Relativity Question



I've probably got something basically wrong with the General
Relativity ideas, as they lead me to a contradiction. for example, I
understood that it states that any coordinates system is legitimate,
i.e. any observer can decide he's the center of the universe and
measure all particles' locations and velocities relative to himself -
even observers who have relative acceleration (contrary to Special
Relativity). So let's assume we on earth decide that the sun revolves
around us - but that can be refuted, as Kepler's third law states that
the retio T^2/R^3 of the orbit depends on the mass of the orbited
body, and of course this ratio is the same whether looking from the
sun or from the earth. So it can be prooved that we revolve around the
sun and not vice versa (Relativity doesn't change Kepler's law so
much, does it?).

Another Relativity question I came upon years ago, and I'm sure
bothers a lot: if I have two static charges, say at coordinates
(0,0,0) and (0,1,0), I have an electric force. Now assume another
ovserver who moves at a constant velocity (in the x axis) - he'll see
these two charges as moving, adding a magnetic force, resulting in a
different total force (and a different acceleration of the charges,
which can be measured). That's because the electric force is the same
(as the observer's velocity doesn't change the charges nor their
distance, as it's on the x axis) and the magnetic force depends on its
own velocity relative to the charges. In Classic Physics we could
solve this by assuming an absolute space, but of course in Special
Relativity this is unacceptable (and the observer's velocity can be
non-relativistic, so the answer isn't here).

Any one can help me with these? thanks a lot in advance.

.



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