Explanation Given: The planet's greatest distance from the sun is 43.38 million miles, and the shortest distance is 28.58 million miles. Approach: The standard equation of the ellipse centered at origin is given as, x 2 a 2 + y 2 b 2 = 1 Here, a and b are positive constants. The foci are located on the longer axis of the ellipse and are found by solving the equation, c = ± a 2 − b 2 Calculation: Assume the major axis be a , the minor axis be b and the foci be c . Consider the elliptical orbit from figure ( 1 ) , Figure ( 1 ) From the figure ( 1 ) the greatest distance is ( a + c ) and the shortest distance is ( a − c ) . Then, from the given data the greatest distance can be written as, a + c = 43.38 … ( 1 ) And, the shortest distance can be written as, a − c = 28.58 … ( 2 ) Equate the equation ( 1 ) and the equation ( 2 ) to calculate the value of a . a + c + a − c = 43.38 + 28.58 2 a = 71.96 a = 71.96 2 = 35.98 Substitute 35.98 for a in the equation ( 1 ) to calculate the value of c . 35.98 + c = 43.38 c = 43.38 − 35.98 = 7.4 The foci equation can be written as, c = ± a 2 − b 2 c 2 = a 2 − b 2 … ( 3 ) Substitute 35

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ISBN: 9781305464858

Author: MOWRY

Publisher: CENGAGE LEARNING - CONSIGNMENT

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Chapter 8.7, Problem 28E

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The equation of the Mercury's elliptical orbit.

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The equation of the Mercury's elliptical orbit.

Solution Summary: The author explains how the equation of the Mercury's elliptical orbit is x2(35.98), and the foci are located on the longer axis of

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To find:

The equation of the Mercury's elliptical orbit.