John Mallinckrodt and Hugh Haskell have made good responses about
Hewitt's explanation of Aristarchus' estimation of the ratio of the size
of the Earth to that of the Moon. I would like to add the following.
Hewitt, like many other authors, often "explains" some of the things
early scientists did without really making it clear what was done, or
why it works, or what all the simplifying assumptions were. Hugh is
correct that some of these early scientists were really clever, but they
were also often working with bad instruments and bad data and got
results that were way off.
Hewitt does say that Aristarchus was way off on his estimate of the
earth-sun distance; more than an order of magnitude. That means he was
also way off on the sun's diameter. Hewitt claims Aristarchus got the
radius of the moon to within 5% using this shadow business, but sources
I checked say Aristarchus missed this by quite a bit also; about a
factor of 2 off.
Another area where astronomy authors really give a false impression is
on the measurement of astronomical distances using parallax. Most
astronomy texts make parallax measurements sound easy. However, even
though early astronomers reasoned that parallax ought to exist, it took
hundreds of years before any stellar parallax was actually measured.
It's a really tough measurement without the proper equipment/technique.
If you haven't read "Parallax: The Race to Measure the Cosmos" by Alan
W. Hirshfeld, you should get it an read it. A most excellent book.
Only $17 hardback from Amazon or $12 paperback. An incredible bargain.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.