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The initial question sounded to me more like the case that the surface of the Earth was 10,000km from the surface of the Sun (i.e. the center of the Sun was at a distance d=695,700km + 6,370 km+10,000km from the center of the Earth). What would happen in such case?
The intense heat and radiation would be the least of our problems. 10000 km would put us well within the Roche limit of the sun: the Earth would be torn into little pieces, or just fall straight into the sun!
So what would be the best sun screen to use?