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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mathamatical Description of the Cosmological Principle

**Physics Forums | Science Articles, Homework Help, Discussion**