(9a) May Earth be
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Aristarchus: Is the Earth revolving around the Sun?," section #9a : on disk Sarist.htm, on the web |
"From Stargazers to Starships" home page and index: on disk Sintro.htm, on the web
Goals: The student will|
Terms: (none new)
Stories and extras: The entire section is a story, of how Aristarchus was (probably) led to his heliocentric theory.
Start the class by discussing what is a scientific discovery? Historians of science often argue about "who was first"--but what does it mean?
The Greek philosopher Democritus argued that all matter consisted of "atoms", a Greek word meaning "undividable. " He pointed out that a collection of very small particles--e.g. sand or poppyseeds--can be poured like a continuous fluid, so maybe water, too, consists of many tiny "atoms" of water. Does this qualify as a prediction of the atomic theory of matter?
In the early 1700s, the Irish writer Jonathan Swift wrote "Gulliver's Travels, " a satire of the politics and society of his times, in the form of voyages to distant fantastic countries (today it might have been called "science fiction.") In his third voyage he visits an island floating in the air, which is ruled by an academy of scientists (a spoof on the "Royal Society", an association of Britain's top scientists which still exists). He reports that by using improved telescopes, members of the academy had discovered that two small moons orbiting Mars at a close range.
A century and a half later, an astronomer discovered that Mars indeed had two such satellites, quite similar to what Swift had described. Does it mean that Swift had predicted those moons?
By our standards, these are just lucky guesses. To qualify as a prediction, a claim needs not only to be stated, but also justified, it needs a logical reason. In this lesson we discuss a proposal by Aristarchus, around 270 BC, that the Earth went around the Sun, rather than vice versa. It took 1800 years before this claim was made again, and another century before it was generally accepted.
However, this was not guesswork. Aristarchus, who also estimated the distance of the Moon, had a serious reason for his claim: the Sun, he showed, was much larger than the Earth, making it likely that the Sun, not Earth, was at the center.
Let us go through his arguments.
Give the material of section 9a of "Stargazers. Start by assuming that the shadow of the Earth had the same width as the Earth, and that the Earth had twice the width of the Moon. Later, if time and the level of the class allow it, the teacher may continue with a discussion of the actual shadow of the Earth, which is cone-shaped [Section 9b].)
Guiding questions and additional tidbits
-- Who was Aristarchus of Samos?
[The teacher may point out that dates BC seem to proceed in the opposite direction to what we are used to--e.g. born -310, died -230.]
-- What did Aristarchus establish about the Moon?
-- What was the revolutionary proposal Aristarchus made about the Sun?
That the Sun was much bigger than the Earth
That the Earth went around the Sun, not vice versa
-- On what observation did Aristarchus base his claims about the Earth?
-- What is the Moon's relation to the Earth and Sun, when it is half-full?
-- What does the Sun-Earth-Moon angle (corner at Earth) at such times tell about the Sun's distance?
[Draw diagram of the triangle on the blackboard.]
As it happened, the measurement made by Aristarchus was inaccurate. It is hard to tell when the Moon is exactly half full! He believed the Sun-Earth-Moon angle was 87°, short of 90° by 3°. The Earth-Sun-Moon triangle then has a sharp corner of 3 degrees, and its proportions were such, that the Sun was about 20 times further than the Moon.
-- If the Sun is 20 times more distant than the Moon, what does it say about the Sun's size?
-- What did Aristarchus believe about the relative size of the Earth, compared to the Moon and Sun?
-- How did Aristarchus view the Sun-Earth system?
--Did other astronomers agree with Aristarchus?
--What was their argument? (teacher may help fill details)
To the ancient Greeks, that was an enormous distance. The stars were clearly more distant than the Sun, but it was hard to imagine that from two positions so far apart, there should not exist some difference in the apparent positions of stars in the constellations of the sky. Yet none could be seen.
That was the argument of Hipparchus and Ptolemy, leading Greek astronomers. Their view prevailed for about 1800 years.
--Was there a flaw in that argument?
However, the stars were much more distant than anyone had held possible. Any shift in their positions was too small to be observed by the eye.
(Such a shift was first observed in 1838, using some of the best telescopes of the era, and even then, only for the stars nearest to us. See the section on parallax.)
(9b) The Earth's Shadow [optional]
One should start it by making clear that the Sun covers a 0.5° disk of the sky. If we select some point P on Earth and trace all the sun's rays that reach it from that disk, those rays form a narrow cone.
That cone contains all the directions in which the Sun's rays arrive at the Earth's vicinity, and the full shadow of the Earth only extends over the region where all those directions are blocked by the Earth.
It will only extend a certain distance behind Earth. At greater distances, the Earth will cover less than 0.5° of the sky and will appear smaller than the Sun. At those distances, one can never be in the full shadow of the Earth.
The Lagrangian L2 point, 236 Earth radii from Earth on the side opposite from the Sun, is a good location for a distant observatory. Being more distant from the Sun, it should orbit it more slowly than Earth, but because of the added pull of the Earth, it can move a little faster and thus keep up with Earth (more about Lagrangian points is in the last part of "From Stargazers to Starships").
NASA plans to place its next large infrared telescope at this position. It would be just outside the shadow cone. The Earth would be a little too small to cover all the Sun, which would shine in a bright ring around the dark Earth. In full shadow, the telescope would get very cold--a desirable feature for detecting infra-red light. As it is, it will need a light shield to protect it from the remaining sunlight.
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Author and Curator: Dr. David P. Stern
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Last updated: 12 September 2004