Puzzle: About how many times does the Earth turn around its axis each year?
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Great timing! I'm working on a colloquium for next week on this topic (that is, the attempt by the U.S. State Department to redefine the word "day"). Search on the term "synodic" for references. Every planet or moon has one fewer day per year than axial rotations; each laps the Sun once per year unwrapping one rotation. This works for retrograde rotators like Venus since the rotational period is defined to be negative in that case. And it works for rotational periods longer than a year (Venus again).
To apply this to the coin problem, the roll-without-slipping constraint means that the small coin experiences two days per year (the original point of contact repeats halfway around so it is "noon" again). Two days means three rotations.
Puzzle: Due to a spin-orbit resonance, Mercury rotates precisely 3 times in 2 of its years. How long is its day to within a couple of Earth hours? Hint: The semi-major axis of Mercury's orbit is 0.387 AU.Apr 5, 2012
On the original question: about 1000/3. I use this approximation quite frequently.Apr 5, 2012
+John Baez wrote: "When he was asked how he saw the quark theory before everyone else, he said 'because I was surrounded by a sea of dwarves.'"
Probably referring to Murray Gell-Mann's former coauthor and later nemesis, Abraham (Bram) Pais. Who happened to be not very tall. Gell-Mann also called him "evil dwarf". Once again showing that the difference between a kid and an adult is much smaller than what we imagine it to be.Apr 5, 2012
Earth rotates more than 360° relative to the fixed stars in one solar day:
360.9856°/day
(according to <http://en.wikipedia.org/wiki/Earth%27s_rotation>).
That's
1.00273778 rotations/day.
Now
1 year = 365.242199 days.
So (assuming I did the calculations right):
There are 366.242152 rotations of Earth in one year.Apr 5, 2012
That looks about right, +Philip Thrift! I don't vouch for all the decimals, but 366 1/4 should be close to the right answer, and it's close to your answer.Apr 5, 2012
ABOUT how many times does our Earth's moon rotate in a year? ROFL
<cue the Jeopardy music>Apr 5, 2012