روش ِ بیرونی raveš-e Biruni
*Fr.: méthode de Biruni *
A method devised by the Iranian astronomer Biruni (973-1048)
to measure the Earth radius, using trigonometric calculations. In contrast to
foregoing → *Eratosthenes' method* and
→ *Mamun's method*, which required
expeditions to travel long distances, Biruni's method was on-site.
He carried out the measurement when he was at Nandana Fort
(at the southern end of the pass through the Salt Range, near Baghanwala in the
Punjab).
He first calculated the height of a hill (321.5 m). To do this he used the usual method
of observing the summit from two places in a straight line from the hill top.
He measured the distance, *d*, between the two places and the angles
θ_{1} and θ_{2} to the hill top from the two points,
respectively. He made both measurements using an astrolabe.
The formula that relates these angles to the hill height is:
*h* = (*d*. tan θ_{1} . tan θ_{2}) / (tan
θ_{2} - tan θ_{1}).
He then climbed to the hill top, where he
measured the → *dip angle*
(θ), that is the angle of the line of sight
to the horizon. He applied the values he
obtained for the dip angle and the hill's height to the following
trigonometric formula to derive the Earth radius:
*R* = *h* cosθ / (1 - cos θ).
The result for the Earth radius was 12,851,369.845 cubits
(or 6335.725 km, using favorable conversion units).
Despite the fact that the method is very ingenious, such a precise value is only
by chance, because of several drawbacks:
The plane was not perfectly flat to serve as the smooth surface of the sea.
A measuring instrument more accurate than the alleged 5 arc minutes was needed. And
the method suffered from the → *atmospheric refraction*
(See, e.g., Gomez, A. G.,
2010, Journal of Scientific and Mathematical Research). Abu Rayhân Mohammad Biruni (973-1048 A.D.), one of the greatest scholars of the
medieval era, was an Iranian of the Khwarezm region;
→ *method*. |