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Re: Nautical almanac 1773
From: Paul Hirose
Date: 2007 May 02, 11:30 -0700

```Michael Dorl wrote:
>
> In reference to the almanac page posted by Walden that shows the lunar
> distance for Antares on 8/1/773 at noon to be 48-18-36.
>
> 1) What delta T would be appropriate for that date?

The Astronomical Almanac (2006), page K8, says +16s for 1765 through
1774. In the 1700s all the values in the table are integers, from which
I infer that delta T isn't known any better for that period. In the
early 1800s tenths appear, and in the late 1800s the value is given to a
hundredth of a second.

Using +16s delta T, my lunar distance program generated this:

Moon-star separation angle.
star designation = "name Antares"
UT1 = 1773 08 01 12:05:49.9
Terrestrial Time = 1773 08 01 12:06:05.9
apparent time - mean time = -00:05:49.9
geocentric angle, Moon center to star = 48 18 16

The value that should match the almanac is the last line: 48° 18′ 16″.

> Just curious and trying to reconcile my almanac program with this
data.  My
> program gives a lunar distance using dT =15 of
>
> topo (greenwich) 48-12-37
>
> apparent 48-14-56

Assuming your values are at noon UT1, I get this for Greenwich:

UT1 = 1773 08 01 12:00:00.0
Terrestrial Time = 1773 08 01 12:00:15.0
Sun GHA = 1 27 29
apparent time - mean time = -00:05:50.0
geocentric angle, Moon center to star = 48 14 55
geocentric semidiameter = 16 02
observer latitude = +51 28 38.5
longitude (ephemeris meridian) = -0 03 45.6
height = 67 m
Sun az, el (unrefracted) = 177 deg, 56 deg
Moon az, el, zd (unrefracted) = 24 58 48  -53 39 48  143 39 48
topocentric unrefracted semidiameter = 15 49
phase angle = 16 deg (0 = full moon, 180 = new)
Moon to Sun position angle = 291 deg
star az, el, zd (unrefracted) = 89 24 12  -34 25 29  124 25 29
Moon to star position angle = 266 deg
unrefracted distance from center = 48 12 36

> For whatever it's worth, my windows almanac program based on routines
> from Mosier at JPL gives the following....
>
> On 8/1/1773 at 12:05:50 (I can't set time to any finer precision)
>
> 12:05:50 UT
> dT = 15.314
> GHA of Sun is 359-59-54
> apparent lunar distance of antares 48-18-16.05

With those parameters, my program says:

UT1 = 1773 08 01 12:05:50.0
Terrestrial Time = 1773 08 01 12:06:05.3
Sun GHA = 0 00 01
apparent time - mean time = -00:05:49.9
geocentric angle, Moon center to star = 48 18 15

Bottom line: all my values agree with yours, give or take a second of
arc. I used the JPL DE406 ephemeris for the Sun and Moon positions, the
rigorous Astronomical Almanac vector method (in Section B) for reduction
to apparent place, the IAU 2000A precession and nutation model, and IAU
GST00A Earth rotation algorithm. Position of Antares came from the
Hipparcos catalog and was reduced to the apparent place of date with the
Astronomical Almanac rigorous method.

The program also outputs refracted distances to the near and far limbs
of the Moon, but I deleted all that since the Moon and Antares are below
the horizon at this time. My refraction algorithms have undefined
results below the horizon! (But the values looked reasonable.)

The program is written in C++, and I'll make the source code public in a
few days.

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