Explanation Given: The points Q = ( a , b , c ) and N o r t h P o l e P = ( 0 , 0 , R ) Radius of Earth is R Key concepts applied: The geodesic distance between two points The geodesic distance between two points given the Radius of the sphere R and the central angle ψ is given by, Geodesic distance = R ψ When the point vectors are given, the central angle can be calculated using the dot product formula, ψ = cos − 1 ( v ⋅ u R 2 ) where v and u are the point vectors representing the two given points. Proof: From given we have the two points Q = ( a , b , c ) and P = ( 0 , 0 , R ) . Let the point vectors of these points be v = 〈 a , b , c 〉 and u = 〈 0 , 0 , R 〉 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 13.7, Problem 85E

To determine

To prove:

The geodesic distance between the given points is equal to $R \cos^{- 1} (\frac{c}{R})$

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Chapter 13.7, Problem 84E

Chapter 13.7, Problem 86E

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Chapter 13 Solutions

Calculus - Standalone book

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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To prove: The geodesic distance between the given points is equal to R cos − 1 ( c R )

Solution Summary: The author explains that the geodesic distance between two points is equal to R cos 1 ( c R) and the central angle can be calculated using the dot product formula.

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To prove:

The geodesic distance between the given points is equal to $R \cos^{- 1} (\frac{c}{R})$

Want to see the full answer?

Chapter 13 Solutions

To prove: The geodesic distance between the given points is equal to R cos − 1 ( c R )

Solution Summary: The author explains that the geodesic distance between two points is equal to R cos 1 ( c R) and the central angle can be calculated using the dot product formula.

Videos

To prove: The geodesic distance between the given points is equal to Rcos−1(cR)

Want to see the full answer?

Chapter 13 Solutions

To prove:

The geodesic distance between the given points is equal to $R \cos^{- 1} (\frac{c}{R})$