phys203 - homework 8_Solutions

phys203 - homework 8_Solutions - The lunar parallax...

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Homework 8 6. Hipparchus and Tycho made many detailed maps and advancements in the field of astronomy. Tycho’s observations were definitely more accurate however. He came hundreds of years after Hipparchus and so was able to update old instruments as well as create new ones with all of the advancements that had occurred in technology over the years. Despite Tycho’s vast achievements and great contributions to discovering details of the universe he was ultimately not at the point where he could measure the annual parallax of the stars. His instruments simply did not provide him with the precision necessary in calculating such a specific figure. Unfortunately he merely could not achieve arc-second accuracy. 7. It is known that comets belong to the heavens, as opposed to our atmosphere because they are too far away. It was Tycho who was able to accurately determine their vast distance from earth.
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Unformatted text preview: The lunar parallax displacement found by Tycho was smaller than one degree, which led him and others to believe that the comet observed is at least six times farther from the earth than the moon, placing it way outside our atmosphere. 8. Kepler’s third law states that the squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits. Based on this and the given information we can calculate the periods of Neptune in years. R = 30.06 R^3 = 27162.324 If R^3 : T^2 T = (R^3)^(1/2) T = 164.810 9. Parallax = (distance sun to earth/distance to star)(180/ ∏ ) = (1210/20000)(180/ ∏ ) = 3.466 This would not have been observable by Hipparchus or Tycho because neither of them had the instrumentation powerful enough to measure the annual stellar parallax. They could not achieve arc-second accuracy....
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