Explanation Formula used: Velocity = Distance Time Calculation: For a circular orbit of radius R , we can write its circumference as 2 π R . Therefore, using the formula Velocity = Distance Time , we get: ⇒ Velocity = Distance Time ⇒ v = 2 π R T ⇒ v T = 2 π R As per Kepler’s Third Law, we can write: T 2 = 4 π 2 G M R 3 Plugging T = 2 π R v , we get:

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 14.6, Problem 9E

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To prove:

For a planetary orbit of circular radius R, we have: $v T = 2 π R$ .

Where v is planet’s speed and T is period.

Furthermore, using Kepler’s Third Law, show that $v = \sqrt{\frac{k}{R}}$ .

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Chapter 14.6, Problem 8E

Chapter 14.6, Problem 10E

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Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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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To prove: For a planetary orbit of circular radius R , we have: v T = 2 π R . Where v is planet’s speed and T is period. Furthermore, using Kepler’s Third Law, show that v = k R .

Solution Summary: The author proves that v T = 2 R for a planetary orbit of circular radius R.

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To prove:

For a planetary orbit of circular radius R, we have: $v T = 2 π R$ .

Where v is planet’s speed and T is period.

Furthermore, using Kepler’s Third Law, show that $v = \sqrt{\frac{k}{R}}$ .

Want to see the full answer?

Chapter 14 Solutions

To prove: For a planetary orbit of circular radius R , we have: v T = 2 π R . Where v is planet’s speed and T is period. Furthermore, using Kepler’s Third Law, show that v = k R .

Solution Summary: The author proves that v T = 2 R for a planetary orbit of circular radius R.

Concept explainers

Videos

To prove: For a planetary orbit of circular radius R, we have: vT=2πR. Where v is planet’s speed and T is period. Furthermore, using Kepler’s Third Law, show that v=kR.

Want to see the full answer?

Chapter 14 Solutions

To prove:

For a planetary orbit of circular radius R, we have: $v T = 2 π R$ .

Where v is planet’s speed and T is period.

Furthermore, using Kepler’s Third Law, show that $v = \sqrt{\frac{k}{R}}$ .