   Chapter 10.6, Problem 65E

Chapter
Section
Textbook Problem

# Planetary Motion In Exercises 63–66, use Exercise 62 to find the polar equation of the elliptical orbit of the planet, and the perihelion and aphelion distances. Neptune a = 4.498 × 10 9   kilometers e = 0.0086

To determine

To calculate: The polar equation, the perihelion and aphelion distances of the elliptical orbit of the planet Neptune having the value of eccentricity as e=0.0086 and the value of a as a=4.498×109km.

Explanation

Given:

The value of eccentricity is e=0.0086 and the value of a is a=4.498×109km.

Formula used:

The perihelion distance is

p=a(1e)

The aphelion distance is

ap=a(1+e)

Calculation:

Consider the values, e=0.0086 and a=4.498×109km.

Consider the equation of polar form,

r=(1e2)a1ecosθ

Substitute 0.0086 for e, and 4.498×109 for a,

r=(1(0.0086)2)(4.498×109)1(0.0086)cosθ=(10.00007396)(1.427×109)1(0.0086)cosθ=44976673281(0

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