Archive for May 7th, 2015

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.

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     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.