SteelyKid is a big fan of the classic children’s book Goodnight Moon, which, if you haven’t spent the last sixty-odd years in a cave, you probably know features a bunny saying goodnight to a variety of objects in a great, green room. The attentive toddler will find a lot to look at in the pictures– there’s a mouse in every one that SteelyKid delights in pointing out– but an inquiring adult might well ask “Just how long does it take this bunny to say goodnight to all this stuff, anyway?”
Well, we can answer this question with SCIENCE! You see, there are six pictures in the book showing the moon through one of the room’s windows, and as the book goes along, the moon moves higher in the window. This provides a way to estimate the passage of time in the book. The full sequence looks like this:
(The first and fifth pictures do not show the top of the window. I’ve cropped them to the same size as the full-window illustrations; the remainder of those frames is filled with part of our dining-room table. )
So, how much time has elapsed over the course of the book? Well, in the first picture showing the left-hand window, we can just barely see the moon in the lower left:
This is actually the second color illustration, so it’s a reasonable approximation to guess that the moon was just at the edge of the window frame at the start of the story. In the final illustration, the moon has moved up and to the right by a substantial amount:
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. Coincidentally, this is approximately the time required to read the book to SteelyKid at bedtime, as she points out all the important features of every picture (“Mouse right there! Mouse is sneaky!”).
Of course, there’s another way to estimate the passage of time in the book, which is the clocks shown in the various pictures. The clock in the first picture shows almost exactly 7:00, while the clock in the final picture shows approximately 8:10, for an hour and ten minute duration. Coincidentally, this is approximately the time it takes to get SteelyKid to go to sleep after reading Goodnight Moon…
These two methods clearly do not agree with one another, which means one of two things: either I’m terribly over-analyzing the content of the illustrations of a beloved children’s book, or the bunny’s bedroom is moving at extremely high velocity relative to the earth, so that relativistic time dilation makes the six-minute rise of the moon appear to take an hour and ten minutes. Calculating the necessary velocity is left as an exercise for the interested reader.
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