Explanation Since the planetary motion is periodic, thus, the vector r ( t ) is a trigonometric function...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.6, Problem 2PQ

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How the fact that, $r''$ is proportional to r in the relationship $r'' (t) = - \frac{k}{{‖ r (t) ‖}^{2}} e_{r} = - \frac{k r (t)}{{‖ r (t) ‖}^{3}}$ , is used to prove Kepler’s Second Law.

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Chapter 14.6, Problem 1PQ

Chapter 14.6, Problem 3PQ

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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How the fact that, r ' ' is proportional to r in the relationship r ' ' ( t ) = − k ‖ r ( t ) ‖ 2 e r = − k r ( t ) ‖ r ( t ) ‖ 3 , is used to prove Kepler’s Second Law.

Solution Summary: The author explains how Kepler's Second Law proves that the vector r (t) is a trigonometric function, so its double derivative is same as the original function.

Videos

To explain:

How the fact that, $r''$ is proportional to r in the relationship $r'' (t) = - \frac{k}{{‖ r (t) ‖}^{2}} e_{r} = - \frac{k r (t)}{{‖ r (t) ‖}^{3}}$ , is used to prove Kepler’s Second Law.

Want to see the full answer?

Chapter 14 Solutions

How the fact that, r ' ' is proportional to r in the relationship r ' ' ( t ) = − k ‖ r ( t ) ‖ 2 e r = − k r ( t ) ‖ r ( t ) ‖ 3 , is used to prove Kepler’s Second Law.

Solution Summary: The author explains how Kepler's Second Law proves that the vector r (t) is a trigonometric function, so its double derivative is same as the original function.

Videos

To explain: How the fact that, r'' is proportional to r in the relationship r''(t)=−k‖r(t)‖2er=−kr(t)‖r(t)‖3, is used to prove Kepler’s Second Law.

Want to see the full answer?

Chapter 14 Solutions

To explain:

How the fact that, $r''$ is proportional to r in the relationship $r'' (t) = - \frac{k}{{‖ r (t) ‖}^{2}} e_{r} = - \frac{k r (t)}{{‖ r (t) ‖}^{3}}$ , is used to prove Kepler’s Second Law.