BS: circumference of the Earth

Subject: BS: circumference of the Earth
From: GUEST,Fogie
Date: 29 Oct 06 - 04:33 AM

I was asked by my local publican how much difference an increase of 5 yards would make to the circumference of the earth. My gut feeling was that it would make hardly any difference at all, but he showed me mathmatically that it does make a surprising difference, and I'm still trying to grapple it into my brain.
I cant get a Pi on my keyboard so let P be Pi, C=circ, D= Diam
C=PD
Circ 2 - Circ 1 = C2-C1 = Px ( D2-D1 )
so D2-D1 =5/P = approx 1.59 yds
So the height above ground the new "circumference" is 0.79yds
I find this difficult to get my head round.
I think I've got the maths right, but if I havent I'm sure some clever member will put me right.

Subject: RE: BS: circumference of the Earth
From: GUEST, Topsie
Date: 29 Oct 06 - 06:38 AM

An increase of 5 yards in what?

Subject: RE: BS: circumference of the Earth
From: gnu
Date: 29 Oct 06 - 06:57 AM

an increase of 5 yards (would make) to the circumference

Neat, eh?

Subject: RE: BS: circumference of the Earth
From: Lox
Date: 29 Oct 06 - 07:06 AM

The question is what's unclear.


What difference would an increase in 5 yards make? a difference of 5 yards!

Oh.

I see.

You mean, what difference would an 5 yard increase in the circumference make to the radius? 0.79 yards.

There's the question, so the answer makes sense.

To deal with the other point of how weird that seems, just try to conceptualize slightly differently.

Think of the earth as a circle. An increase of 5 yards to the circumference is negligable compared to the total.

Likewise, an increase of 0.79 yards to the radius is negligable.

Don't get confused by images of the ground suddenly being higher. You wouldn't notice that happening any more than you would notice it being "stretched" by the extra 5 yards.

I think I have understood your mistake, and hopefully I have helped you understand your quandary.

Subject: RE: BS: circumference of the Earth
From: JohnInKansas
Date: 29 Oct 06 - 07:44 AM

If 5 yards is added to the length of a string wrapped around the earth, and the string is uniformly elevated above the earth, the string will be 0.79 yards from the earth's surface (assuming the earth is a little "rounder" than it actually is).

If 5 yards is added to the length of a string wrapped around a tennis ball, and the string is uniformly spaced away from the tennis ball, the string will be 0.79 yards from the tennis ball surface.

It makes no difference what the original diameter/circumference is. For the same change in length of the string, the answer is always the same. The "conceptual barrier" to seeing this problem is that 0.79 yards is very small compared to the earth's dimensions. Just remember that you are also very small compared to the earth's dimensions.

Since the earth's diameter is on the order of 126,720 yards, the elevation of the string in that case is equivalent to a a change of 0.00000006% in the diameter/circumference of the string relative to the diameter/circumference of the earth. Hardly noticeable, but you could crawl under the string on your hands and knees; but couldn't walk upright under it unless you're very short - because you (and the rest of us) are also "hardly noticeable" when measured against earth dimensions.

John

Subject: RE: BS: circumference of the Earth
From: Georgiansilver
Date: 29 Oct 06 - 08:31 AM

Academic really unless someone is thinking of increasing it!...Where would the material come from to do that though?

Subject: RE: BS: circumference of the Earth
From: Rapparee
Date: 29 Oct 06 - 09:32 AM

I know some people who know how to knit....

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 29 Oct 06 - 10:21 AM

"Where would the material come from to do that though?"

At the rate we're pilling up mass waste in the States, I have no trouble imagining the average elevation increasing. Why that could happen with just styrofoam packaging materials from our household alone!

Another process that could produce a greater circumference would be the melting of the arctic and anarctic ice caps by global warming. As the water level of the oceans increase, so would the earth's circumference. Or would it all average out? Is the circumference of the earth actually measured at sea level?

Charley Noble

Subject: RE: BS: circumference of the Earth
From: Amos
Date: 29 Oct 06 - 11:00 AM

I think the question being asked originally was the other way 'round: what increase in circumference would result from an increase of 5 yards in the radius?

A

Subject: RE: BS: circumference of the Earth
From: Little Hawk
Date: 29 Oct 06 - 11:30 AM

It's only slightly larger than CH's hatband.

Subject: RE: BS: circumference of the Earth
From: Paul from Hull
Date: 29 Oct 06 - 03:32 PM

*ROFL*

Subject: RE: BS: circumference of the Earth
From: Dead Horse
Date: 29 Oct 06 - 03:58 PM

Would that mean flights from UK to USA would be a bit longer, and therefore add even more polution to our atmosphere?
Mebbe a solution would be for them bloody planes to fly accross the pond instead of all the bloody way round it, huh?

Subject: RE: BS: circumference of the Earth
From: Rowan
Date: 29 Oct 06 - 04:41 PM

Don't worry about height increases, Charlie. With all the collections of back issues of National Geographic scattered about across the US, someone has calculated that the entire continent has been depressed by 6 inches. We need more depression, but not a lot.

Cheers, Rowan

Subject: RE: BS: circumference of the Earth
From: Mr Red
Date: 29 Oct 06 - 06:42 PM

depends how you slice Pi

Anyway are we talking polar or equatorial circumference - there is a difference since centrepetal acceleration creates a bulge at the equator. the difference is 50 miles in those circumferii (sic)

Subject: RE: BS: circumference of the Earth
From: Lox
Date: 29 Oct 06 - 06:53 PM

Dead horse.

The flight plan isn't really "round" the atlantic, it is in fact the short route over the top of the globe. draw a straight line on a globe from uk to east coast usa and you start off going north.

Now am I really clever for pointing that out or really dumb for not seeing that it's obviously a joke?

Ah well, too late now ... I'm hitting the submit button

Subject: RE: BS: circumference of the Earth
From: Donuel
Date: 29 Oct 06 - 06:55 PM

50 miles!

Wow, no wonder equatorial volcanoes can be so ferocious.

Subject: RE: BS: circumference of the Earth
From: GUEST,padgett
Date: 30 Oct 06 - 06:24 AM

This assumes that the Earth is round ~ no I dont mean that; I mean perfectly spherical I think

Ray

Subject: RE: BS: circumference of the Earth
From: GUEST,Mr Red
Date: 30 Oct 06 - 06:25 AM

Donuel

Not only that but the Greek mathematician in the Nth centuary BC calculated the circumference of the earth and he was 50 miles out!

He did it by measuring the angle of the sun at mid-day in Alexandria and in the ????? well on the eqator (vertical shadow).

I was curious but I have seen pictures of this well on TV and it is very deep and 50-100 metres in diameter.

Now I am sure there is someone who can remind me of the name of this Greek geyser.

Just in case no-one mentions it - the shortest distance over the the Globe is called the Great Circle Route.

puts pedant hat on peg and relaxes........................

Subject: RE: BS: circumference of the Earth
From: Bunnahabhain
Date: 30 Oct 06 - 08:27 AM

He was further out than that, Mr Red, but then he was measuring distance in camel-days, so was remarkably accurate ( +/- 10%, IIRC)

I can't rememebr his name either.


Padgett, It's an oblate speroid, flattened at the poles by about 1/300 of it's diameter, and is virtually perfectly smooth. Mountains and ocean trenches really don't make much difference at this scale.

Subject: RE: BS: circumference of the Earth
From: Hand-Pulled Boy
Date: 30 Oct 06 - 10:09 AM

Fogie, your local publican is a social menace!

Subject: RE: BS: circumference of the Earth
From: Dead Horse
Date: 30 Oct 06 - 02:32 PM

Let me get this straight (yes, I am aware of the pun).
The direct route from London UK to Houston, Texas, is :-
North West to fly over Wales, the Irish Sea, Northern Ireland, just clipping Iceland, curving slightly more westward to skirt Greenland, then dipping across Nova Scotia, the Great Lakes, southwards over Central USA, out into the Gulf of Mexico a wee bit,and then finally on up to good ole Houston. ???
I think we have a problem...........

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 30 Oct 06 - 05:16 PM

Was Magellan the first sailor to circumcize the Earth?

Charley Ignoble

Subject: RE: BS: circumference of the Earth
From: Rowan
Date: 30 Oct 06 - 05:17 PM

Try Eratosthenes

Subject: RE: BS: circumference of the Earth
From: John Hardly
Date: 30 Oct 06 - 05:25 PM

It's always a good idea, when covering the Earth, to use rubber to allow for when the Earth expands and contracts.

When it contracts it uses a lawyer who is well versed in contract law.

A good contract lawyer can be very expansive on the subject of contracts. Expensive too.

Subject: RE: BS: circumference of the Earth
From: Bunnahabhain
Date: 30 Oct 06 - 05:31 PM

Try a globe, and a piece of string. Or a basketball, that works it's got a pole, and lines of longtitude. Makes it easier to see what the shortest route actually is.

Most people aren't very good at going from a rectangular map, to a round earth. It does take some visualising.

Subject: RE: BS: circumference of the Earth
From: Amos
Date: 30 Oct 06 - 05:40 PM

The Earth's equatorial radius, or semi-major axis, is the distance from its centre to the equator and equals 6,378.137 km (?3,963.189 mi; ?3,443.917 nmi). But as you will see here there are half-a-dozen ways to measure the radius of the earth so the question itself is ambiguous.

A

Subject: RE: BS: circumference of the Earth
From: John Hardly
Date: 30 Oct 06 - 05:48 PM

The earth is round -- curvy, really. But not "S" curvy. "S"curvy would require vitamin C.

Subject: RE: BS: circumference of the Earth
From: The Shambles
Date: 30 Oct 06 - 06:01 PM

I do know that if the population of the world joined hands around the globe

- a lot of them would drown.

Subject: RE: BS: circumference of the Earth
From: Georgiansilver
Date: 30 Oct 06 - 06:40 PM

Charley..I always thought it was Christopher Columbus who circumcized the earth with a 90 ft clipper!

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 30 Oct 06 - 09:35 PM

Georgiansilver-

It was the cabinboy who circumcized Columbus, lining his arse with broken glass as you well know!

It's true that Columbus thought the world was round, or at least he had read that it was somewhere. But he also was convinced it was a much smaller round world than it turned out to be. And he died thinking he had re-discovered the East Indies, not the West Indies. As Tom Lewis says, "I know some navigators who could still do that today!"

Cheerily,
Charley Noble

Subject: RE: BS: circumference of the Earth
From: Little Hawk
Date: 31 Oct 06 - 02:16 AM

I think that it was quite clear to most sailors and navigators in Columbus' time that the Earth was round, as it had been clear to the Greeks and Romans before them. What they did not know was how big it was...and how far they might have to travel west across the Atlantic before reaching land. This was something to be concerned about, because one does not want to run out of provisions and die of hunger and thirst in the middle of a gigantic uncharted ocean. For this reason, navigators in unknown waters preferred to stay within sight of land if at all possible, and that explains the concerns of Columbus' sailors.

It was Washington Irving in the 1800's who made up all the nonsense about them thinking the Earth was flat and they would fall off the edge, and that got repeated in American school history classes for generations afterward as though it were gospel! The sailors' dispute with Columbus was not about whether the Earth was round or flat, they knew it was round, it was about whether they would reach land soon enough to survive if they kept sailing west.

They had good reason to be concerned, as it turns out, because Columbus grossly underestimated the distance to China. If the Americas had not been in the way for them to bump into, so to speak, they would have all died out there for Columbus' dream of reaching the Orient by the westward route.

Subject: RE: BS: circumference of the Earth
From: The Shambles
Date: 31 Oct 06 - 06:06 AM

You mean the earth it is not flat?

Subject: RE: BS: circumference of the Earth
From: GUEST
Date: 31 Oct 06 - 06:41 AM

That explains a lot of your other utterances, Roger

Subject: RE: BS: circumference of the Earth
From: The Shambles
Date: 01 Nov 06 - 05:01 AM

If the current Chief of the Mudcat Editing said the Earth is flat - I am sure that many posters would now tell us that it was unanimously agreed.

Wynona Ryder is flat.

Subject: RE: BS: circumference of the Earth
From: Snuffy
Date: 01 Nov 06 - 08:22 AM

Wynona Ryder is flat. - only if you listen to her. Otherwise she's quite bumpy.

Subject: RE: BS: circumference of the Earth
From: Joe Offer
Date: 02 Nov 06 - 04:52 AM

π


π

Now you know.
-The Chief of the Mudcat Editing Team-
(Go, Team!!!)

Subject: RE: BS: circumference of the Earth
From: Rowan
Date: 02 Nov 06 - 10:41 PM

Thanks Joe.
You could have put it up in the air. Then we could have had pi in the sky! And started a music thread on feasting.

You will eat
bye and bye

Cheers, Rowan

Subject: RE: BS: circumference of the Earth
From: Jim Dixon
Date: 03 Nov 06 - 03:30 PM

The original problem might be easier to "get your head round" if you imagined the earth as a cube rather than a sphere.

Your formula would be the same, using 4 instead of pi.

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 03 Nov 06 - 05:26 PM

Jim-

Are you suggesting that the Earth has eight corners? I thought there were only four: North, East, South and West.

Charley Noble

Subject: RE: BS: circumference of the Earth
From: Mr Red
Date: 03 Nov 06 - 07:06 PM

That's a cardinal point you made there Charley.........

Subject: RE: BS: circumference of the Earth
From: Mr Red
Date: 03 Nov 06 - 07:08 PM

Bunnahabhain -
Those "camel-days" - was that bactrian or drumaderry - it would make a difference you know.

Subject: RE: BS: circumference of the Earth
From: gnomad
Date: 03 Nov 06 - 07:25 PM

These guys have another take on it.

Subject: RE: BS: circumference of the Earth
From: Slag
Date: 04 Nov 06 - 12:02 AM

Think of the area of a Pizza. When they ad an inch or two to the circumference they double the price and you'd get sick trying to eat it all (well, maybe).

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 04 Nov 06 - 09:30 AM

Slag-

OK, I'll have my earth with sausage, feta cheese, spinach, and black olives!

Cheerily,
Charley Noble

Subject: RE: BS: circumference of the Earth
From: Bernard
Date: 04 Nov 06 - 10:16 AM

The Equator is a menagerie lion running round the middle of the Earth...

Subject: RE: BS: circumference of the Earth
From: The Shambles
Date: 04 Nov 06 - 11:53 AM

You mean Leo the line?

Subject: RE: BS: circumference of the Earth
From: Slag
Date: 05 Nov 06 - 02:36 AM

That would be Tear Along, the dotted lion.

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 05 Nov 06 - 10:21 AM

Now if we read between the lions,
We might get to the truth of the matter;
Unless the lions are lying,
Then it's probably best to leave them undisturbed.

Charley Noble

Subject: RE: BS: circumference of the Earth
From: GUEST
Date: 06 Nov 06 - 07:34 AM

I fear those ruining lions are going to find the wet margins pretty aluvial

and then they would be true Mudcats

Subject: RE: BS: circumference of the Earth
From: fogie
Date: 06 Nov 06 - 10:33 AM

Lordie Lordie, I never thought this would run and run -far less that it would become Pythonesque. Well done. I'm even more confused now trying to visualize the circumferences of cubes

Subject: RE: BS: circumference of the Earth
From: The Fooles Troupe
Date: 07 Nov 06 - 07:23 AM

When Harry Secombe (of the Goons fame) got his knighthood, he joked that he was now Sir Cumference.

Subject: RE: BS: circumference of the Earth
From: Slag
Date: 12 Nov 06 - 01:35 AM

Oy Vey! He could have been Sir Cumcision! That could be the unkindest cut of them all.

Subject: RE: BS: circumference of the Earth
From: open mike
Date: 12 Nov 06 - 03:37 AM

So i was wondering how fast an airpoane would have to go heading west
in order to keep watching a perpetual sun set?

of course it would depend on the altitude at which it flies..

1,000 miles an hour? (or 26,000 -- if that is the circumference...divided by 24??)

and at a speed greater than that could you go faster than time?

Subject: RE: BS: circumference of the Earth
From: Amos
Date: 12 Nov 06 - 10:47 AM

The circumference of the earth at the equator is 24,902 mi. If you went 1,000 miles an hour you would lose a little bit of ground, but not much, to the receding sunset. The sunset (as viewed from the surface) recedes at 1,037.5 miles per hour.

If you go up from the surface, there is a point where you can see one half of the planet, and the rate of recession of the terminator would be much slower relative to your viwpoint.

A

Subject: RE: BS: circumference of the Earth
From: Mr Red
Date: 12 Nov 06 - 11:09 AM

11901.3163986855401311913363250915 mph

approximately. Isn't that just under Mach 2 (at the altitude)

assuming you fly at 20,000 feet above sea level. Didn't Concorde fly faster than that on a good day?

Subject: RE: BS: circumference of the Earth
From: Amos
Date: 12 Nov 06 - 11:43 AM

I think that number is way too high, Mister Red. How did you arrive at it?


A

Subject: RE: BS: circumference of the Earth
From: Charley Noble
Date: 12 Nov 06 - 11:51 AM

Amos-

What's a decimal point or two?

But the intriguing question is how fast must we fly to go back in time, or do we just end up encountering the sunset of the next day as we cross the International Date Line? And would it make any difference which direction we traveled, East or West?

I'll go away now while you and others ponder these inscrutables.

Cheerily,
Charley Noble, Geographer without Portfolio

Subject: RE: BS: circumference of the Earth
From: The Fooles Troupe
Date: 12 Nov 06 - 06:51 PM

The circumference of the earth gets smaller as volcanoes expel gas - in other words as the eart farts.

So, the theory goes, if you want to get a smaller waist measurement...

Perhaps our local expert could give us the benefit of his experience...

Subject: RE: BS: circumference of the Earth
From: Slag
Date: 22 Nov 06 - 06:44 PM

If you were at one of the poles which was in sunlight you could walk a slow circle around in 24 hours and keep the sun in the same position. It depends more on your lattitude than your elevation. The closer to the pole, the slower the speed.

Subject: RE: BS: circumference of the Earth
From: JohnInKansas
Date: 23 Nov 06 - 01:17 AM

Sideral rate of the earth is very close to 15 degrees per hour (360 degrees / 24 hours).

One degree (at the equator) is 60 nautical miles.

15 degrees/hour * 60 nautical miles/degree = 900 nautical miles per hour, at the equator at sea level.

If I recall correctly, a nautical mile is 6,080 feet, while a statute mile is 5,280. Ratio 1.1515.

900 nautical miles/hour * 1.1515 = 1,036 mph (statute miles per hour) - at sea level at the equator.

At higher latitudes, the distance varies as the cosine of the latitude, so that at the pole the flight speed required is zero. In summer, you're in daylight all the time whether you move at all; and in winter you won't see the sun no matter how fast you go.

The speed required can be significantly reduced if you start at sunrise flying west, if all you want to do is go once around in daylight, since you can land back at your starting point at sunset, gaining a nominal 12 hours or so in the total time you can use to complete the trip.

Flying at 20,000 feet won't change the speed requirement by much. The additional distance to be travelled is small (40,000*Pi feet = 238 miles approximately - see original problem) in 24 hours (or about 10 mph faster - at the equator).

John

Subject: RE: BS: circumference of the Earth
From: Slag
Date: 23 Nov 06 - 11:10 AM

The Day the Earth Stood Still. "If time were not an endless highway..." Fire in the Sky. Don't Let the Sun Go Down On Me. Singing in the Sunshine. Keep on the Sunnyside of Life. Any others???

Subject: RE: BS: circumference of the Earth
From: robomatic
Date: 23 Nov 06 - 03:25 PM

"Time Has Told Me"