Geodesic Deviation: Deriving Formula with Schtuz's Book

In summary, the conversation discusses the derivation of the formula for geodesic deviation and suggests using a direct and straightforward approach, possibly by assuming an inertial coordinate system for one of the observers. A website is also provided as a resource for further explanation and clarification.
  • #1
Terilien
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Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
 
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  • #2
You can try, for instance, http://www.mth.uct.ac.za/omei/gr/chap6/node11.html

This seems like a rather direct and straightforwards approach to me, even more direct than MTW's. Of course it is a bit mathematically impure, in that it assumes a convenient coordinate system, but I think assuming an inertial coordinate system for one of the observers makes the physics more apparent.
 
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  • #3
Terilien said:
Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
The derivation I placed on my web page at

http://www.geocities.com/physics_world/gr/geodesic_deviation.htm

started out being a translation from Ohanian's book to my web page. However it seemed to end up being Ohanian's book and part of what I had to say since Ohanian made somethings hard to understand there. Enjoy. Any problems then e-mail me so we can set straight if there is something wrong.

Pete
 

1. What is Geodesic Deviation?

Geodesic Deviation is a concept in differential geometry that describes the change in the distance between two points along a geodesic (a straight line on a curved surface) due to the curvature of the surface.

2. How is Geodesic Deviation derived?

The formula for Geodesic Deviation can be derived using the concept of parallel transport, which involves moving a vector along a geodesic while maintaining its direction. This is done with the help of Christoffel symbols, which represent the curvature of the surface.

3. Who developed the formula for Geodesic Deviation?

The formula for Geodesic Deviation was derived by the German mathematician and physicist, Hermann Schutz, in his book "Geometrical Methods of Mathematical Physics". He used the concept of parallel transport and the equations of motion to derive the formula.

4. What is the significance of Geodesic Deviation?

Geodesic Deviation is an important concept in the study of general relativity, as it helps us understand the effects of gravity on the motion of objects in space. It is also used in navigation and geodesy to determine the shortest distance between two points on a curved surface.

5. How is Geodesic Deviation applied in real-world situations?

Geodesic Deviation has various applications in fields such as astronomy, physics, and engineering. It is used to calculate the trajectory of space probes, to predict the motion of celestial bodies, and to design structures that can withstand gravitational forces. It is also used in the study of black holes and other phenomena related to gravity.

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