NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Working a lunar
From: Christian Scheele
Date: 2009 Aug 6, 21:50 +0200
From: Christian Scheele
Date: 2009 Aug 6, 21:50 +0200
Well I'm not in the league of most members in here
but let me try to answer your questions:
"1. Is it
true that:
on land, the culmination of a heavenly body, including the moon, can be established rather accurately in reference to altitude and in reference to time as indicated by a stable local clock? "
on land, the culmination of a heavenly body, including the moon, can be established rather accurately in reference to altitude and in reference to time as indicated by a stable local clock? "
Yes, and not just on land but anywhere on earth.
The almanacs publish this data, tabulating time against declination and GHA
of the sun and Aries for all major celestial bodies used for navigation
pruposes. Of these celestial bodies, the moon's declination changes most
rapidly. The altitude of a celestial body at culmination will be a function of
your latitude and the declination of that body at that time extracted from the
almanac directly against the relevant GMT or found by interpolation.
The function of the sun's declination can be approximated to a high degree of
accuracy using a simple equation, a slightly more complex equation does so
for the equation of time, the effects of precession and nutation can
also be estimated (it would interesting to hear from other members how this is
done exactly, I do not know), but you will need an almanac for
navigation involving the planet, moon and stars unless you are an
expert. Inaccuracies may occur as the result of anomalies in the
surface of the earth and the usual practical problems involved in taking
sights.
"2. Is it true that:
for any given time, there exists on the surface of the Earth a Geometric Locus of all those positions that have the same time difference DT between the culminations of two heavenly bodies?" Yes and I agree with you when you say that
this Geometric Locus of points excatly half-way between
the culmination of two celestial bodies "changes with
time". I think it takes the form of a great circle arc and
changes in two ways. Assuming declination and SHA remain the same, as
they never realistically do, I reckon this arc rotates around on
the earth's axis similarly to the image of any celestial body
projected onto the earth. This arc would change position as the effects of
precession and nutation change the global positions of the two celestial
bodies in question. I wonder what the best way would be to plot
this line, plotting great circle arcs using Napier's laws rather
than transferring them from a Gnomonic chart is laborious,
I won't deny that I haven't done it, being very much a
layman in this area.
Christian Scheele
|
----- Original Message -----
From: Hanno IxTo: NavList@fer3.comSent: Thursday, August 06, 2009 7:34 PMSubject: [NavList 9388] Re: Working a lunar--~--~---------~--~----~------------~-------~--~----~
George:
Thank you for taking the time to think through this concept of mine - as of yet still half baked.
Let me get to the core of the concept in form of a couple of questions:
1. Is it true that:
on land, the culmination of a heavenly body, including the moon, can be established rather accurately in reference to altitude and in reference to time as indicated by a stable local clock?
Neglect for now culminations near the horizon.
Typcally, on land a transit is being used for this measurement.
How well the observed culmination refers to the real local Noon or GMT is not at issue in this question. The "stable" clock need only proceed accurately from second to second, but may not indicate GMT or even the local time.
2. Is it true that:
for any given time, there exists on the surface of the Earth a Geometric Locus of all those positions that have the same time difference DT between the culminations of two heavenly bodies?
(The Geometric Locus need not be contiguous over the surface of the Earth and will change with GMT. I assume it to be close to a straight line locally.)
Affirmative ansers to these two questions form my basic assumptions. If they are not valid I will hold my peace.
Best regards.
H
PS: Found your prior article and enjoyed it.
--- On Thu, 8/6/09, George Huxtable <george@hux.me.uk> wrote:
From: George Huxtable <george@hux.me.uk>
Subject: [NavList 9385] Re: Working a lunar
To: NavList@fer3.com
Date: Thursday, August 6, 2009, 1:29 AM
Hanno Ix suggested a different approach to lunars.
I don't follow some details of that proposal. He wrote-
"A ship reaches land of unknown coordinates. Land makes it practical for the
navigator to measure the meridian passages of Heavenly Bodies rather
reliably. Given GMT, he can calculate LAT and LONG. (One shot method.)"
What is this "one shot method", which allows both lat and long to be
obtained? Does it exist?
However, leaving that aside, Hanno seems to be reinventing the wheel, as he
suspected, when writing "I doubt if it is new".
Obtaining time, and thus longitude can, in theory at least, be done by
measuring simultaneous (or nearly so) altitudes of the Moon and
another-body, rather than the lunar distance, across the sky, between them.
Effectively, two-time-sights are being taken, which, because of the motion
of the Moon with respect to any other-body, will only correspond to each
other if the correct GMT has been assumed. Just as with any other
time-sight, it's most accurate when the altitude changes rapidly with time,
so is worst anywhere near meridian passage.
Such a method has been proposed several times over the years, notably by
Francis Chichester, in an article in "Journal of Navigation", misleading
named "longitude without time", and followed up in other forums. It's
described best, I think, in chapter 17, "Time by lunar lines of position",
of John Letcher's book "Self-contained celestial navigation with H.O. 208"
(1977).
The method has been discussed on this list a few times, under various
threadnames which I can't now recall, but that's no reason why Hanno
shouldn't raise it again.
The proposed method has the advantage of using the sextant, and making the
corrections, in a familiar way, unlike lunar distances; hence its appeal.
But it has serious snags. The lunar-distance method itself has the great
drawback of lack-of-precision. A lunar distance, measured with an accuracy
of 1 arc-minute, can establish longitude only within an error 30x greater,
or 30' of longitude. So it has been useful in marginal circumstances when
any rough notion of longitude is better than no notion at all: but not much
better than that.
The lunar-by-altitudes method is, most of the time, significantly less
accurate, even, than lunar distances, for several good reasons, and that's
enough to rule it out of court, or it least to outweigh any advantage it
might have. With a lunar, the thing hinges on a measurement of a single
quantity, the angle in the sky itself. Provided the observer possesses
enough skill, and the ship's motion is kind, this can be measured with some
accuracy, because the horizon isn't involved (except for use with auxiliary
corrections, not needed to high precision). In contrast, in any altitude
observation, uncertainties in the horizon itself provide most of the
inherent errors, and there have to be two such altitude measurements, not
one, so increasing the scatter.
With a lunar distance, angles between Moon and other-body are changing,
increasing or decreasing, at a rate that's always in the region of 30' per
hour, provided certain simple rules are followed. That can also apply to
altitude measurements made in the tropics, when the Moon and other-body will
pass nearly overhead, but not from higher latitudes, when the rate-of-change
will always be less, and indeed much less when anywhere near meridian
passage.
These are practical problems that conspire against the altitude method;
sufficient to explain why it has never been adopted in practice.
If I've misunderstood what Hanno was proposing, perhaps he will explain
further.
George.
contact George Huxtable, at george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Hanno Ix" <hannoix@sbcglobal.net>
To: <NavList@fer3.com>
Sent: Thursday, August 06, 2009 6:57 AM
Subject: [NavList 9382] Re: Working a lunar
Gentlemen:
I am a novice to CelNav, and I certainly have no experience in lunars.
Some algorithm occurred to me, though, that I would like to share and
discuss. However, given the age of this business, if it is a valid one I
doubt it is new. If anyone has seen it before, please let me know, so I
could read up on it. The objective is to find GMT and location.
Let's make a Gedanken experiment:
A ship reaches land of unknown coordinates. Land makes it practical for the
navigator to measure the meridian passages of Heavenly Bodies rather
reliably. Given GMT, he can calculate LAT and LONG. (One shot method.)
But now we pose GMT as unknown. Sitting on land, measure the meridian
passages of, say, sun and moon which moves. Can I find GMT, too, using the
now available data not using the classical moon distance methods?
If I see things right, there must be a LOP which connects all locations on
Earth with a given, fixed difference DT between the meridian passages of sun
and moon.
However, along this LOP, the same DT occurs at a different GMT. In this
scenario, the LOP referring to a given DT is pre - calculated, listed in an
almanac and annotated with GMT at each LAT. So, by having found the LAT
before we just read the GMT of the DT-specific LOP.
There is another opportunity:
By accepting preliminarily this GMT, we can calculate LAT again, namely from
the meridian passage of the MOON, and compare both values found. If there is
a gross difference we must have made an error. This, by itself, would be of
value. Otherwise, though, we have good reasons to accept the GMT we found.
I appologize if I am talking about a method I have not gone through myself
yet! I fear there is a hick-up in this somewhere. But I would like to hear
the critique of you specialist navigators before I spend alot of time trying
to do something long known as wrong.
If, however, you find it sound, and has not done before I will pusue it.
Best regards
NavList message boards: www.fer3.com/arc
Or post by email to: NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---