I think this belongs here, while not relativistic, is is about objects moving relative to one another.(adsbygoogle = window.adsbygoogle || []).push({});

Summery:

This stems from the description of 'Dark Energy' in a mathamatical context to show that you can place a 'center of the universe' at any point in space, and the accelaration vector between two bodies is inderpendant of the position vectors to this 'arbitary center of the universe'.

Body:

The presumption is that there exsits a 'center of the universe', and that from it we can draw a diagram

A

...\

....\___________________

.....B............................C

Where A is our 'center of the universe', B is one body, C is the other body. There is a radial distances r_{B}and r_{C}respectfully, and the magnitude of radial accelaration from this 'center of the universe' is proportional to these distances.

From B, an oberserver notes that C is accelarating away from him at some accelaration a'_{C}and reversely, from C an observer notes that B is accelarating away from him at some accelaration a'_{B}

How do I show that no matter where I place A, the magnitude of accelaration is not dependant on the 'center of the universe'?

I thought you could describe a'_{C}and a'_{B}as;

a'_{C}= r_{C}K*cos( 1/2 n ) - r_{B}K

a'_{B}= r_{B}K*cos( 1/2 n ) - r_{C}K

Where K is the constant of proportionality and n is the angle between the bodies. Using the geometry between them. I guess that the cosine formula is now somehow incorperated into this;

a^{2}=b^{2}+c^{2}-2bc*CosA

Because there are simmilarities in both equations, but I'm not sure where to go from here in the proof...

Haths

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# Mathamatical Description of the Cosmological Principle

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