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George Huxtable wrote:
>
> It's easy to convert between those ecliptic coordinates and the RA / dec of
> a modern prediction, for which you need an accurate value of the Earth's
> tilt of axis, at that date. And you need to be aware that the time scale of
> the old almanacs (up to 1834) was in terms of apparent time not GMT, so the
> Sun really was exactly on the Greenwich meridian at noon. For comparison,
> modern Moon predictions have to be taken, not for noon and midnight UT, but
> offset from that by the equation of time.

JPL's online HORIZONS system can give the Moon's apparent geocentric
ecliptical coordinates directly.
http://ssd.jpl.nasa.gov/?horizons

Copy and paste the following lines (starting with !$$SOF and ending with
!$$EOF) into an email. Use JOB for the subject and send to:
horizons@ssd.jpl.nasa.gov
(Do not fill in the blank after EMAIL_ADDR. By default HORIZONS will
return its result to the same address that sent the command.)

!$$SOF (ssd)       JPL/Horizons Execution Control VARLIST
  EMAIL_ADDR = ' '
  COMMAND    = '301'
  OBJ_DATA   = 'NO'
  MAKE_EPHEM = 'YES'
  TABLE_TYPE = 'OBS'
  CENTER     = 'geo'
  START_TIME = '1776-Jul-4 00:00'
  STOP_TIME  = '1776-Jul-4 21:00'
  STEP_SIZE  = '3 hours'
  QUANTITIES = '31'
  ANG_FORMAT = 'deg'
  APPARENT   = 'AIRLESS'
  TIME_DIGITS = 'MIN'
  TIME_ZONE   = '+00:00'
  SUPPRESS_RANGE_RATE= 'NO'
  ELEV_CUT   = '-90'
  SKIP_DAYLT = 'NO'
  SOLAR_ELONG= "0,180"
  AIRMASS    = '38.0'
  EXTRA_PREC = 'NO'
  CSV_FORMAT = 'NO'
  R_T_S_ONLY = 'NO'
!$$EOF++++++++++++++++++++++++++++++++++++++++++++++++++++++


The system is fast; by the time I can get to my inbox and check mail,
the reply is waiting.

You should get back a table of the Moon's longitude and latitude for one
day. The time scale is UT1. George says the old almanacs used apparent
time, and I see no way to get HORIZONS to calculate with that time
scale, or give the equation of time. However, it can give the local
apparent solar time at Greenwich with this command:

!$$SOF (ssd)       JPL/Horizons Execution Control VARLIST
  EMAIL_ADDR = ' '
  COMMAND    = 'sun'
  OBJ_DATA   = 'NO'
  MAKE_EPHEM = 'YES'
  TABLE_TYPE = 'OBS'
  CENTER     = 'Greenwich'
  START_TIME = '1776-Jul-4 00:00'
  STOP_TIME  = '1776-Jul-4 21:00'
  STEP_SIZE  = '3 hours'
  QUANTITIES = '34'
  ANG_FORMAT = 'deg'
  APPARENT   = 'AIRLESS'
  TIME_DIGITS = 'MIN'
  TIME_ZONE   = '+00:00'
  RANGE_UNITS = 'AU'
  SUPPRESS_RANGE_RATE= 'NO'
  ELEV_CUT   = '-90'
  SKIP_DAYLT = 'NO'
  SOLAR_ELONG= "0,180"
  AIRMASS    = '38.0'
  EXTRA_PREC = 'NO'
  CSV_FORMAT = 'NO'
  R_T_S_ONLY = 'NO'
!$$EOF++++++++++++++++++++++++++++++++++++++++++++++++++++++

 From that you could determine the UT corresponding to a given apparent
time, and use that to generate the Moon's position. It's not the easiest
way to work, but at least HORIZONS is free and very accurate.

If I were researching the accuracy of those almanacs, I'd write software
to take the input directly in apparent time.

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