# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Luni-Solar Distance
From: George Huxtable
Date: 2010 Oct 26, 20:52 +0100

```Thanks to Lars Bergman, for contributing the following thoughts about
calculating the altitudes, to go with a lunar distance observation. Sorrry
for the delay in responding, but my old boat has taken some priority just
now: but that has provided a bit of useful pondering-time.

Lars wrote-

===========

George wrote, in reply to Douglas Denny, in 14133:
“If the time was known, there would be no point in taking a lunar. That's
the purpose of measuring a lunar-distance; to determine the time. So
there's a bit of a paradox, in calculating altitudes with which to clear a
lunar, for which time and position are both needed. To get round it, you
have to assume a trial longitude first, and then use the lunar observation
to refine that assumption.”
And in 14145:
“I don't know of any texts which have considered this question of a need
for reiteration when altitudes have been calculated, and wonder whether
travellers were even aware of its potential for causing error. Can anyone
point to such a publication?”
---
In above context, the purpose of measuring a lunar-distance is to determine
a standard time, i.e. the time at Greenwich. To calculate an altitude,
knowledge of Greenwich time is not necessary, but the local time must be
known. Latitude is assumed known and an approximate Greenwich time in order
to find the declination from the almanac. Thus, an altitude observation to
determine the local time should therefore be executed as near in time to
the distance observation as possible. The error in time then depends only
on the regularity of the watch and of the ship’s (or traveller’s) reckoning
between the two observations.
To find the altitude corrections, some rework may be necessary. Normally,
parallax and refraction are found from the apparent altitude, thus all
tables are arranged with apparent altitude as argument. When altitudes have
been calculated, some iterations are necessary to find the proper values.
The aim is to end up with an apparent altitude that, reduced in the normal
way, gives the same value of true altitude as that found by calculation.
process of calculating altitudes are described in some detail, involving
iteration not of the lunar calculation but of the altitude calculations.

==============

On reflection, I think that Lars has got the matter right. As long as an
observation to determine local time has been made, at or near to the time
of the lunar, that can provide sufficiently good data on which to base the
necessary altitude calculations. In which case, the laborious iteration
procedure that I had thought necessary could be circumvented. Thanks to
Lars for putting me right.

However, sometimes a lunar is taken for a different purpose than to
establish an immediate longitude. Sometimes, it might just be to set, or
correct the error of the chronometer, and it might not be thought
necessary, in mid-ocean, to make such a time-sight for local time, there
and then. Can the altitudes be successfully calculated under those
circumstances, I wonder?

And I still wonder about the use of Frank's lunar-distance calculator, at-
http://www.historicalatlas.com/lunars/lunars_v4.html , to solve the
converse problem from that it was intended for.  I would be grateful for
any step-by-step guidance on how to go about using that calculator to
establish the GMT at the moment of a lunar distance observation, from an
unknown longitude, without observing the altitudes. Can it be done? How
much iteration is involved? With observed altitudes, there seems to be no
such problem.

===========

"A navigator is somewhere on the Equator, at
lat = 0º, and knows it from his previous observations. We know (though he
doesn't) that at midnight, 00:00 hrs at the start of 26 March 2005, he is
exactly on the Greenwich meridian, at long = 0º, at which moment he takes a
precise lunar distance between the Moon's near limb (it's full Moon, so
either limb will do) and Regulus, of 36º 48.9'.
However, not knowing his exact longitude, he guesses it to be 01º 00'
East."

===========

Can anyone explain to me the most efficient way to go about it, using that
lunar calculator?

George.

contact George Huxtable, at george{at}hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

```
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