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Can somebody who understands the subject (or have read the paper more carefully than me) say how the moment of the shadow on the earth would be? Would it be fixed on a part of the earth or move, and if it moves, how fast and in what "orbit". I.e, would some part of the earth get more (much more?) cloudy days if this would to be implemented?

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The inner Lagrange point is always between the sun and the earth (by definition), so the "shadow" would always be centered on local "noon" and would pass the each longitude at the same time every day.

But the sun isn't a single point, it is big! In the same way that a pencil can have a sharp shadow but an office building will have a blurry shadow, the satellites would produce blurry shadows.

I'm not sure of the dimensions of the inner Lagrange point-- I agree that the shadow would be centered on astronomical noon, but I think it would be so blurry, and have such a wide blur radius, as to be unnoticeable except as a change in absolute light.

You wouldn't see the shadows individually. The sun would just be a little bit (1.8%) less bright.

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