In english? Seriously? Well, my very few readers, just this time because I’d like to see what
[…] click[ing] the like button so hard that Facebook’s servers would poop their pants
does look like if one does not (and never will) use facebook. (Actually even just writing this word in my holy sacred blog gives me the creeps.)
Anyway, the comment section can be used instead of such a button.
And here is the explanation.
The (mean equatorial) radius of the sun is approx. 695.500 km.
The (mean) radius of the moon is approx. 1.737 km.
The ratio of these two figures is 400.
Now the distance.
The (mean distance) from earth of the sun is 1 astronomical unit. Which is approx. 149.000.000 km
The (mean distance) from earth of the moon is more complicated. In perigee it is approx. 363.000 km (And even this is just a mean value. The movement of two bodies really can be a bitch sometimes.) In apogee it is approx. 405.000 km. For the sake of keeping it simple I just take the mean value of these two figures: 384.000 km
Again the ratio of these two figures is 388. Well, not exactly the same value as above but within perigee and apogee there is a position where the sun is 400 times as far away as the moon. I’ll stick with the value 400 also for the ratio of the distances. The reason is the following. Let’s assume the radius of the sun is be just 388 times greater than that of the moon. In this case the angle between the beams looking at the upper/lower edge of the sun (coming from earth) would differ just by approx. one arc minute compared to the angle between the same beams but pointing to the sun with the „real“ mean diameter. But please don’t look directly into the sun. It might mean serious harm to you. (Just in case you haven’t seen the movie „PI“.) This little difference can be seen by the human eye under optimal conditions (as far as I remember my basic physics course; sorry I don’t have a source for that). Still I will consider it negligible with respect to the meaning of the original question and if it just is because most people’s eyes aren’t that good or because of air-disturbances etc.
So. This is the laymans explanation: the sun is 400 times bigger than the moon but it is also 400 times farther away.
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Well, I wouldn’t been me if I just would except that and I don’t expect that you do.
Therefore follows the explanation why this laymans explanation really is valid.
We’ve all learned in school the theorems of intersecting lines. I guess you remember the following drawing.
The lines denoted with „p“ are parallel of course.
Now one of these theorems is: the ratio of the distances CA to CA‘ is the same as the ratio of the distances AB to A’B‘. In our case CA is the distance earth – moon. CA‘ is the distance earth – sun which is [earth – moon] times 400. While AB is the mean radius of the moon and A’B‘ is the mean radius of the sun which is [mean radius moon] times 400.
And finally you have your identity.
Edit: FUCK! I just realized I do need a facebook account that this work hasn’t been in vain. This will never happen, but I’m working on a solution.
