Explanation Given: Planet moves around the sun in elliptical orbit with sun at one focus and given graph of the orbit with θ = 0 at aphelion and θ = π at perihelion. Approach: We are given planet moves around the sun in elliptical orbit so we use the polar equation from 43(a) . Substitute value of θ corresponding to aphelion and perihelion in the polar equation. Calculation: From 43(a) , r = a ( 1 − e 2 ) 1 − e cos θ Set: θ = 0 we get: r = a ( 1 − e 2 ) 1 − e = a ( 1 − To determine b) To find: Distances from earth to the sun at perihelion and at aphelion.

Algebra and Trigonometry (MindTap Course List)

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ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 12.6, Problem 44E

To determine

a)

To prove:

The perihelion distance from a planet to the sun is a(1−e) and aphelion distance from a planet to the sun is a(1+e).

To determine

b)

To find:

Distances from earth to the sun at perihelion and at aphelion.

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY

a) To prove: The perihelion distance from a planet to the sun is a ( 1 − e ) and aphelion distance from a planet to the sun is a ( 1 + e ) .

Solution Summary: The author explains how planet moves around the sun in elliptical orbit, and uses the polar equation from 43(a).

Concept explainers

Videos

a)

To prove:

The perihelion distance from a planet to the sun is a(1−e) and aphelion distance from a planet to the sun is a(1+e).

b)

To find:

Distances from earth to the sun at perihelion and at aphelion.

Chapter 12 Solutions

a) To prove: The perihelion distance from a planet to the sun is a ( 1 − e ) and aphelion distance from a planet to the sun is a ( 1 + e ) .

Solution Summary: The author explains how planet moves around the sun in elliptical orbit, and uses the polar equation from 43(a).

Concept explainers

Videos

a) To prove: The perihelion distance from a planet to the sun is a(1−e) and aphelion distance from a planet to the sun is a(1+e).

b) To find: Distances from earth to the sun at perihelion and at aphelion.

Chapter 12 Solutions

a)

To prove:

The perihelion distance from a planet to the sun is a(1−e) and aphelion distance from a planet to the sun is a(1+e).

b)

To find:

Distances from earth to the sun at perihelion and at aphelion.