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7.4 Fibonacci & Other Patterns

7.4 Fibonacci & Other Patterns
  • Math Help

    In Example 5, an astronomical unit is defined as the mean distance between Earth and the Sun, or about 93 million miles.

    Johannes Kepler published the laws of planetary motion based on observation. After they were published, the laws were validated by Isaac Newton (1642-1727). Further, Newton showed that each law can be deduced from a set of universal laws of motion and gravitation that govern the movement of all objects in space, including comets and satellites. For instance, consider the comet named after Edmund Halley (1656-1742), as shown in the figure. The orbit of Halley's comet is an ellipse.

  • Consumer Suggestion

    Have you ever wanted to be an astronaut and explore outer space? Check out the Zooniverse project where you can use data from NASA's Kepler Mission, which is named after Johannes Kepler, to help discover new galaxies that the Kepler Mission team missed. So far volunteers have discovered 90 possible planets that went unrecognized by NASA's Kepler team.

  • Checkpoint Solution

    The completed table is below.

    The square of the period is approximately equal to the cube of the mean distance for each planet listed, which verifies Kepler's Third Law. There are some differences, but these are most likely due to rounding or inaccuracy in measurement. Notice that the error increases as the planets' periods and distances increase.

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      ____     __   __     _____    _____    _____    
     |  _ \\   \ \\/ //   / ___//  |  ___|| |  __ \\  
     | |_| ||   \ ` //    \___ \\  | ||__   | |  \ || 
     | .  //     | ||     /    //  | ||__   | |__/ || 
     |_|\_\\     |_||    /____//   |_____|| |_____//  
     `-` --`     `-`'   `-----`    `-----`   -----`   
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