A *pseudo isotropic* light source (with infinite intensity) of radius \(800 \text{ km}\) illuminates 23% of the surface of a nearby sphere of radius \(6000\text{ km}\).

What is the nearest distance (in \(\text{km}\)) between the two spheres?

Give your answer to 3 decimal places.

**Note**: It is pseudo isotropic in the sense that the light rays seem to emanate from the center of the source and leaves perpendicular to the surface of the source at any point from it.

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