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

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Re: formula for refraction
From: Alexandre Eremenko
Date: 2007 Mar 21, 09:39 -0400

```
Bill,
Thanks.
I should read the almanac more:-)

Alex

On Tue, 20 Mar 2007, Bill wrote:

>
>
> > 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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