## View Poll Results: What do you think about my work and article "Dilation as field"? (post #56 and links)

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# Thread: Kepler's third law rules the Gravity

1. ## Kepler's third law rules the Gravity

Hello all.

I would like to show something that I hope, you may like.
You will see, that Kepler was perfectly right, but in some unexpected way.

I provide references as links in text.
In whole post we assume that c=1 to simplify calculations.

We take 3rd Keppler law for some rotation in R distance where T is period. We may transform it to form of:

Let our constans for considered rotation will be equal to Schwarschild radius R_s, then:

Let us derive time dilation factor gamma for such move:

As you probably see, it is the same factor that is present in Schwarzschild metric, where for geodesics we have:

Let us differentiate our gamma factor by R. Surprise! - we obtain gravitational acceleration...

If you do not believe it is correct, look at the reference, formula (25), keeping in mind, that:

Looks interesting?
Take a look at this. Now, we derive rest of Schwarschild metric...

At first we recall and transform simply Newtonian formula for accelerated move for our case:

as it is easy to calculate if we differentiate above by "R" we obtain:

thus:

Now, we define observer resting in R distance to source of gravity (f.e. we on Earth).
His proper time formula we may denote as:

Thanks to above observer, Schwarzschild metric may be rewritten for "every particular observer" (without any bad looking "dt" in infinity). For geodesics Schwarzschild metric will be in form of:

Let us rewrite above as:

Now, we show, that difference between Schwarzschild and Minkowski is equal to t_g:

If we denote spatial increment as dx

Schwarzschild metric appears to be consequence of some Kepler rotation in Minkowski timespace...

If you are interested why it works this way, I explain it in my article draft and partly in my previous posts.
Last edited by pogono; 2011-Dec-11 at 06:47 PM. Reason: mistake corrected, thanks to grapes

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