Spinning Around

[Paul Howe]

Here's a puzzle that's not very difficult, but most people find the solution surprising. It comes in two parts:

i) Everyone knows there are 365 days in a year. Well, actually it's more like 365 1/4 days which is why we need leap years, but to make things simpler we'll assume that a year is exactly 365 days. How many times does the Earth rotate around its own axis in a year? To answer this, you'll need to know that the Earth rotates around its own axis in the same direction as the Earth orbits the sun.
ii) Now assume that the Earth rotates around its own axis the same number of times as in part (i), but in the opposite direction. How many days are there in a year now?

Please no googling, no answering if you've seen it before, and include an explanation with your answer!

[Jason Larsen]

I thought there were 365 days in a year regardless.

What has this turned into? An analytical section of the forum?

[Richard_Brittain]

.

[Craig Beevers]

This is just for i)

364 times?

If you imagine the earth in 2 dimensions at 3 o'clock to the sun, then at 6 o'clock to the sun. At 3 o'clock the left side of the earth faces the sun, at 6 o'clock it's the top side. So you've effectively gained an extra 1/4 of a rotation there (as the moving around the sun and the earth spinning is the same direction). So throughout a year you'll get an extra full rotation, so that leaves another 364 to make up the full 365.

I hope.

[Jason Larsen]

Oh.

I forgot about leap years.

[Paul Howe]

Craig, it's not 364, but you're reasoning along the right lines.

Jason, this has nothing to do with leap years, they're just a human timekeeping device, not an astronomical phenomenon. I've edited the original post to make this clearer.

[Jason Larsen]

Thank you

You all must have very interesting imaginations.

[Richard_Brittain]

.

[Charlie Reams]

it is a mere technical quango

I'm not sure that word means what you think it means...

[Jason Larsen]

And this has nothing to do with leap years!

Amazing!

[Richard_Brittain]

.

[Jason Larsen]

I'm not sure what this section of the forum is turning into.

[Gavin Chipper]

OK, well according to Craig's logic the answer is probably 366. But I still wouldn't count the Earth's orbit around the Sun as an extra rotation. Pedantically speaking, yes, but surely it has no actual relation to reality. Also, the question asked, 'How many times does the Earth rotate around its own axis in a year?' which confuses things further. The normal 365 rotations of the Earth are about its axis, but is this extra one? For all practical intents and purposes, this extra 'rotation' is completely meaningless, it is a mere technical quango. I will, however, admit that it makes for a good puzzle to confuse people. Good one.

If there Earth didn't rotate at all around it's axis then it would be like having one day. Rotating clockwise has the effect of reducing the number of days (try it with one hand going round the other - assuming you have an above average number of hands). So to get 365 days, it would have to rotate 366 times, so I agree with you.

Then if it spun the other way, it must be increasing the number of days by one, so 366 rotations gives you 367 days.

[Jason Larsen]

We're all still here. That's a good thing. If we weren't, there would be no Countdown.

[Howard Somerset]

It's 366.

The earth rotates on its axis once every 23 hours and approx 56 minutes. It needs the extra 4 minutes to continue rotating so that the Sun is in approximately the same place relative to it's apparent position on the previous day. All of those 4 minute chunks add up to an extra 24 hours, so we rotate one more time in a year than there are days in a year.

The 23 hours and approx 56 minutes is the Sidereal Day, a term which came up in Countdown only a few days ago.

[Paul Howe]

OK, well according to Craig's logic the answer is probably 366. But I
still wouldn't count the Earth's orbit around the Sun as an extra
rotation. Pedantically speaking, yes, but surely it has no actual
relation to reality. Also, the question asked, 'How many times does the
Earth rotate around its own axis in a year?' which confuses
things further. The normal 365 rotations of the Earth are about its
axis, but is this extra one? For all practical intents and purposes,
this extra 'rotation' is completely meaningless, it is a mere technical
quango. I will, however, admit that it makes for a good puzzle to
confuse people. Good one.

Yes, the answer is 366, but no I'm not counting the Earth's orbit around the sun as an extra orbit. I'm not sure you've understood what Craig was saying at all.

If there
Earth didn't rotate at all around it's axis then it would be like
having one day. Rotating clockwise has the effect of reducing the
number of days (try it with one hand going round the other - assuming
you have an above average number of hands). So to get 365 days, it
would have to rotate 366 times, so I agree with you.

Then if it spun the other way, it must be increasing the number of days by one, so 366 rotations gives you 367 days.

Right on both counts, and pretty well explained too. I've drawn a rather nice diagram to illustrate all this, but typically my scanner's packed in. Another good way to think of it is what if the Earth had no days at all? It would have to rotate once during a year to keep the same bit of the Earth facing the sun. I think it's kind of cool that if someone were to set the Earth spinning at the same rate but in the opposite direction, our year would be two days longer!

It's 366.

The earth rotates on its axis once every 23 hours and
approx 56 minutes. It needs the extra 4 minutes to continue rotating so
that the Sun is in approximately the same place relative to it's
apparent position on the previous day. All of those 4 minute chunks add
up to an extra 24 hours, so we rotate one more time in a year than
there are days in a year.

The 23 hours and approx 56 minutes is the Sidereal Day, a term which came up in Countdown only a few days ago.

Yes, that about sums it up, although methinks you may have seen this before

[Howard Somerset]

Yes, that about sums it up, although methinks you may have seen this before

Well, it's one of the many things that have interested me ever since I came across a young Patrick Moore, some years before he started his Sky at Night TV prog.

[Jon O'Neill]

http://www.weebls-stuff.com/toons/patrick+moore/

[Paul Howe]

Haha, I was just going to post that Jono. Also, if Patrick Moore can get to Mars on his rocket powered xylophone, just landing on the moon seems a pretty simple thing in comparison.

[Gavin Chipper]

Yes, that about sums it up, although methinks you may have seen this before

Well, it's one of the many things that have interested me ever since I came across a young Patrick Moore, some years before he started his Sky at Night TV prog.

He's been doing that for 50 years! When was this?! Presumably when he was solely the Gamesmaster.

http://www.weebls-stuff.com/toons/patrick+moore/

That's just weird.

[Jason Larsen]

Who came up with this philosophy?

[Howard Somerset]

He's been doing that for 50 years! When was this?! Presumably when he was solely the Gamesmaster.

It was in the early 1950s. The first book I ever borrowed from my school library was one of Patrick Moore's first books. It concerned the subject which he still says interests him the most - the moon. I was then interested to learn that he was starting his series Sky At Night, but was unable to see it for a few years because our family didn't get tv until some years later.

[Kirk Bevins]

If there Earth didn't rotate at all around it's axis then

I just had to quote Gevin-Gavin and correct him - you mean "its" not "it's" don't you! And why "there" and not "the"?

[M. George Quinn]

"It's"
That one confuses me. If your cat is neutered can you say "it's tail"?

[Gavin Chipper]

If there Earth didn't rotate at all around it's axis then

I just had to quote Gevin-Gavin and correct him - you mean "its" not "it's" don't you! And why "there" and not "the"?

"there" instead of "the" is less embarrassing than the other one, because no-one would ever think that you would not know the difference. But I can assure you that it was just carelessness and not lack of knowledge.

[Gavin Chipper]

"It's"
That one confuses me. If your cat is neutered can you say "it's tail"?

Only if it is tail. Is it?

[M. George Quinn]

No, but it's an it.

[Gavin Chipper]

No, but it's an it.

And the tail of it would be its tail (unlike the way I described the Earth's axis). But then if you named it "it"...

[M. George Quinn]

Wahey, we got there eventually.

[Jon O'Neill]

Basically yeah, 'its' is an exception to the rule, stupidly.

[Charlie Reams]

No, all pronouns work that way. You don't write "hi's" or "her's" so "its" behaves consistently.

[Jon O'Neill]

Pronouns are an exception to the rule, stupidly.

[Kirk Bevins]

Pronouns are an exception to the rule, stupidly.

haha

[Gavin Chipper]

http://www.weebls-stuff.com/toons/patrick+moore/

A follow-up was made to this.