The Astrophysics of Goodnight Moon

Chad Orzel's young son recently read the classic children's book Goodnight Moon by Margaret Wise Brown. He asked his father how long it took the rabbit to say goodnight to everything. Orzel ran some calculations based upon the movements of the moon (pictured above) over the course of the story:

So, how can we use this to measure the passage of time? Well, we know that the full moon in the sky covers an angle of about half a degree of arc. On our big copy of the book, the diameter of the moon in the final illustration is just about 7/8" (I only have an English-unit tape measure here), while the distance from the corner of the window to the outer edge of the moon is 2 and 5/8", exactly three times the diameter. So the moon has moved through about 1.5 degrees in the course of the story.

Now, the Earth rotates through 360 degrees in just about 24 hours, which is 15 degrees per hour (the Moon's motion is slightly slower, owing to its orbital motion, but it's not a significant difference for our purposes). This suggests that the bunny's goodnight ritual takes about 0.1 hour, or six minutes.

Link via Geekosystem

Previously on Neatorama:
Goodnight Keith Moon
Goodnight Forest Moon

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