[meteorite-list] (no subject)

From: Dan Brumleve <jdb1729_at_meteoritecentral.com>
Date: Wed, 26 Aug 2009 14:46:33 -0700
Message-ID: <c3be09060908261446m3b6548b2wda0ee9d9eba3c335_at_mail.gmail.com>

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_webb at 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" jdb1729 at gmail.com
> To: mojave_meteorites at cox.net
> cc: "meteorite-list" meteorite-list at 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
>> ______________________________________________
>
>
Received on Wed 26 Aug 2009 05:46:33 PM PDT