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Since the Sun is larger than the earth, it will illuminate slightly more than 50% of the earth at any given time, illuminating more the closer it is.

To determine the exact percentage of the earth the sun illuminates, requires either a very accurate scale model and light monitoring equiptment, or if you are good at math, requires you to find one common tangent to the surface of both Sun and Earth i.e. a straight line that touches the surface of the Earth and Sun at only one point each. This will allow you calculate the answer to your question. Unfortunately, I have forgotten some of the differential calculus I think you need to do this.

I can tell you that if the Sun were infinitely large, it would illuminate an infintesimal amount less than 100% of the earth and if the Earth and Sun had the same diameter, it would illuminate exactly 50% of the earth.

Good luck and cheers.

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16y ago

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