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2019-2020: CXL
THE DAILY ASTRONOMER
Tuesday, May 5, 2020
Remote Planetarium 27: The Sun Part I: Putting the Sun in its Place
Let's try this thought experiment.
Pretend you're living on a happy planet on which astronomy never developed. You then spend a blissful day and night observing the sky. What do you notice? Every celestial object, including the Sun, seems to revolve around our planet. One can see the stars, Sun, moon and planets moving each night east to west. However, by watching the sky over many nights, one notices that the planets exhibit different motions. They move west to east over many nights. Mercury and Venus travel along their respective paths much more quickly than Mars, Jupiter or Saturn. (Remember, without any astronomers, we won't know of any planet beyond Saturn.) Saturn moves the slowest, Mercury the fastest. We reason that the slower a planet moves in our sky, the longer its orbit must be. The Sun also exhibits such a motion relative to the stars. It requires more time than Venus to complete a cycle relative to the zodiac constellations, but less time than Mars. (Note: its revolutionary period is about 365 days.)
Conclusions:
Earth must occupy the Universal center.
The planets follow rigid orbits, or spheres centered on Earth. The moon closest to Earth, followed by Mercury, Venus, the Sun, Mars, Jupiter and then Saturn. The stars, do not exhibit any of the independent motions we've observed in the other bodies. The stars occupy the most distant shell at an indeterminate distance.
Being part of the perfect celestial realm, all the planets are spherical and their orbits circular. No mechanism surpasses the solar system for the elegance of its design and the regularity of its mechanisms.
Oh, but wait!
Over a long time period you notice the planets exhibiting a strange motion. First, the speed of their motion isn't constant, as you would expect it to be were the orbits perfectly circular. Also, and more disturbingly, at various times, the planets appear to stop before reversing course so as to move east to west. Eventually, this "retrograde motion" will cease. The planet will stop again before resuming prograde motion. Let's assume you decide to track the motion of Mars as it progresses through this retrograde loop. You note the planet's position at regular intervals and then chart its progress.
Brilliant! The most beautiful retrograde loop imaginable. Aesthetics apart, however, such motion does present a problem. How can only possibly explain this weird planetary behavior while maintaining Earth's position at the solar system's center? Why would a planet moving around Earth describe such a loop?
Well, here we should allow one astronomer to make an appearance:
Claudius Ptolemy (circa 1st century AD), the mathematically ingenuous fellow who developed a geocentric model that will explain the retrograde motions you've observed. He formalized a system developed by two equally clever mathematicians: Apollonius of Perga and Hipparchus of Rhodes. This system included such clever contrivances as deferents, epicycles and equants. See below:
All the celestial bodies revolving around Earth except for the moon and the Sun travel along epicycles. An epicycle is a small, perfect circle surrounding an equant that travels along a rotating shell (deferent) centered on Earth. As the planet moves around the epicycle, it will sometimes appear to be moving in the same direction as the shell and at other times will appear to move backward. This model, which you decide to call Ptolemaic out of appreciation for Ptolemy's contribution, explains the retrograde motion and the apparent planetary speed changes while maintaining Earth's position in the solar system's center.
How lovely that this situation is working itself out so nicely.
Well. Eventually, you decide that you want to predict future planetary positions based on this Ptolemaic model. You naturally believe that such a mathematically intricate and geometrically perfect system should enable you to make perfect predictions. Perhaps it should, but it doesn't. Discrepancies develop between predicted and actual planet predictions. Granted, only you know about this problem. The others who rely on you for planet information remain blissfully oblivious to this troubling systematic problem.
Perhaps we can allow another astronomer to intervene:
Copernicus (1473-1543) was actually a Polish clergyman and mathematician, not an astronomer, per se. Though history regards him as one of the world's greatest intellectual revolutionaries, Copernicus did not intend to revolutionize astronomy. He instead meant only to develop a system that would enable him to calculate Easter more accurately. The mathematical method he developed to improve these calculations necessitated switching the positions of the Sun and Earth. In the Copernican model, the Sun occupied the solar system center and so became "heliocentric," meaning Sun-centered as opposed to "geocentric" meaning Earth-centered.
The Copernican system neatly explains retrograde motion:
As Earth revolves around the Sun, it will pass a more distant planet such as Mars. From our perspective on Earth, Mars will appear to stop, reverse course, top and then resume its prograde motion relative to the more distant stars while Earth approaches, catches up to and then passes Mars. This effect is similar to watching a car on the freeway as you drive past it. The car actually appear to reverse course against the more distant objects.
Alas, we find that, well, the planet position predictions don't improve at all! Sometimes the planet predictions are evenly slightly less accurate that those based on the Ptolemaic model. Hmmm....Before we decide to place Earth back in its exalted position, let's bring forth one more astronomer. Well, he is more a physical scientist.
Galileo Galilei believed in the heliocentric model because such a system was consistent with his telescopic observations of the solar system. He noticed satellites revolving around the planet Jupiter. (We now call these satellites "Galilean moons.") Also, when he observed the planets Mercury and Venus through his telescope, they exhibited phases, just as the moon does. See below:
On these sketches of Galileo we see Saturn (upper left), followed by Jupiter and Mars. Below, many different phases of Venus. Only in the heliocentric model do the Venusian and Mercurian phases make sense.
We need only two more people; Tycho Brahe (1546-1601) and Johannes Kepler (1571-1630). The first was the grand patriarch of astronomers. He devoted twenty years to studying the planet Mars. Kepler was a mathematician who devoted twenty more years to studying and analyzing Brahe's observations. He developed the three planetary laws, one of which states that every planetary orbit is an ellipse with the Sun at one focus. Copernicus retained the circular orbits in his heliocentric model, hence the inaccuracy. Kepler replaced the perfect circles with slightly elongated ellipses, rendering his model more accurate than the Copernican or Ptolemaic.
The accuracy of Kepler's system and the observations of Galileo have destroyed our lovely geocentric model. The Sun is firmly set in the solar system's center. Earth has been relegated to the lower status of planet, a "moon of the Sun."
Of course, as we will come to learn this week. Putting the Sun in its proper place was only the first step. We'll have much more to do before we can know how we came to know so much about our parent star.
Part II tomorrow.
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