Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 391: 81b

Answer

We can see the graph of the four orbits below: We can see that the Earth's distance from the sun is much smaller than the others' distances from the sun.

Work Step by Step

$r = \frac{a~(1-e^2)}{1+e~cos~\theta}$ Earth: $a = 1.00$ $e = 0.017$ $\theta = 0^{\circ}~~~~~~~r = 0.98$ $\theta = 90^{\circ}~~~~~~r = 1.00$ $\theta = 180^{\circ}~~~~~r = 1.02$ $\theta = 270^{\circ}~~~~~r = 1.00$ Jupiter: $a = 5.20$ $e = 0.048$ $\theta = 0^{\circ}~~~~~~~r = 4.95$ $\theta = 90^{\circ}~~~~~~r = 5.19$ $\theta = 180^{\circ}~~~~~r = 5.45$ $\theta = 270^{\circ}~~~~~r = 5.19$ Uranus: $a = 19.20$ $e = 0.047$ $\theta = 0^{\circ}~~~~~~~r = 18.30$ $\theta = 90^{\circ}~~~~~~r = 19.16$ $\theta = 180^{\circ}~~~~~r = 20.10$ $\theta = 270^{\circ}~~~~~r = 19.16$ Pluto: $a = 39.40$ $e = 0.249$ $\theta = 0^{\circ}~~~~~~~r = 29.59$ $\theta = 90^{\circ}~~~~~~r = 36.96$ $\theta = 180^{\circ}~~~~~r = 49.21$ $\theta = 270^{\circ}~~~~~r = 36.96$ We can see the graph of the four orbits below: We can see that the Earth's distance from the sun is much smaller than the others' distances from the sun.
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