Since force is transformed via: F'(adsbygoogle = window.adsbygoogle || []).push({}); _{x}= F_{x}; F'_{y}= F_{y}/ ϒ; F'_{z}=F_{z}/ ϒ

(F' is the force related to the moving frame, F is the force on the rest frame and ϒ=1/√1-v^{2}/c^{2}).

I expect that G (Gravitational constant) will be transformed between moving and rest frame in order to satisfy force transformation since

F=-Gm_{1}m_{2}/r^{2}

Can you please refer me to a paper or text book on that specific topic?

It is posable to see that substituting the mass Lorentz transformation m=moϒ and Lorentz-FitzGerald's contraction - r_{o}/ϒ without applying a transformation on G, do not settle the force to get the force transformation like. Instead it gets F'=-Gm_{1}m_{2}ϒ^{3}/r^{2}. Namely F'=F ϒ^{3}.

Can you please refer me to a paper or text book on that specific topic?

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# I Lorentz transformation of the Gravitational constant

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