Greenwood press
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book-20600
CONIC SECTIONS
19 Johannes Kepler (1571–1630) revolutionized astronomy when he recognized that the motion of planets about the sun was elliptical and not circular. Working with the detailed planetary observations of Tycho Brahe (1546–1601), Kepler found some very slight errors in Brahe’s figures for the circular orbit of Mars. He attempted to correct the values, but finally concluded the data was correct and that the orbit of Mars was elliptical with the sun at one of the focal points of the orbit. His verification of this for the other known planets of his time is known as “Kepler’s first law.” (See Variation.) Some comets, like Halley’s comet, follow an elliptical path around the sun just like planets. Hence Halley’s comet “returns” to earth’s view on a regular basis. However, some comets appear to follow parabolic or hyperbolic paths. Once past the sun, they leave our solar system. These comets may have traced elliptical orbits at one time, but were thrown off trajectory by a gravitational encounter with a major planet such as Jupiter. Many machines contain elliptical gears. These develop a nonuniform motion from a uniform power source. The momentary speedup or slowdown they pro- duce is important in rotary shears, conveyers, motorcycle engines, and packag- ing machines. Statisticians conceptualize plots of many variables on large numbers of sub- jects as elliptical swarms of points. By finding the axes of such swarms, they syn- thesize the information from many variables into important structural variables. online sources for further exploration Artistic views of conics Conics in general Pictures of Appollonius’s analysis Explore conic sections dynamically Hyperbolic mirrors A video view of Statuary Hall in the U.S. Capitol Parabolic reflectors and antennas Download 1.81 Mb. Do'stlaringiz bilan baham: |
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