[Gllug] Public IPs - When are they appropriate
Stephen Harker
steve at pauken.co.uk
Thu Nov 15 13:17:41 UTC 2001
On Thursday 15 November 2001 11:55, you wrote:
> Re: [Gllug] Public IPs - When are they appropriate
> Date: Thu, 15 Nov 2001 11:55:40 +0000 (GMT)
> From: David Damerell <damerell at chiark.greenend.org.uk>
> To: gllug at linux.co.uk
> Reply to: gllug at linux.co.uk
>
> On Thursday, 15 Nov 2001, Stephen Harker wrote:
> >I'm afraid the Earth is 12756 km in diameter, not 10000 km, and it
> > is not a sphere, but an equatorially oblate spheroid (surface
> > topography notwithstanding).
>
> 's why I said something like "assume it's a sphere 10000km in
> diameter, which it's not". We don't really care about a factor of
> two or so. However, if people get pedantic, we should probably
> point out their silly errors;
>
> >The surface area of spheroids is
> >4 * pi * cuberoot(r1 ^ 2) * cuberoot(r2 ^ 2) * cuberoot(r3 ^ 2)
> >where r1, r2 and r3 are the perpendicular axial radii (x, y, z
> > axes).
>
> This looks plausible enough; in particular, if the object is a
> sphere (and so r1 = r2 = r3), it's 4 * pi * r^2, which is right.
>
> >In an equatorially oblate spheroid, r1 = r2, so you can simplify
> > to 4 * pi * cuberoot(r1 ^ 4) * cuberoot(r2 ^ 2)
> >where r1 is the equatorial diameter and r2 is the polar diameter.
>
> Unfortunately, the diameter is not the radius, giving us an answer
> four times as large as it needs to be!
>
> >Given a maximum polar oblateness of +/- 35 km, we can say the SA
> > is roughly
>
> ... such a tiny difference as to suggest it's insignificant.
>
> >4 * pi * cuberoot(12756000 ^ 4) * cuberoot(12721000 ^ 2) square
> > metres = 2.04 * 10^15 square metres
>
> ... which we now know is 4 times too large; the right answer is 5.1
> x 10^14. Curiously, the surface area of a sphere of that diameter
> is also 5.1 x 10^14. My 'rough and ready' figure was 3.14 x 10^14,
> which is out by less than two.
>
> So; as anyone could have told you, the whole 'oblate spheroid'
> thing was a pointless exercise in pedantry which made no difference
> whatsoever compared to assuming the Earth is a sphere; and the
> answer thus obtained was actually out by a larger error than mine
> based on a blatant guess, owing to an elementary mistake.
--
Stephen Harker
steve at pauken.co.uk, http://www.pauken.co.uk
"Beep Beep" - R2D2
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