Sterling,
The solution I had in mind is the Newtonian one (curiously the value
is related to the probability of a random integer being divisible by a
square). But I don't agree that an infinite number of anything is
necessarily nonsensical... In this case (an infinite line of planets
with one end), the force is finite everywhere and never much larger
than 1G. (Alternatively, if we were on the edge of an infinite
half-space packed with planets, the force would be infinite and the
situation much less reasonable, essentially as you described.)
I had never heard of Charlier universes, looks like an applicable
framework, I will read more about it, thanks!
Dan
On 8/26/09, Sterling K. Webb sterling_k_w...@sbcglobal.net wrote:
Hi, Dan, Rob, List,
The key weasel-word in that puzzle is infinite.
An infinite number of anything, no matter how
small, even neutrons, has infinite mass and hence
exerts infinite gravitational force.
Your infinite stack of Earths will collapsr at the
speed of light, having wrapped all space and time
around itself. You are a string of particles stretched
out over light years, with the tip of your nose pressed
against the event horizon at the speed of light where
you feel infinite force, but you are not moving because
time is standing still for you, and you will stay that
way forever... in your inertial frame.
The Newtonian solution is simple. Using the central
force assumption of Newtonian gravitation (hey! works
for me!), the gravity you feel is the sum of an infinite series:
1 + (1/3)^2 + (1/5)^2 + (1/7)^2 + (1/9)^2 + (1/11)^2 +
(1/13)^2 + (1/15)^2 + (1/17)^2 + (1/19)^2 + ... =
1.208722 G's! (approximately, OK?)
Your problem is that your Earths are too close together.
There is a cosmological solution that allows an infinite
static universe with infinite mass to have a finite and low
mass density. They're called Charlier universes, but I
never met one. They're awfully empty...
Experiment is the key to all knowledge. You stack up
an infinite number of Earths, then time falling objects
with a pendulum, or even better, time the pendulum...
right in the heart of downtown Gedankenland.
Sterling K. Webb
--
- Original Message -
From: Dan Brumleve jdb1...@gmail.com
To: mojave_meteori...@cox.net
cc: meteorite-list meteorite-list@meteoritecentral.com
Sent: Wednesday, August 26, 2009 2:57 AM
Subject: [meteorite-list] (no subject)
Reminds me of a thought-experiment that I thought of...
If there are an infinite number of Earths stacked on top of each
other, how much gravity do you feel standing on top?
Dan
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