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Re: formula for refraction
From: Bill B
Date: 2007 Mar 20, 19:10 -0400

> What is the exact formula for refraction (for stars)
> used in the Almanac?

Page 280 0f our almanacs:

Ro = 0d.0167/tan(H + 7.32/(H + 4.32))

H is elevation corrected for IC and dip

Temperature and P correction where T is degrees Cs and P is mb
R = f Ro

f = 0.28/(T + 273)

> The formula given in Meeus does not match the
> almanac table sometimes by more than 0'1.
> Meeus's formula is certainly approximate (and he says so)
> but it does not match the almanac table with the precision
> Meeus claims.
> Chuvenet has complete theory but no useful simple formula.
> My question is practical: I want to incorporate automatic refraction
> computation in my spreadsheet for star distances.

This not work out exactly using it backwards (Hc to Ho). Approximately
November of 2005 George posted the following addressing that matter.  It is
what I use in my separation spreadsheet, with broadcast (sea level) pressure
corrected for altitude above sea level, temperature and pressure.

"The formula quoted above by Paul can be found in several texts and is a
good and simple approximation to observed mean refraction. It's worth
pointing out that it uses two different units of angular measure. The
altitude H must be given in degrees, the refraction correction being in
minutes: very convenient (but needs to be kept in mind).

If H is the observed altitude, then R gives the correction in minutes as a
positive quantity to subtract from it (which was what the expression was
intended for).

It can also be used the other way round, with only a little resulting error.
This is how Paul was using it. If H is a calculated altitude, then R gives
the positive correction in minutes to add to it to show the altitude an
observer would measure with his sextant. For this latter purpose, the
accuracy is slightly reduced, but is restored if an amended version by
Saemundssen, quoted in Meeus, is used, of

R = 1.02 / tan ( H + 10.3/ (H + 5.11)) where H is the CALCULATED altitude.

I don't expect that there would be sufficient divergence between these two
expressions to affect Paul's conclusions.

George"

Bill

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