Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10.3, Problem 53E

(a)

To determine

To find: Which satellite has the most circular orbit? Explain your reasoning.

(a)

Expert Solution

Answer to Problem 53E

The GOES 4 has the most circular orbit

Explanation of Solution

Given information: Astronomy: The satellites orbiting Earth follow elliptical paths with the center of Earth as one focus. The table below lists data on five satellites that have orbited or currently orbit Earth.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 53E , additional homework tip 1

Calculation:

The GOES 4 has the most circular orbit because its eccentricity is closest to 0.

(b)

To determine

To find: The greatest distance Sputnik I orbited from the surface of Earth to the nearest kilometer, if the radius of Earth is approximately 6357 kilometers. Soviet satellite Sputnik I was the first artificial satellite to orbit Earth.

(b)

Expert Solution

Answer to Problem 53E

960 kilometers

Explanation of Solution

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 53E , additional homework tip 2

Calculation:

Given,

Semi-major axis a=6955 km

Eccentricity e=0.052

Radius of Earth r=6357 km

Therefore,

Distance of foci from center c=ae=6955×0.052=361.66 km

Distance of farthest vertex =c+a=6955+361.66=7316.66 km

Maximum distance from Earth surface =7316.66−6357=959.66≈960 km

Chapter 10.3, Problem 52E

Chapter 10.3, Problem 54E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

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