Maths help two :)

[lunar]

You want me to factorise it?

2*pie*(r+1/r)


You need to know the radius to calculate the specific change. Even if you don't know it, radius/diam is still required in the equation.

The Earth's radius is about 6400 km.
Your equation above is what I thought it would be too. However, I was reluctant to respond because I think there is more to the question than meets the eye.
I recall a similar question been asked in Dr Kharl's radio 5 Science phone-in.

 

[esmozz]

He isn't asking about spheres. He's asking about circumferences which are based on circles, and the equator is a circle.

Technically he's asking about the great circle on a spherical earth which corresponds to the equator. If the earth is not spherical then the calculation may be different.

The WGS84 datum is reference oblate spheroid used to define the earths surface. It was my understanding that using this datum the earth is defined to approximate a ruby ball, making calculation different. However having just checked it again I may well be wrong, in which case you can ignore everything I've written previously.

Also, since I'm going to be awkward, the answer is 1m (give or take). I got this by drawing a slice of pie and marking the two radii, the earths radius is so huge compared to the difference between the two radii that the end approximates a box 1m square. Hence 1m. I have no idea if this is a good answer.

Edited to add: Having thought about it a bit more, I think it's a rubbish answer. I'm going to give up now.

 

[h4rm0ny]

The second would be shorter, would it not?

I think they meant floating magically above the first string at the same latitude, rather than lying on the ground slighty North of the first one.

It's a problem to demonstrate that to calculate the change in circumference of a circle as a result of change in diameter/radius doesn't require you to know the original circumference or diameter/radius.
You're looking at it too literally if you're worrying about sea level vs ground level.

I'd be fascinated to know how you could do that, as the question is "how much longer". It's asking for an absolute value (e.g. 400km) so we need an absolute value to insert into the formula. I.e. the diameter of the Earth.

The world is'nt a sphere.

Google WGS84 and then work it out. Personnally I would have no idea.

Yes, it's an oblate spheroid. But that doesn't make any difference unless we're talking volume. Any given lateral cross section is still going to be a circle (give or take some mountains).

 

[Kenai]

I'd be fascinated to know how you could do that, as the question is "how much longer". It's asking for an absolute value (e.g. 400km) so we need an absolute value to insert into the formula. I.e. the diameter of the Earth.

If the radius increased by 1m, the circumference increased by 6.28m. It doesn't matter whether you started with a basketball, the moon, the earth or the sun. The answer will always be the same.

 

[esmozz]

Yes, it's an oblate spheroid. But that doesn't make any difference unless we're talking volume. Any given lateral cross section is still going to be a circle (give or take some mountains).

Surely if you took a circle round the poles, i.e. normal to the equator you would get an oval. Not that it makes any diffence here.

If the radius increased by 1m, the circumference increased by 6.28m. It doesn't matter whether you started with a basketball, the moon, the earth or the sun. The answer will always be the same.

So 1m then (give or take)

 

[h4rm0ny]

If the radius increased by 1m, the circumference increased by 6.28m. It doesn't matter whether you started with a basketball, the moon, the earth or the sun. The answer will always be the same.

Someone can shoot me now, please. I wont object.

Surely if you took a circle round the poles, i.e. normal to the equator you would get an oval. Not that it makes any diffence here.

Equator was specified. That is a measurement at a specific latitude.

 

[FoxEye]

So what's the answer then?

Not that I care. Maths sucks donkey balls.

 

[Kenai]

So 1m then (give or take)

I think you're pushing it a bit to say that 6.28 is 'give or take' the same as 1

 

[Crpwned]

As usual there's an XKCD explaining this, amongst other things - https://what-if.xkcd.com/67/

 

[esmozz]

I think you're pushing it a bit to say that 6.28 is 'give or take' the same as 1

I dunno, over 6400,000m its not bad.

Equator was specified. That is a measurement at a specific latitude.

Hard to argue against that so i won't.

I think the point I was originally trying to make was (and I've had to go away and check since it was 20 odd years since I studied this, so I may still be wrong) that the surface of the earth can be represented mathematically by a geoid based on the WGS84 datum. That geoid is an irregular surface, nonetheless, at the equator you could approximate the circumference using a mathematical series (up to n = as high as you like) - it would not be a circle.

However all I seem to have proved is I completely missed the point of the original question. Also:

Someone can shoot me now, please. I wont object.

Me too please.

 

[LuckyBenski]

This thread made me feel really smart until I failed to account for the 1m applying to both sides of the earth, and so the answer is 2π and not just π

 

[lunar]

So what's the answer then?

Not that I care. Maths sucks donkey balls.

Ironic, where would we be without Maths (and Physics)?
No Internet, no TV, no mobile phones, no satellites, no radio, no mains electricity.......

 

[Angilion]

[..] Yes, it's an oblate spheroid. But that doesn't make any difference unless we're talking volume. Any given lateral cross section is still going to be a circle (give or take some mountains).

It's also only just an oblate spheroid. The question treats the surface of the Earth as being smooth. Treating Earth as a sphere is an approximation in the same ballpark as that.

I have to admit that my initial thought about the answer was that the outer rope would be much longer than the inner one, hundreds of kilometres longer. I felt a bit silly when I read the correct answer and realised that yes, of course that was the correct answer. I've known the formula for the circumference of a circle for a very long time and should have gone straight to the correct answer.

 

[D3K]

Post #10 on the front page

Yeah ok fml it's 2 pie... meh

 

[FoxEye]

Ironic, where would we be without Maths (and Physics)?
No Internet, no TV, no mobile phones, no satellites, no radio, no mains electricity.......

Subjective post was subjective.

It's hard and I'm not very good at it. Ergo it sucks balls

 

[Double07]

BEER

 

[dl8860]

I'd be fascinated to know how you could do that, as the question is "how much longer". It's asking for an absolute value (e.g. 400km) so we need an absolute value to insert into the formula. I.e. the diameter of the Earth.

How can you say these words and then go on to talk about oblate spheroids. Are you clever or not?

Yes, it's an oblate spheroid. But that doesn't make any difference unless we're talking volume. Any given lateral cross section is still going to be a circle (give or take some mountains).

 

[h4rm0ny]

How can you say these words and then go on to talk about oblate spheroids. Are you clever or not?

I am usually very clever but occasionally can make statements without thinking things through and which are cripplingly embarrassing sometimes.

Example above.

 

[Illgresi]

1/r times bigger

or

100/r expressed as a percentage.