Re: (TFT) Re: TFT Digest V3 #721

[pvk@oz.net]

On Mon, February 6, 2006 9:44 am, Mark Tapley wrote:
> PvK wrote:
>
>>Just like in the middle of the Earth
>>(or, probably, off some distance because of the curvature of the shell,
>> at
>>your zero point, with your anti-grav center balanced for 1g at the
>> surface,
>>there would be zero gravity, and not more than 1g, as you wrote. Gravity
>>goes steadily down as you get closer to the zero point, because the mass
>>"over your head" is pulling you up, not down.

Mark, you wrote a very nice explanation/proof of the gravity situation
inside a ball without Grouchy's anti-matter magic!

However I didn't make my terms clear enough; that's not the situation I
was talking about in the part you quoted above. By "shell" here I mean the
outer solid layer, not the entire spherical world. I was responding to
Grouchy's description of the experience of someone making a trip through
the outer shell; not of someone inside the interior, having already passed
all the way through the shell.  Starting at the surface and taking the
(perhaps ~10,000km) staircase downwards, gravity would gradually decrease,
not increase.

Now, _without_ the anti-grav device in Grouchy's scenario which I was
talking about, the situation described in your proof would be reached as
soon as the figure reached the interior of the shell.

So as I understood Grouchy's original world design, the total mass of the
sphere would be enough that at whatever (undetermined, but at least 3 x
Earth radius) radius of the world, the natural gravity would be a little
under 2g. Then, he summons a magic anti-grav device at the center that
exerts an outward acceleration on all mass, with a strength at the
interior of the shell (where the stairs emerge on the inside) of 1g. The
result is you get 1g gravity both on the inside and the outside, directed
towards the interior of the physical part of the shell (the crust - I'm
don't remember what the geometrical term would be - the solid part of the
ping pong ball - the 0 in Grouch's ASCII diagrams).

So in that case, I was talking about the half-way part along the
crust-penetrating staircase, would be a zero-G point, with gravity
steadily dropping along the way, not getting stronger. As we both pointed
out, though, there had better be lots of serious air locks (not to mention
ventilation - good thing for TFT's Fresh Air spell) or the air pressure
would become lethal.

By the way, I would like to point out one thing at this point that could
be rather fun. If there were a straight bottomless shaft through the crust
of Grouchy world, it would be a relatively effortless way to get to the
other side. Just hop in and let it drop. Gravity would make you fall all
the way through and come to rest near the other side (except for
friction... so it'd be best if it were an elevator in a vaccuum or
something).

Back to inconvenient points, though, as I worried before, the need to
rotate a very huge world to get an Earth-like day/night cycle on the
outside, might start to be a problem, or a source of a significant
centripetal effect in equatorial regions compared to poles. However, if
Grouchy's Mnoren can magic up the anti-grav device, perhaps they can make
it variable strength in certain directions - if it pushes less on the
equator than on the poles (not done by natural gravity, but maybe magic
anti-grav devices can do this), then it could (mathematically speaking) do
it - of course, with that degree of anti-grav control, you can probably
get around nearly any such problem... which gets back to "the GM can fiat
whatever they want". ;-) But at least they can mathematically describe
what they want, which does seem more consistent, cool and interesting to
me, at least on one level.


...
> Some of what you'd see:
...

Nice conjectural images of how it would be without the anti-grav device!

Consider if more atmosphere were stuffed into the interior, though.
Perhaps the equatorial regions would have too much pressure for vanilla
humans, so there would be habitable bands further up the sides, one ring
on either side of the high-pressure region. As for river directions, if
the Mnoren could shape the whole thing by design, perhaps they could
arrange for artificial tilts to make more varied drainage patterns.

With Grouchy's anti-grav device, and the ability to graduate it to
compensate for high centripetal force, the whole interior could have
constant pressure varying only by altitude.


PvK
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