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Re: Biruni and the radius of the Earth by dip
From: John Huth
Date: 2011 Jan 4, 19:07 -0500
From: John Huth
Date: 2011 Jan 4, 19:07 -0500
Sorry to be long winded - here's a cursory set of numbers.
Dip from horizon effects = approx sqrt(2h/R) in radians, this gives a dip of 43 minutes for a 500 m mountain (close to what exists in the Punjab in this region).
Dip from some average refraction = approx 1.75 arc min * sqrt (h in meters) which gives 39 min (I pulled this off the web)
The author of the quoted article quotes al-Biruni's dip as 34 arc minutes, but goes on to give a value of 40 minutes for the dip from refraction, but *then* says that this is 6/5 correct, which I don't understand. It looks to me like the dip for a mountain this high and some "nominal" atmospheric corrections, the two effects are roughly the same size, but then atmospheric effect can drive things all over the map.
Just eyeballing it - it seems like a tough way to go. Maybe he just got lucky or, as the geodesy article suggests, he got the answer he wanted from Sultan Mahmud's result.
Someone can check my numbers.
