Really Simple Circumference Question

[Iritscen]

I was just trying to get the actual range of circumferences for the Earth depending on which way you measure (just based on math, of coure, I know the actual circumference could be considered nearly infinite depending on the length of your ruler).

Wikipedia has a very nice table of stats:
Ellipticity: 0.003 352 9
Mean radius: 6,372.797 km
Equatorial radius: 6,378.137 km
Polar radius: 6,356.752 km
Aspect Ratio: 0.996 647 1
Equatorial circumference: 40,075.02 km
Meridional circumference: 40,007.86 km
Mean circumference: 40,041.47 km

Now, here's the thing: I wanted to check their circumference numbers using their radius numbers.

The mean radius does equal their mean circumference when you double it and multiply by pi. So does the equatorial radius agree with the circumference. But the polar (which I understand is synonymous with "meridional") radius yields 39940.65km, as opposed to the 40007.86 they actually list in the table.

Does anyone have an answer for this? It looks like their numbers are what you will find anywhere, give or take a kilometer.

Also, is the polar radius measured from geographic pole to pole or magnetic pole to pole?

 

[cesiumfrog]

That's an odd concept, a "mean" circumference and to such "precision". Anyway, you can check the math by comparing the equatorial radius and circumference; the rest sounds like a misunderstanding (keep thinking about the shape of the planet, look up the terms you're unsure of in a dictionary, draw a big picture, and if you're still not sorted, get string and make a model - perhaps from a mandarin).

 

[mathman]

But the polar (which I understand is synonymous with "meridional") radius yields 39940.65km, as opposed to the 40007.86 they actually list in the table.

This is a guess: If you take a circumference through the poles, you will get an ellipse, with the polar diameter being the minor axis and the equatorial diameter the major axis. The calculation of the ellipse circumference is more complicated, but I believe you will come up with the table result.

 

[Chronos]

Earth is an oblate spheroid, as is all the other bodies in the solar system. A centripetal force thing - no surprise there

 

[Iritscen]

Of course! I didn't picture the line going through the poles as viewed from the side -- it's an ellipse! Using 2*pi*r would understate the perimeter of that shape. OK, that explains why their circumference is greater than what I calculated.

Well, does anyone have an answer to whether the Earth's polar radius is based on geographic or magnetic poles? I know, that's a pretty obscure question, but it makes a difference. I just thought someone here might, just maybe, happen to have a job in a geographically-oriented field.

 

[cesiumfrog]

Which would you guess, and why?

 

[Iritscen]

Well, I'd guess geographical, because that would make the polar circumference line perpendicular to the equatorial circumference line. That's why I'd like to get the magnetic circumference if at all possible.

 

[cesiumfrog]

If you can look up how far those poles differ (at a particular time.. note the magnetic poles move around a fair bit), should only be a little trig to calculate what you'd like to get.