Solved: Keplers Law of Planetary Motion The time it takes for a planet to complete its

Chapter 14, Problem 23

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Keplers Law of Planetary Motion The time it takes for a planet to complete its orbit around the sun is called the planets sidereal year. Johann Kepler studied the relation between the sidereal year of a planet and its distance from the sun in 1618. The following data show the distances that the planets are from the sun and their sidereal years. Planet Distance from Sun, x (millions of miles) Sidereal Year, y Mercury 36 0.24 Venus 67 0.62 Earth 93 1.00 Mars 142 1.88 Jupiter 483 11.9 Saturn 887 29.5 Uranus 1785 84.0 Neptune 2797 165.0 Pluto* 3675 248.0 * Plutos status was reduced to a dwarf planet in September 2006. (a) Determine the least-squares regression equation, treating distance from the sun as the explanatory variable. (b) A normal probability plot of the residuals indicates that the residuals are approximately normally distributed. Test whether a linear relation exists between distance from the sun and sidereal year. (c) Draw a scatter diagram, treating distance from the sun as the explanatory variable. (d) Plot the residuals against the explanatory variable, distance from the sun. (e) Does a linear model seem appropriate based on the scatter diagram and residual plot? (Hint: See Section 4.3.) (f) What is the moral?