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We’ve been working on calculating Earth’s distance to the sun and discussing how past scientists, including Johannes Kepler and Edmund Halley, contributed to the discussion. Today we’ll see how Halley used his theory on the transit of Venus together with Kepler’s Third Law of Planetary Motion and combined them with known mathematical principles to solve the riddle of this enormous distance, known as one astronomical unit, or AU. Halley’s solution began with stationing two observers with telescopes aimed at Venus on opposite sides of the Earth. Their different lines of sight would cause the principle of parallax to come into play, resulting in them seeing Venus from different perspectives. Their sight would converge at Venus’ center and an angle, α, would form between them. Halley posited that if this angle could be measured, it would be an important first step in calculating the distance between Earth and the sun. See Figure 1.
Due to their differing perspectives, Observer A would see Venus traveling a path lower on the sun’s face, while Observer B would see it following a path higher up. See Figure 2.
The net result was that the length, LA, of Venus’ path as seen by Observer A was significantly shorter than length, LB, of Venus’ path as seen by Observer B. Because of this, Observer B would have seen Venus pass in front of the sun before Observer A. These differing observations meant that even if both observers were to set their telescopic crosshairs on Venus at the exact same moment it became visible to each of them, it would serve no purpose, because they lacked a common point of reference at which to aim in order to take measurements. This fact made measuring the angle α with a physical device such as a protractor impossible. So Halley gave up on the idea of physically measuring α. Instead, he proposed calculating it based on the time it took for Observers A and B to watch Venus traverse the sun’s face from one side to the other along each of their observational paths. Next time we’ll see how Halley put his idea to work to calculate α and used it in conjunction with Kepler’s Third Law to calculate the AU.
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Posts Tagged ‘Venus’
The Transit of Venus from Different Perspectives
Wednesday, June 3rd, 2015
The Transit of Venus
Monday, May 18th, 2015|
Last time we learned of Johannes Kepler’s Third Law of Planetary Motion and his development of the astronomical unit (AU) and how these contributed to bringing ancient scientists a step closer to calculating Earth’s distance to the sun. Today we’ll see why Kepler’s focus on Venus, specifically its travel through space in relation to Earth and the sun — the so-called transit of Venus — would become the crucial element to solving the puzzle. Astronomers had previously used the Earth itself as an optical rangefinder to calculate distance to the moon. But unlike the moon which is relatively close to Earth, the sun is many tens of millions of miles away, too distant to be used in that manner. When it came to finding the distance from Earth to its sun, they were stumped. Then in 1716 Edmund Halley had the insight to combine Kepler’s Third Law and the parallax principle with Venus’ orbital journeys to devise an ingenious solution to the problem. The transit of Venus, first predicted by Kepler in 1627, is a rare astronomical phenomenon which only occurs every 243 years. At this time Venus becomes clearly visible from Earth and appears as a black dot traveling a straight path across the fiery backdrop of the sun’s surface. Figure 1 shows this phenomenon as it would look from Earth.
According to Halley’s plan, two observers with telescopes would be positioned on opposite sides of the Earth. Due to the principle of parallax their lines of sight would provide different perspectives of Venus’ path. See Figure 2.
From the perspective of Observer B, Venus’s path would appear higher on the sun’s face than the path seen from the perspective of Observer A. As their lines of sight converge on Venus’ center, an angle forms between them, which we’ll name α. The same angle forms as they look past Venus to the sun in its backdrop. Halley theorized that if the angle α could be measured, Kepler’s Third Law could be used together with trigonometry to calculate the distance between Earth and the sun, Kepler’s so-called AU. We’ll review Halley’s methodology next time.
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The Astronomical Unit — It’s So Relative
Thursday, May 7th, 2015|
Last time we learned that early scientists used the Earth itself as an optical rangefinder to gauge its distance to the moon, and we posed the question: Can Earth be used in the same way to gauge distance to the sun? Unfortunately not. As we learned earlier in this blog series, the more distant the object, the larger the rangefinder that’s required, and the Earth just plain isn’t big enough to be used to compute that distance. The sun is 390 times farther away than the moon is, and that presents a real problem. Today we’ll learn about an alternate method to gauge this great distance. Johannes Kepler made a great contribution towards finding Earth’s distance to the sun when he developed his Third Law of Planetary Motion. Through his observation of planetary movements he was able to determine each planet’s relative distance from the sun in terms of what he dubbed the astronomical unit (AU), a yardstick by which the distance between all planets in our solar system and our shared sun could be judged. Kepler established the distance between Earth and the sun to be that astronomical unit, depicted in the illustration as r.
The reason Kepler developed the AU was because in his day there was no known way to measure the distance to the sun. The AU, an abstract term with no real numerical value in terms of the distance being measured became a sort of placeholder term until r could actually be measured. The best the AU could do was allow him to determine how far a planet was from the sun relative to Earth’s distance from it. For example, his Third Law states that Venus’ distance to Earth is approximately one-quarter the distance between Earth and the sun, or 0.28 AU. That meant that Venus’ distance to the sun was three-quarters the distance of Earth to the sun, or 0.72 AU. Together, these two distances equaled one AU, the as yet unquantifiable distance r between Earth and the sun. Why all the fuss over Venus? Because Edmund Halley, a scientist who came after Kepler and shared in his fascination with interplanetary distances, would use Venus’ proximity to Earth to set up an optical rangefinder relationship between them and the object of his fixation, the sun. Crucial to this accomplishment would be making use of Venus’ orbital movement and the moment it would come into a direct line between Earth and the sun. We’ll explore that further next time.
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