Orbit of the Moon Because its orbit is elliptical, the

Chapter 5, Problem 5.1.1.97

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Orbit of the Moon Because its orbit is elliptical, the distance from the Moon to the Earth in miles (measured from the center of the Moon to the center of the Earth) varies periodically. On Friday, January 23, 2009, the Moon was at its apogee (farthest from the Earth). The distance of the Moon from the Earth each Friday from January 23 to March 27 is recorded in Table 5.1.

(a) Draw a scatter plot of the data, using “day” as x and “distance” as y.

(b) Use your calculator to do a sine regression of y on x. Find the equation of the best-fit sine curve and superimpose its graph on the scatter plot.

(c) What is the approximate number of days from apogee to apogee? Interpret this number in terms of the orbit of the moon.

(d) Approximately how far is the Moon from the Earth at perigee (closest distance)?

(e) Since the data begin at apogee, perhaps a cosine curve would be a more appropriate model. Use the sine curve in part (b) and a cofunction identity to write a cosine curve that fits the data.