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Peter Hakel wrote, referring to my comments about Frank's posting, in which 
he had pointed to certain simplifying assumptions which could be applied to 
star-star distance calculations, to avoid the need for any trig when both 
bodies exceeded 45� in altitude-

"George,

I am not sure that I understand this particular brand of your objections."

There's a common feature of many postings from Frank, about which he and I 
have argued more than once, mostly about the way the topic is taught. It's 
an old bone of contention. I'm not intending to widen the discussion here, 
but that includes celestial navigation at other times, and with other 
bodies, than the Sun around noon. Lunar distances, in which simplifications 
can be made with certain geometries. Lunar altitudes, which, under special 
circumstances only , might be substituted for lunar distances. It's all very 
well to take advantage of special situations in which a calculation can be 
simplified. But unless a navigator has learned the hard way to handle a 
general case, using trig as necessary, he is handicapped unless those 
special conditions happen to apply. This was another case, in which trig 
could be bypassed, in certain conditions, but not all. But Frank did make it 
clear, right from the outset, that "you should do this as a spherical trig 
problem if you're not doing so already, to cover the general case", so 
really, he and I are not far apart about that aspect, in this case.

"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."

I agree completely. Approximations, such as the spherical Earth, are 
important, as long as we remember their limitations.

"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."

It is indeed clever, and it's to Frank's credit that he has noted it and 
brought it to our attention. It certainly surprised me, that such a 
simplification was possible, and over such an extensive part of the 
sky-area. I note the limit that Frank set, to altitudes above 45�, and agree 
with it, but am not sure where Peter's 15� figure enters, in his "(altitudes 
above 15 and 45 degrees, respectively)"

 Peter ended-" 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?""

Not me. I'm rather an advocate of the use of portable on-board calculators 
or computers to overcome the need for log tables; particularly in view of 
the pernicious effect that the need to adapt formulae for logs has had in 
obscuring their meaning. The result has been that generations of mariners 
have gone through routine calculations by rote, without understanding what 
was going on. Now, it's easier than ever for navigators to apply the 
necessary trig, and understand what they are doing. I am all for that.

Peter draws attention to the most important difference between GPS and 
celestial navigation; that of availability. The target for availability of 
GPS is something like 99.99%, and users would be unhappy with anything less. 
Under the cloudy skies in my own sailing grounds, availability for celestial 
nav is more like 35%. It's a big difference.

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.







--------------------------------------------------------------------------------
From: George Huxtable 
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?




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: "P H" 
To: 
Sent: Wednesday, March 10, 2010 7:14 PM
Subject: [NavList] Approximations: WAS: Star - Star Observations


| 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
|
|
|
|
|
| ________________________________
| From: George Huxtable 
| 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?
|
|
| 

   

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