Re: A newcomer here

"Logan Kearsley" <chrono.surfer@xxxxxxxxxxx> wrote in message
news:PrqVe.6937$b37.3139@xxxxxxxxxxx
> "David Friedman" <ddfr@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
> news:ddfr-DAA931.18240812092005@xxxxxxxxxxxxxxxxxxxxxxxx
> > In article <GepVe.3508$XO6.2586@trnddc03>,
> > "Logan Kearsley" <chrono.surfer@xxxxxxxxxxx> wrote:
> >
> > > With constant crust thickness and density, the surface gravity
> > > increases as the radius increases.
> >
> > No. It stays constant.
> >
> > Area goes as the square of radius, so with constant thickness and
> > density mass goes as the square of radius.
>
> Except that it doesn't, exactly. It's somewhat off. Assuming constant
> density, the mass is dependent on the volume of the shell, which is the
> volume of the spherical world minus the volume of the empty spherical
> interior. This will only scale with the surface area / square of the
radius
> if the ratio between the outer sphere and the inner sphere is constant,
but
> if the shell thickness is constant, that ratio won't be.

Whoops! I just realized the flaw in my reasoning there. If the ratio were
constant, the mass would scale with the volume, or cube of radius. The
constant thickness and therefore inconstant ratio still means that the mass
doesn't scale exactly with either surface area or volume, though, and the
shell will have to get thinner for the same surface gravity at larger radii.

-l.
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