Chapter 10.6, Problem 66E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Comet Hale-Bopp The comet Hale-Bopp has an elliptical orbit with the sun at one focus and has an eccentricity of e ≈ 0.995 . The length of the major axis of the orbit is approximate 500 astronomical units. (a) Find the length of its minor axis. (b) Find a polar equation for the orbit. (c) Find the perihelion and aphelion distances.

a)

To determine

To calculate: The length of the minor axis of Comet Hale-Bopp which has an elliptical orbit with sun at its focus and has eccentricity e0.995 and the length of major axis of orbit is 500 astronomical unit.

Explanation

Given:

An elliptical orbit (Comet Hale-Bopp) with sun at its focus and has a eccentricity eâ‰ˆ0.995 with the length of major axis of orbit is 500au.

Formula used:

The eccentricity of an ellipse as follows:

c=ea And c=a2âˆ’b2.

Calculation:

Consider the eccentricity and length of major axis to find the length of minor axis:

eâ‰ˆ0.995

Length of the major axis of orbit is 500 astronomical unit.

Then,

2a=500a=250

Therefore,

c=ea=250Ã—0

b)

To determine

To calculate: The polar equation of Comet Hale-Bopp which has an elliptical orbit with sun at its focus and has eccentricity e0.995 and the length of major axis of orbit is 500 astronomical unit.

c)

To determine

To calculate: The perihelion and aphelion distance of Comet Hale-Bopp which has an elliptical orbit with sun at its focus and has eccentricity e0.995 and the length of major axis of orbit is 500 astronomical unit.

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