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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Halley’s Comet

Probably the most famous of all comets, Halley’s comet, has an elliptical orbit with the sun at one focus. Its maximum distance from the sun is approximately 35.29 AU (1 astronomical unit is approximately 92.956 × 10 6 miles), and its minimum distance is approximately 0.59 AU. Find the eccentricity of the orbit.

Chapter 10.1, Problem 77E, Halleys Comet Probably the most famous of all comets, Halleys comet, has an elliptical orbit with

To determine

To calculate: The eccentricity of elliptical orbit of Halley’s Comet, where the nearest and farthest distance of the Sun from the Halley’s Comet is 0.59 AU and 35 AU respectively.

Explanation

Given:

The nearest and farthest distance of the Sun from Halley’s Comet is 0.59 AU and 35 AU respectively.

Formula used:

The eccentricity of ellipse, e=ca.

Calculation:

Consider an elliptical orbit for Halley’s Comet such that, 2a is the length of major axis and 2b is the length of minor axis.

Let farthest and closest point on an elliptical curve from foci of an ellipse are A and P respectively. Let c is radius of Halley’s Comet.

So, the nearest point from Halley’s Comet is,

A=ac …...…... (1)

The farthest point from the Halley’s Comet is,

P=a+c …...…... (2)

Add equation (1) and equation (2),

A+P=2aa=A+P2

Put the value of a in equation (2), to find the value of c,

P=a+cc=aP=A+P2P

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