Subject: Re: [HM] Indian astronomy and mathematics
From: James A. Landau (JJJRLandau@aol.com)
Date: Thu Feb 17 2000 - 08:00:19 EST
In a message dated 02/16/2000 6:48:07 PM Eastern Standard Time, Milo Gardner
writes:
> Dinesh 's 1/6th of a degree reading of the sky became ONLY available
> during the time that telescopes appears, after 1600 AD (as I read the
> history). As a counter example to the 1/6th of a degree suggestion,
> 10-15 minutes of accuracy is the best that I have read than ancients
> took single 'readings's of solar and sidereal star clocks. Improved
> accuracies, needed for longitude computations (after Eratosthenes
> conducted his 'well experiment) had to wait for the telescope.
The resolving power of any optical instrument (including the human eye) is
limited by the diameter of the optical system. (Resolving power means the
ability to distinguish two separate light sources a given angular distance
apart). For the human eye the resolving power is roughly one-half minute of
arc.
The full moon is about thirty minutes of arc in diameter. Thus the human eye
(under optimal conditions, of course!) can see things 1/60 of the diameter of
the full moon. Or in computer jargon, when you look at the full moon in the
sky, you are seeing an object which is 60 pixels across.
Hence the theoretical limit to accuracy of naked eye astronomical
observations is 1/2 minute of arc. According to one source (Giorgio Abetti
)Storia dell'Astronomia_ page 88 of the English translation by Betty Burr
Abetti) Tycho Brahe's observational errors were not greater than 2 minutes
of arc. I think we can say that Tycho demonstrates the PRACTICAL limit of
naked eye accuracy.
The 1/6 of a degree accuracy you refer to is therefore only five times the
error achieved by Tycho. It is also equal to 1/3 of the diameter of the
full moon. Yes, it is possible to get this accuracy WITHOUT telescopes.
I have no information on the observational techniques of the ancient Indian
astronomers and therefore I cannot say whether they in fact did achieve such
accuracy.
James A. Landau
This archive was generated by hypermail 2b28 : Thu Feb 17 2000 - 12:11:47 EST