# NavList:

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

**Refraction**

**From:**Dave Walden

**Date:**2008 Jul 3, 16:21 -0700

WITH attachments!

The link below is supposed to take you to page 41 of Modern Astrometry by Jean Kovalevsky which shows graphically the effect of wavelength on refraction

http://books.google.com/books?id=s4azHlUeIYgC&pg=PA40&lpg=PA40&dq=%22+laplace+formula%22+refraction&source=web&ots=4XjmkRNN2W&sig=AAwTVxxyNkTwP_Rm6ZVyJGbq7oQ&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA41,M1

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Refraction

Attached is a small spreadsheet that calculates the K coefficent for the horizontal mulitlayer atmosphere and the A and B coefficents for spherical layer atmosphere. (Errors may remain. Please comment.) They are functions of pressure, temperature and wavelength. Two sets of conditions can be caluclated for easy comparisons. Those included are for the Nautical Almanac conditions and a more conventional set to conditions: 760mb, 0 deg C, lamda .54 microns. The K =60.4 sec, should look familiar. The Naut Alm STP yields 58.2, also familiar. Neither is right. They're just different. Starting with either and adjusting to conditions for a specific observation will yield the same answer.

The formulas can be found in Spherical Astronomy by Green. This is the "successor" to Smart's work. Green was coauthor with Smart on later editions and finally wrote his own. (To my way of thinking, it's better.)

Also attached is a plot of errors of Bennett and simpler formulas (minutes refrac vs degrees alt). There is indeed, nothing magic about Bennett. It get 34 min at 0 deg in case you've forgotten, but the added complication to do so only makes things worse at higher altitudes. (the curve labeled 1term is the planar atmosphere model with just K. It's better than Bennet at all angles above 13 degrees. The hoen-walden is a LaPlace formula with A and B. Its better at all angles above 7 degrees. (The 1 and 2 term formulas blow up at zero, so just don't use them for very small angles.)

The link below is supposed to take you to page 41 of Modern Astrometry by Jean Kovalevsky which shows graphically the effect of wavelength on refraction

http://books.google.com/books?id=s4azHlUeIYgC&pg=PA40&lpg=PA40&dq=%22+laplace+formula%22+refraction&source=web&ots=4XjmkRNN2W&sig=AAwTVxxyNkTwP_Rm6ZVyJGbq7oQ&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA41,M1

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Kent, you wrote:

"The factor 60,35” has been provided to me from the Observatory in Stockholm

to be used with the true zenith altitudes for altitudes above approx. 10

degrees. The factor is taken from modern English litterature."

"The factor 60,35” has been provided to me from the Observatory in Stockholm

to be used with the true zenith altitudes for altitudes above approx. 10

degrees. The factor is taken from modern English litterature."

What color light? It's not often mentioned explicitly that this factor

applies only for one specific frequency in the visible spectrum. That's one

reason why two people can quote factors differing by an arcsecond and still

be technically correct. It's also why we shouldn't worry too much about the

tenths and hundredths of an arcsecond. And it's a big reason why we

shouldn't shoot lunars when the objects are below about ten degrees: the

stars and the limbs of the Sun and Moon are stretched out into colorful

bands at very low altitudes. Incidentally, I use 58" usually.

applies only for one specific frequency in the visible spectrum. That's one

reason why two people can quote factors differing by an arcsecond and still

be technically correct. It's also why we shouldn't worry too much about the

tenths and hundredths of an arcsecond. And it's a big reason why we

shouldn't shoot lunars when the objects are below about ten degrees: the

stars and the limbs of the Sun and Moon are stretched out into colorful

bands at very low altitudes. Incidentally, I use 58" usually.

And:

"Yes, this is correct. For altitudes below 20 degrees I use the formula

defined by Smart."

"Yes, this is correct. For altitudes below 20 degrees I use the formula

defined by Smart."

Since you're modeling historical methods, you could just input the whole

refraction table as printed. Then the software would interpolate between

values much as a 19th century navigator would have done on paper. This

approach bypasses all this chatter about various formulae for different

altitudes. It's also a reasonable approach for a modern analysis. Sometimes

people doing these calculations obsess over the "Bennett" formula. This is

because we carry around "baggage" from the calculator era and the early

years of programming small computers. There's no real advantage to a short

formula today (except saving a few keystrokes).

refraction table as printed. Then the software would interpolate between

values much as a 19th century navigator would have done on paper. This

approach bypasses all this chatter about various formulae for different

altitudes. It's also a reasonable approach for a modern analysis. Sometimes

people doing these calculations obsess over the "Bennett" formula. This is

because we carry around "baggage" from the calculator era and the early

years of programming small computers. There's no real advantage to a short

formula today (except saving a few keystrokes).

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