So this has got me stumped.

The Earth orbits the Sun once a year and revolves daily. During the height of Summer at midday one hemisphere of the Earth is bathed in sunlight while the opposite hemisphere in darkness.

Now exactly 6 months later these positions are reversed.

Now my question is this:

If a hemisphere is facing the Sun at 12noon in Summer, shouldn’t it be facing away from the Sun exactly 6 months later meaning that it should be night time at 12noon? How come our days aren’t 12 hours out of sync over a period of six months?

I know I must be missing something but can’t think what.

“6 months” is not precisely half the Earth’s orbital period bit is a time that is approximately equal to that while being counted out in days.

If the earth’s axis were tilted fully 90 degrees, you would end up with whole hemispheres in complete darkness or sunlight at seasonal extremes. As it is, it is only tilted a little, so only parts of the arctic and antarctic are in full sunlight or darkness.

>The Earth orbits the Sun once a year and revolves daily. During the height of Summer at midday one hemisphere of the Earth is bathed in sunlight while the opposite hemisphere in darkness”

Not sure I understand

Seasons …… axis tilt offset from perpendicular to sun
Hemisphere…that extending from a pole to equator
Day….more sunward facing portions of both hemispheres

In general there is no reason to expect any particular rational relationship between the totational and orbital periods of Earth (since the planet is not gravitationally locked to the Sun.)

>any particular rational relationship

not disagreeing, but what does ‘rational’ mean in “…any particular rational relationship…”

Does this help?

https://www.youtube.com/watch?v=q4_-R1vnJyw

On a related subject, what is the origins of the hour, minute and second, I can see it could have been done differently.

http://en.wikipedia.org/wiki/Season

“A season is a division of the year, marked by changes in weather, ecology, and hours of daylight. Seasons result from the yearly orbit of the Earth around the Sun and the tilt of the Earth’s rotational axis relative to the plane of the orbit. In temperate and polar regions, the seasons are marked by changes in the intensity of sunlight that reaches the Earth’s surface, variations of which may cause animals to go into hibernation or to migrate, and plants to be dormant.

During May, June, and July, the northern hemisphere is exposed to more direct sunlight because the hemisphere faces the sun. The same is true of the southern hemisphere in November, December, and January. It is the tilt of the Earth that causes the Sun to be higher in the sky during the summer months which increases the solar flux. However, due to seasonal lag, June, July, and August are the hottest months in the northern hemisphere and December, January, and February are the hottest months in the southern hemisphere.”

http://en.wikipedia.org/wiki/Hour

“The hour (common symbol: h or hr) is a unit of measurement of time. In modern usage, an hour comprises 60 minutes, or 3,600 seconds. It is approximately 1/24 of a mean solar day.

An hour in the Universal Coordinated Time (UTC) time standard can include a negative or positive leap second, and may therefore have a duration of 3,599 or 3,601 seconds for adjustment purposes.”

Witty Rejoinder said:

So this has got me stumped.

The Earth orbits the Sun once a year and revolves daily. During the height of Summer at midday one hemisphere of the Earth is bathed in sunlight while the opposite hemisphere in darkness.

Now exactly 6 months later these positions are reversed.

Now my question is this:

If a hemisphere is facing the Sun at 12noon in Summer, shouldn’t it be facing away from the Sun exactly 6 months later meaning that it should be night time at 12noon? How come our days aren’t 12 hours out of sync over a period of six months?

I know I must be missing something but can’t think what.

I think (not sure, happy to be corrected) that the shortest answer to your question is “sidereal time”. http://en.wikipedia.org/wiki/Sidereal_time

“Sidereal time is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky. Briefly, sidereal time is a “time scale that is based on the Earth’s rate of rotation measured relative to the fixed stars….

“Because the Earth orbits the Sun once a year, the sidereal time at any given place and time will gain about four minutes against local civil time, every 24 hours, until, after a year has passed, one additional sidereal “day” has elapsed compared to the number of solar days that have gone by.”

So, in six months of orbiting an additional half day of sidereal time has elapsed, putting any particular point on the Earths surface facing the Sun at one time also facing the Sun exactly (not quite, because leap years and stuff) six months later.

Days would not be the same absolute length of time as they are now if, for example the Earth was orbiting the Sun in the opposite direction or even if the Earth were magically frozen in its orbital position, whilst in both cases keeping the same rotational velocity.

Rational as in rational number eg 1:1, 3:2 etc.

With respect my answer was shorter and more accurate.

“6 months” is a time period counted in days, so of course it correlates with the day.

“6 months” is not exactly half the Earth’s orbit so the premise of the question is incorrect.

There is no rational relationship between the period of the Earth’s orbit and the period of its rotation.

I was going to say that I think you people are missing the point, but I see essellte just said it (without actually saying it).

MartinB said:

With respect my answer was shorter and more accurate.

“6 months” is a time period counted in days, so of course it correlates with the day.

“6 months” is not exactly half the Earth’s orbit so the premise of the question is incorrect.

There is no rational relationship between the period of the Earth’s orbit and the period of its rotation.

With respect, I think Esselte’s answer answered the actual question.

i.e. it wasn’t about “exactly” six months, but rather about rotation after int(365.25/2) days.

MartinB said:

With respect my answer was shorter and more accurate.

“6 months” is a time period counted in days, so of course it correlates with the day.

“6 months” is not exactly half the Earth’s orbit so the premise of the question is incorrect.

There is no rational relationship between the period of the Earth’s orbit and the period of its rotation.

Hi Martin,

The important point here is that one sidereal day is four minutes longer than a solar day.

That is the simplest answer to the question.

To be clear, Martin, I understand what you are saying, I just think you are not answering the intended question; or as RevD said, you are missing the point.

To be clear, Martin, I understand what you are saying, I just think you are not answering the intended question; or as RevD said, you are missing the point.

I see that a ‘controversial try’ was awarded in the RL game last nigh.

I suggest that it be written into the rules.

“You were fouled, so i’ll award you a penalty for that”, says the ref.

“Come on, ref”, says the player, “surely that was worth a controversial penalty!”

“i.e. it wasn’t about “exactly” six months, but rather about rotation after int(365.25/2) days.”

In which case my third sentence covers it. The details of sidereal time are an unnecessary complication.

Why do we have a leap year?

Sorry, should have been in the chat thread.

wookiemeister said:

Why do we have a leap year?

Because the solar year is not exactly 365 X 24 hours long, and if we didn’t have a leap year to ‘absorb’ the creeping error, then the months of the calendar would eventually creep right through the seasons.

Not huge problem these days perhaps, but it was seen as such back in the more agrarian days when our calendar was formulated.

MartinB said:

“i.e. it wasn’t about “exactly” six months, but rather about rotation after int(365.25/2) days.”

In which case my third sentence covers it. The details of sidereal time are an unnecessary complication.

Oh well, WR can let us know which answer he likes best.

mutters: but Esselte answered the question.

No, I answered the question that was asked.

Esselte answered the question that you thought WR really meant to ask but didn’t. (Which I also answered :-p )

MartinB said:

No, I answered the question that was asked.

Esselte answered the question that you thought WR really meant to ask but didn’t. (Which I also answered :-p )

1) A collection of words in any human language rarely have a single definite meaning; they usually require interpretation. Certainly that is the case in this instance.

2) I don’t think you did answer the second interpretation.

3) Any idea how huge stars can have such a low density?

Hope this works, haven’t html’d in ages.

And yes, the website this image comes from is totally sus. It’s the only image I’ve found which shows the entire orbit though.

Martin, do you agree that the OP is describing the situation on the left and asking why instead we see the situation on the right?

esselte said:

Hope this works, haven’t html’d in ages.

And yes, the website this image comes from is totally sus. It’s the only image I’ve found which shows the entire orbit though.

Martin, do you agree that the OP is describing the situation on the left and asking why instead we see the situation on the right?

Hmm. Ok.
http://wing makers.co.no/images/timecomparison.jpe

Is this like you buy three lights to go in your ceiling and you want them all equally spaced so you divide the length of the room by three and go into crisis.

transition said:

Is this like you buy three lights to go in your ceiling and you want them all equally spaced so you divide the length of the room by three and go into crisis.

In that you have to stop and think for a moment?

Yes, it is.

>Yes, it is.

:) let me have my bit of fun.

There’s a couple of ways of interpreting the question… :-)

Possibly, although that diagram is not terribly clear unless you already understand it IMO.

Ok, to address what Esselte is talking about.

Take 12 noon, when you are facing the Sun.
After ~180 exact rotations of Earth you will be facing the same direction in space.
But since you are on the other side of the sun, you are now facing away from the sun.

The resolution to this, as Esselte says, is that ‘one day’ is not one exact rotation of Earth, but is one and a little bit, precisely to account gor the effect of the orbital motion.

transition said:

On a related subject, what is the origins of the hour, minute and second, I can see it could have been done differently.

From a book, “How Long is a Piece of String” by Rob Eastaway and Jeremy Wyndham:

“All whole numbers have factors – that is, smaller whole numbers that divide exactly into them. The factors of 12 are 6,4,3,2 and 1’ which add up to 16. A number whose factors add up to more than the number itself is called “abundant” and 12 is the smallest such number….the number 60 is highly abundant because so many numbers divide in to it, and this is why it became a popular base for counting.”

Also, the number 12 has connections with a circle. One of the easiest ways to divide a circle is to use a pair of compasses set at the radius of that circle. Using the compasses to mark out around the circle will divide the circumference in to six equal parts. These can then be easily divide in half again to give 12 equal parts – very handy for dividing the sky into 12 zodiacs and for dividing the clock face in to hours.

If the Earth orbited in a perfect circle, rotating 365 times as it went, it will have rotated 182 and a half times by the time it reached the opposite point. So the point for which it was noon, would again be noon a half year later, as the half rotation brings it to face the sun again.

But how could it be noon again after 182 and a half days? The answer lies in the distinction between the sidereal day and the solar day. Basically there is an extra solar day per year because, if you imagine a non-rotating Earth orbiting the sun, you’ll see it experiences a ‘day’ as it completes and orbit. This bonus day still occurs even when the planet rotates. So our 365 days a year are made up from 364 Earth rotations and one Earth orbit. So a half year has 182.5 Earth rotations and 0.5 Earth orbits making up 183 solar days. Thus the half-year separated noons are 183 solar days apart, and there’s no problem.

But in reality the Earth’s orbit is elliptical, so generally the time taken to travel to the position directly opposite is not a half year anyway, and would not be an integral number of days even if the year had an exact integral number of days.

esselte said:

A number whose factors add up to more than the number itself is called “abundant” and 12 is the smallest such number…

My learning for the day.

sibeen said:

esselte said:

A number whose factors add up to more than the number itself is called “abundant” and 12 is the smallest such number…

My learning for the day.

Two of the factors of any number will be 1 and the number itself, therefore the factors of any number must add up to greater than the number.

In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.

In mathematics a divisor of an integer n, also called a factor of n, is an integer that can be multiplied by some other integer to produce n.

From Wikipedia articles “Abundant number” and “Divisor”.

————————

A positive proper divisor is a positive divisor of a number , excluding itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not.

From wolfram “proper divisor”.

———————————

So, I think it fair to say “well spotted PWM.”

I am composing a stern letter to the authors of “How Long is a Piece of String” as we speak, pointing out the difference between factors and proper divisors. I’d appreciate your co-signing it before I send… To give it some weight and authority.

:)

IHRTFT but I think the crux of the matter that perplexes Witty is that “a day” (24 hours) is not the rotational period of the earth. The earth rotates in slightly less than that, about 23 h 56 m).

24 hours is the mean solar day. It can be expressed in various ways but you can think of it as the average time between successive middays at some location.

dv said:

IHRTFT

Lab notified.

>IHRTFT but I think the crux of the matter that perplexes Witty is that “a day”

I thought it were more just if you take a full year of complete days and divide it in half it bangs you half a day out, like 365/2 = 182.5 :), hence the example of dividing a room up to fit lights.

About to pour concrete, better stick to what I know, well, it’s been a fead huck actually the formwork.

captain_spalding said:

wookiemeister said:

Why do we have a leap year?

Because the solar year is not exactly 365 X 24 hours long, and if we didn’t have a leap year to ‘absorb’ the creeping error, then the months of the calendar would eventually creep right through the seasons.

Not huge problem these days perhaps, but it was seen as such back in the more agrarian days when our calendar was formulated.

Indeed, captain.

Curiously, the ancient Egyptians used a 365 day calendar with no leap years for a while, so their calendar drifted with respect to the seasons.

Egyptian calendar

The ancient civil Egyptian calendar had a year that was 365 days long and was divided into 12 months of 30 days each, plus five extra days (epagomenae, from Greek ἐπαγόμεναι) at the end of the year. The months were divided into three weeks of ten days each. Because the ancient Egyptian year was almost a quarter of a day shorter than the solar year and stellar events therefore “wandered” through the calendar, it has been referred to as the annus vagus, or “wandering year”.

This wandering through the seasons wasn’t a huge problem for their agrarian activities, though. The major natural event for Egyptian agriculture was, of course, the flooding of the Nile. Many centuries before that calendar was adopted they’d been using the heliacal rising of Sirius (when Sirius rises just before sunrise) to predict the flooding of the Nile, and they continued to do so after adopting that crazy calendar. :)

…

FWIW, 1461 * 365 = 1460 * 365.25, so 1461 Egyptian years = 1460 Julian years, thus it takes that amount of time for that Egyptian calendar to do a full cycle around the seasons. At least, with respect to the Julian year.

But the Julian year itself is inexact – it’s 365.25 days make it a tiny bit too long. With respect to our more accurate Gregorian year of 365.2425 days, the Egyptian calendar takes a little over 1505 years and 56 days (Gregorian) to do a full cycle.

Gruners Spring Frost is bathed in sunlight and one of my favourite paintings.

AwesomeO said:

Gruners Spring Frost is bathed in sunlight and one of my favourite paintings.

Aye, it is very evocative of gentler times or of a childhood lost.

Peak Warming Man said:

AwesomeO said:

Gruners Spring Frost is bathed in sunlight and one of my favourite paintings.

Aye, it is very evocative of gentler times or of a childhood lost.

It makes you feel cold just looking at it which is quite an achievement.

AwesomeO said:

Peak Warming Man said:

AwesomeO said:

Gruners Spring Frost is bathed in sunlight and one of my favourite paintings.

Aye, it is very evocative of gentler times or of a childhood lost.

It makes you feel cold just looking at it which is quite an achievement.

Nice.

Much art doesn’t do it for me, but Gruner, Heidelberg School and some other turn of the century Aussie stuff does.

Although it’s a bit kitsch, I’ve always liked the light and mood of Maxfield Parrish’s Daybreak

OCDC said:

Much art doesn’t do it for me, but Gruner, Heidelberg School and some other turn of the century Aussie stuff does.

I like the French and English Academic school of art. I have a huge framed Cave of the Sea Nymphs by Poynter. Just right for a bathroom.

ooops storm nymphs .

Autumn sunlight snapped through the kitchen window recently:

Thanks for all the responses everyone.

Witty Rejoinder said:

Thanks for all the responses everyone.

I try to help.

536981

Endless recursion

dv said:

Endless recursion

Bloody smart-arse Google.

When you search for recursion it says:

“Did you mean recursion?”

Urban dictionary is a bit of a smart-arse in its definition of smartarse:

““Oh, Alice, you’re such a smart ass.”
“Actually, Bob, I would prefer to be insulted using the correct, British English pronunciation: ‘smart arse’.”
“But, Alice, I think you’ll find ‘arse’ has been pronounced ‘ass’ since at least Shakespeare’s time, and therefore far pre-dates the division of English into British and American variants.” “

A learned study on the use of the word “ass” by Shakespeare:

On Shakespeare’s ass

I think I’ll stop now.

The Rev Dodgson said:

A learned study on the use of the word “ass” by Shakespeare:

On Shakespeare’s ass

I think I’ll stop now.

Quite few Americanisms appear to be old British English that have fallen into disuse in Britain.

You wouldn’t normally hear anyone say gotten in England, we think it’s American, but no, it’s just not normally used in Britain anymore.

A classic hyper-pedantic hair-splitting multi-interpretation thread, and all we get is “Thanks”?

Sheesh.

The big clue was that Bottom was turned into an ass.

dv said:

The big clue was that Bottom was turned into an ass.

I thought that Shakespeare dude was supposed to be subtle!