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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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