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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 accelerating away from him at some accelaration a'

_{C}and reversely, from C an observer notes that B is accelerating 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