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Re: Sun's distance



In 1963, as a senior undergrad physics major at Cornell University, I
took a course in the History of Science. For a term paper, I
researched the work of the French 18/19th century astronomer de La
Lande, who published a three-volume Encyclopedia of Astronomy circa
late 1790's, with a supplement published around 1810, all four volumes
of which were available for my perusal in the Cornell Main Library.
(Exact dates of publication and of the events described below are,
regretably, no longer accessible in my long-term memory.)

While relative sizes of orbits were known since antiquity, the absolute
scale (i.e., the length of the Astronomical Unit (A.U.) -- the semimajor
axis of the Earth;s orbit) was very difficult to find. During the time
between the first and fourth volumes of Lalande's treatise, the problem
was solved as follows:

Mercury's orbit is quite eccentric, and also inclined a few degrees from
the Earth's orbital plane, the ecliptic. Thus it is a rare event that
Mercury actually passes across the solar disk as seen from Earth. Such
"transits" of Mercury happen in pairs, about two years apart, with an
interval of about 125 years between pairs of transits.
Keplerian/Newtonian theory was quiite up to the task of predicting the
details of the East-West motion of Mercury across the solar disk, but
the apparent latitude of Mercury's transit across the solar disk (i.e.,
where between the North and South limbs of the solar disk) depends very
sensitively on the value of the A.U. AND on the terrestrial observer's
geographic latitude. Since a transit of Mercury takes a matter of 4 or
5 hours, one also has to be at the correct terrestrial longitude to
observe the event.

Lalande's work shows detailed advance calculations of what the two
transits occurring circa early 1800's would look like at various
terrestrial latitudes for various assumptions about the value of the
A.U. Various European astronomers made plans to view the two transits
of the early 1800's -- these, however, involved travel to the
longitudes of Eastern Asia.

One young astronomer (whose name eludes me now) volunteered himself to
travel by sea to Indonesia for the critical observations during the
first transit. (If I remember right, another volunteered to travel
overland to central or eastern Siberia.) Our dedicated astronomer
spent several difficult and unpleasant months sailing from western
Europe around the Cape of Good Hope to Indonesia, arriving several
months before the big event, with plenty of time to set up his sizeable
telescope and to determine his latitude and longitude very
precisely. The day of the transit dawned -- with total overcast,
which did not clear up all day!!

Our intrepid hero (fortunately a bachelor) did not wish to waste his
six-plus month roundtrip and time spent in Indonesia -- or lose his
chance for professional fame and glory -- and decided to stay in
Indonesia for the two
years or so until the second transit would occur during daylight hours
at that longitude. (Not surprisingly, he paid the price of several
bouts with malaria.) Fortunately, this time, the sky was clear, and
he succeeded in making the requisite measurements. When combined with
observations of both transits from more northern latitudes, these
observations succeeded in pinning down the A.U. to a fraction of one
percent.

Fast forwarding to the 1960's and 1970's, large radio telescopes around
the globe were used to transmit radar signals to the terrestrial planets
at various positions in their orbits and making meticulous correction
for diffraction in our atmosphere, general relativistic bending of
photons for beams passing near the Sun's limb; gravitational red
shift going up and down (or vice versa) in the Sun's gravitational field
-- these measurements all combined to give the A.U. to its present
number of significant figures.

And now you know some of the rest of the story ....

Peter Vajk
St. Joseph Notre Dame High School
Alameda, CA 94501