Message-Id: <v01540b0eaf32460369c4@[192.174.2.173]>
Date: Thu, 20 Feb 1997 11:58:14 -0800
To: pinhole@exploratorium.edu
From: pauld@exploratorium.edu (Paul Doherty)
Subject: scattering and orbits
Hi Marc
I didn't get a previous e-mail.
Good question as usual.
My reference books don't tell me how the size of the earth's orbit was
measured accurately in 1600. However here is a start at an answer.
Abell's astronomy text says that the value for the radius of the earth's
orbit before 1600 was determined by Aristarchus circa 200 BC. He got, 1200
earth radii as the distance from the sun to earth. (made using geometry and
observations of the first and third quarter of the moon his measurement was
too small by a factor of 20)
The value in 1600 AD was determined by Kepler. He tried to measure the
parallax of Mars as viewed from one side of the earth compared to the other
(Just wait 1/2 a day and the earth's rotation will carry you over that
distance.) The parallax was too small for him to measure so he knew Mars
must be further away than the limiting accuracy of his measurement. Knowing
the minimum size of mars orbit allowed him to determine the minimum size of
the earth's orbit (use geometry to get the relative sizes of earths orbit
and Mar's orbit from observations of the maximum elongation of mars _
details on request.)
His value was 3600 earth radii, a value that was seven times too small.
With telescopes early in the 1600's the parallax of Mars could be measured
and the size of the earth's orbit determined. But my books don't say who
did this.
Gauss after 1800 showed how to use Newton's laws and observations of the
planets to determine thier orbits including their orbital radii. (The
constants in Newton's equation were determined from the earth-moon system)
Blue sky scattering is due to the tyndall effect.
If you have any scatterer small compared to a wavelength of light -
colloidal suspension particle or molecule (component of air) that does not
have an absorption line in the visible spectrum but does have one in the UV
then that small particle will scatter light proportional to the fourth
power of the frequency. So it will scatter blue preferentially over red.
When you gather molecules together so that they are closer than a
wavelength of light (as they are in liquid water and liquid oxygen) then
there are absorptions in the visible which give the liquid oxygen its blue
color and water its green color. These absorptions do not contribute to the
color of the sky.
Paul D