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Subject: Re: accuracy of automatic celestial navigation
From: George Huxtable (george@XXX.XXX)
Date: Mon Dec 09 2002 - 17:58:12 EST
Rodney Myrvaagnes wrote-
>Thanks to Paul Hirose for a most informative post. Just one thing
>bothers me:
>
>On Sun, 8 Dec 2002 23:07:34 -0800, Paul Hirose wrote:
>
>>
>>Earth's lumpy gravitational field is indeed a factor in inertial
>>navigation; it has to be stored in some sort of internal map or table.
>>
>I don't understand how the earth's lumpy gravitation could affect
>inertia in a B2. I know it goes pretty fast, but it would have to get
>close to the speed of light for relativistic effects to become
>comparable to the drift of the ANS. Am I missing something?
============
Comment by George Huxtable.
What I think you are missing, Rodney, is this-
Mapping and charting is usually done on the assumption of a spheroidal
Earth. However, the actual gravity-field of the Earth is indeed "lumpy", as
Paul put it. This has a number of consequences.
If an aircraft or a ship, passed near the traditional "mountain of lead",
this would distort the local gravity, so the vertical would point in a
slightly different direction nearby, which the original chartmaker would
not have known about or allowed for. A sensor of the vertical like a
pendulum, or a sensor of the horizontal like a spirit-level or the
sea-surface, would locally point in the "wrong" direction, and so celestial
altitudes, which are always measured with respect to the local direction of
gravity, would be "wrong" by that amount. In normal navigation by surface
vessels, any such error is ignored.
With inertial navigation, an aircraft integrates up its accelerations, and
presumes that in the absence of any accelerations it continues in a
straight line (I ignore Coriolis effects here). But the aircraft is
affected by gravity in the same way that you and I are, and has to
counteract its accelerating force just to stay in the same place (just as
we do). So an aircraft needs to know the local strength (and direction) of
the gravity-force in order to compensate for that part of its acceleration.
A rocket coasting in space is acting only under the force of gravity, which
varies along its path for a number of reasons, so presumably precise
calculations of its trajectory require a three-dimensional map or model of
the Earth's gravity field.
To this end, the USAF has mapped local gravity around the world to a high
degree of precision, of which the finer details were, and perhaps still
are, classified information.
Relativity, which was worrying Rodney, has nothing to do with the matter.
George Huxtable.
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george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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