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: 81a

Answer

We can see the graph of the four orbits below:

Work Step by Step

$r = \frac{a~(1-e^2)}{1+e~cos~\theta}$ Mercury: $a = 0.39$ $e = 0.206$ $\theta = 0^{\circ}~~~~~~~r = 0.31$ $\theta = 90^{\circ}~~~~~~r = 0.37$ $\theta = 180^{\circ}~~~~~r = 0.47$ $\theta = 270^{\circ}~~~~~r = 0.37$ Venus: $a = 0.78$ $e = 0.007$ $\theta = 0^{\circ}~~~~~~~r = 0.775$ $\theta = 90^{\circ}~~~~~~r = 0.78$ $\theta = 180^{\circ}~~~~~r = 0.785$ $\theta = 270^{\circ}~~~~~r = 0.78$ Earth: $a = 1.00$ $e = 0.017$ $\theta = 0^{\circ}~~~~~~~r = 0.98$ $\theta = 90^{\circ}~~~~~~r = 1.00$ $\theta = 180^{\circ}~~~~~r = 1.02$ $\theta = 270^{\circ}~~~~~r = 1.00$ Mars: $a = 1.52$ $e = 0.093$ $\theta = 0^{\circ}~~~~~~~r = 1.38$ $\theta = 90^{\circ}~~~~~~r = 1.51$ $\theta = 180^{\circ}~~~~~r = 1.66$ $\theta = 270^{\circ}~~~~~r = 1.51$ We can see the graph of the four orbits below:
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