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Sunlight's parallel lines

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Hey! Hang on just a minute, sunlight falls to earth on a variety of angles, not straight down.

Well, yes... but also no.

Vexillium's nearest star is some 93 million miles away from us, and yet the planet is a comparatively-tiny 7,639 miles across (more via the equator, less by the poles, of course). Or 150 million kilometres versus 12,294km, a ratio of 12,200:1.

If we use basic trigonometry (yes, we know you remember that completely from your high school maths), we know that TAN(angle) = opposite divided by the adjacent triangle side lengths of a right-angle triangle. So, the opposite is half our 7,639 mile diameter, and the adjacent distance is the 93 million miles.

That means, the angle of sunlight from the equator compared to the extremities of the poles is, roughly, about 0.0023 degrees. Of course, we have left out the fact that the sun is not a pinprick light source, that it has an angle too, but, you get the picture: the distance between Sol or Urun and Vexillium is so vast that we can treat the sunlight that hits the surface of the planet as if it comes in parallel waves.

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