect is small. For instance, at 2014 March 29 12:00 UT1, latitude,
longitude, and height all zero, the ICE celestial navigation data for
the Moon agree exactly with the USNO online calculator, except that GHA
is .1′ too small.

Compare ICE unrefracted altitude to JPL HORIZONS:
74 01 42  ICE (includes parallax in alt.)
74 01 38  JPL HORIZONS

Greenwich apparent sidereal time:
00 27 15.5401  ICE
00 27 15.5341  JPL HORIZONS

ICE assumes time is UT1 when it computes navigation data and sidereal
time, but HORIZONS assumes UTC. On this date UT1 is .20 second behind
UTC, so 12:00:00.00 UT1 = 12:00:00.20 UTC. The latter time must be input
to HORIZONS to get comparable values. That's what I did.

However, for geocentric position computations ICE assumes the time you
input is TT. HORIZONS will take time in that scale, so no adjustment is
necessary for geocentric apparent Moon RA and dec. at 12 h TT:

23 24 26.401  -00 24 42.98  ICE
23 24 26.39   -00 24 43.1   HORIZONS

The separation between those positions is .2″. HORIZONS has an option to
generate output with more precision, but I didn't think that necessary.


Hc in the navigation data is the only value with significant error, and
that's only about a tenth of a minute. (I converted outputs from both
programs to DMS format for easier comparison.) Since ICE's sidereal time
and geocentric apparent place are practically perfect, the error must
come from the conversion from UT1 to TT. And in fact its delta T is 78.1
s, about 11 s too great. Therefore instead of 12 h, if we use 11:59:49
UT1, the correct Moon position will be extracted from the ephemeris
(which is based on TT). However, in terms of Earth rotation, that
adjusted time will put the observer west of the correct position.

The solution is to adjust the observer's longitude east to compensate
for the time adjustment: 11 s * 15 = 165″ = .046°. Formally, we should
also multiply by 1.002, the sidereal to solar time ratio. But we omit
that step due to the program's relatively low input and output
precision, and get:

74 01 36  ICE Hc (includes PA)
74 01 38  JPL HORIZONS

As I said earlier, correcting for the delta T error makes the old
program as good as new! The same method is applicable to the USNO MICA
program.

I wouldn't do that extra work for Sun navigational data from ICE,
though. Its RA and dec. change so slowly (about 1°/day vs. 12° for the
Moon) that an 11 s error in TT probably wouldn't make any significant
difference.

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