NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Approximations: WAS: Star - Star Observations
From: Peter Hakel
Date: 2010 Mar 10, 11:14 -0800
From: George Huxtable <george@hux.me.uk>
To: NavList@fer3.com
Sent: Wed, March 10, 2010 3:38:50 AM
Subject: [NavList] Re: Star - Star Observations
[parts deleted by PH]
A posting from Frank made some valid points, but was a victim of Frank's
familiar attempts to take the trig out of navigation. There are certainly
applications where, under some special circumstances, the trig can be
simplified into plain arithmetic, and this can be one. But then, the user of
any such tricks needs to know what the tricks are, the conditions under
which they may be valid, the level of approximation that may be involved:
and still remains ignorant of how to proceed in other situations in which
that special rule-of-thumb isn't valid. Isn't it better to know a procedure
which applies all the time, even if a bit of trig is involved?
From: Peter Hakel
Date: 2010 Mar 10, 11:14 -0800
George,
I am not sure that I understand this particular brand of your objections.
Physics is full of examples in which rigorous developments yield simpler, convenient results, which are approximate but still adequately accurate. Thus we all use ray-tracing to model our sextants and our eyes, even though we know that geometric optics is only the short-wavelength limit of a more complete theory of light. We all model the Earth as a perfect sphere with 60 nm per degree; yet we are aware of our planet's imperfect shape and can that into account, if necessary.
Frank has clearly identified the range of validity of his "trick" (altitudes above 15 and 45 degrees, respectively) and backed it up by math (refraction ~ tan(ZD), and tan(x) ~ x, for small x in radians), thus getting his 1.00034. In my opinion that is a clever way of solving this particular problem and the number of decimal digits testifies to its accuracy. I am quite sure it would be possible to determine sextant index errors using Maxwell's equations but I doubt that anyone (including you) would do that. Astronauts got to the Moon and back with Newton; Einstein would have been an overkill, and in that sense, not the right approach for the job at hand. That would be like "shooting a pigeon with a missile," as the saying goes.
All of us on this list could be accused of trying to get electricity and computers out of navigation. Someone (certainly NOT a NavList member :-)) could modify your own question and ask us all: "Are you ignorant of the limitation that you can do celestial only when the sky is clear? Isn't it better to just use GPS which works all the time, even if a bit of electricity is involved?"
Peter Hakel
I am not sure that I understand this particular brand of your objections.
Physics is full of examples in which rigorous developments yield simpler, convenient results, which are approximate but still adequately accurate. Thus we all use ray-tracing to model our sextants and our eyes, even though we know that geometric optics is only the short-wavelength limit of a more complete theory of light. We all model the Earth as a perfect sphere with 60 nm per degree; yet we are aware of our planet's imperfect shape and can that into account, if necessary.
Frank has clearly identified the range of validity of his "trick" (altitudes above 15 and 45 degrees, respectively) and backed it up by math (refraction ~ tan(ZD), and tan(x) ~ x, for small x in radians), thus getting his 1.00034. In my opinion that is a clever way of solving this particular problem and the number of decimal digits testifies to its accuracy. I am quite sure it would be possible to determine sextant index errors using Maxwell's equations but I doubt that anyone (including you) would do that. Astronauts got to the Moon and back with Newton; Einstein would have been an overkill, and in that sense, not the right approach for the job at hand. That would be like "shooting a pigeon with a missile," as the saying goes.
All of us on this list could be accused of trying to get electricity and computers out of navigation. Someone (certainly NOT a NavList member :-)) could modify your own question and ask us all: "Are you ignorant of the limitation that you can do celestial only when the sky is clear? Isn't it better to just use GPS which works all the time, even if a bit of electricity is involved?"
Peter Hakel
From: George Huxtable <george@hux.me.uk>
To: NavList@fer3.com
Sent: Wed, March 10, 2010 3:38:50 AM
Subject: [NavList] Re: Star - Star Observations
[parts deleted by PH]
A posting from Frank made some valid points, but was a victim of Frank's
familiar attempts to take the trig out of navigation. There are certainly
applications where, under some special circumstances, the trig can be
simplified into plain arithmetic, and this can be one. But then, the user of
any such tricks needs to know what the tricks are, the conditions under
which they may be valid, the level of approximation that may be involved:
and still remains ignorant of how to proceed in other situations in which
that special rule-of-thumb isn't valid. Isn't it better to know a procedure
which applies all the time, even if a bit of trig is involved?
