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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

The orbit of Halley’s comet, last seen in 1986 and due to return in 2061, is an ellipse with eccentricity 0.97 and one focus at the sun. The length of its major axis is 36.18 AU. [An astronomical unit (AU) is the mean distance between the earth and the sun, about 93 million miles.] Find a polar equation for the orbit of Halley’s comet. What is the maximum distance from the comet to the sun?

To determine

To find: The polar equation for the orbit and maximum distance from comet to the sun.

Explanation

Given:

  • Eccentricity of the ellipse is 0.97
  • Length of the major axis is 36.18AU

Calculation:

Calculate the semi major axis.

α=Lengthofmajoraxis(2a)2 (1)

Substitute 36.18AU for 2a in the equation (1).

α=2a2α=36.182=18.09AU

Determine the polar equation for the orbit.

r=α(1e2)1+ecosθ (2)

Substitute 18.09AU for α and 0.97 for e in the equation (2).

r=α(1e2)1+ecosθ=18

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