What does the math look like to calculate the size of an object in LEO that when angeled off the sun, would illuminate a part of the Earth's surface?

For example, if I wanted to 'lightup' a square mile of earth surface, how big would the object that's reflecting the sun in LEO need to be to achieve this?

I'd like to see the math that calculates this.

Many thanks in advance.

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    $\begingroup$ How much light do you want? $\endgroup$ – Dan Pichelman Aug 27 '18 at 16:05
  • $\begingroup$ Also, what is the shape of the area to be lit? Square? Circular? And is the light level to be constant over the entire area, or can it vary a little from center to edges, as long as it stays above a minimum value? $\endgroup$ – Tom Spilker Aug 27 '18 at 16:49
  • $\begingroup$ You might want to look into "iridium flares", where something like this happens accidentally. With a normal flat mirror, you're collecting a small amount of sun and spreading it out over a large portion of the Earth. You might be able to accomplish what you want with a parabolic mirror. Under unachievably perfect conditions, you could probably fry ants (or people) from space :) $\endgroup$ – barrycarter Aug 27 '18 at 17:05
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    $\begingroup$ Keep in mind that LEO isn't far away, it is fast. If you are trying to constantly illuminate a fixed point you will need a new satellite every few minutes as the previous one falls toward the horizon. Unrelated, but worth looking into is Rjukan Norway that already does what you are asking on a smaller scale with the mirrors mounted on a hillside. $\endgroup$ – Lex Aug 27 '18 at 20:55
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    $\begingroup$ This has been done as an experiment: smithsonianmag.com/smart-news/… $\endgroup$ – Hobbes Aug 28 '18 at 9:24

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