Re: Hey Mr. Hyde!

From: Alex McDonald (alex_mcd_at_btopenworld.com)
Date: 03/31/04 

Date: Wed, 31 Mar 2004 12:16:15 +0000 (UTC)

"Evenbit" <nbaker2328@charter.net> wrote in message
news:ecdc73cc.0403302004.79127b5c@posting.google.com...
> "Alex McDonald" <alex_mcd@btopenworld.com> wrote in message
news:<c4a1hg$128$1@titan.btinternet.com>...
> >
> > [ Please don't do a Beth on me; this post is meant to be stimulating,
not
> > confrontational. ]
>
> Seems Beth would have us to preface all of our posts with such
> disclaimers.
>
> >
> > That's a tricky one; perhaps it does change, even if by only an iota.
> > There's potential energy in the gravity well (as you note). Imagine a
mass
> > the size of the Earth spread over the area of, say, the solar system. As
all
> > the pieces accrete together, they fall down the gravitational well and
loose
> > potential energy; so the Earth as a ball has less energy (hence mass)
than
> > the pieces spread out.
>
> This is true...
>
> > IIRC, the mass reduction is in fractional parts per
> > billion for an Earth sized object. It is, however, still a prodigious
amount
> > of energy. (Imagine it in reverse; spreading the earth out over an area
of
> > the solar system would cost energy, or mass equivalent.)
> >
> > The magnet is very, very small compared with the Earth, but the energy
lost
> > by dropping the magnet down the gravitational well increased the
> > gravitational force and decreased the mass of the whole system (by the
mass
> > equivalent of the potential energy). The numbers are incredibly small,
true;
> > but try a thought experiment (Gedankenexperiment) with a planet sized
> > magnet...
>
> Auck!! You are creating black holes in my energy description! ;-)
>
> So, since the Moon is moving farther and farther away from the Earth
> and will eventually leave orbit, the gravitational force of the whole
> system will decrease and the total mass will increase? Wait, objects
> in motion loose mass, so the Moon would loose it. You were talking
> about mass increasing because the magnet stopped moving when it hit
> the table, right?

The total mass/energy of the system (moon, earth, magnet) (excluding things
like other solar bodies, radiation etc) is constant.

With the magnet dropping, the total mass of the system decreased at each
point in time until the magnet hit the table and stopped. But the total
energy in the system remained constant; it was just that the act of lifting
up the magnet (out of the gravitational well, giving it potential energy)
increased the mass of the earth and decreased its gravitiational
self-energy; dropping it restored the status quo. The numbers, I repeat, are
vanishingly small. A nit is too big for it.

The energy for the increasing size of the orbit of the moon comes from the
rotational energy of the earth, and that fact that the earth is a deformable
sphere; the tidal bulge (due to the moons gravity) is forward of the moon's
position (due to the rotation of the earth). This is imparting energy to the
moon by dragging it round faster than it would if the earth was a rigid
sphere. Hence the orbit increases to compensate, and the earth's rotation
slows down. But the total energy of the system hasn't changed; it's just
that some is rotational energy of the earth, some the angular momentum of
the moon, some mass and some gravitational self-energy.

The same mechanism is probably responsible for Pluto and Charon facing each
other in lock step; once all the rotational energy is gone in "kicking" the
moon into a higher orbit, the planet and the moon end up with the same face
pointing at each other.

I don't know if there is enough energy in the earth's rotation to allow the
moon to achieve "escape velocity"; I would bet on the answer being no.
Anyone want to do the maths/google for it?

>
> Thanks for making my post more accurate. No, wait -- strike that!
> You frigg'n LYING TOAD! It's a conspiracy! I made a trivial mistake
> of not dotting an "i" and you dogs are all over me! ;-)

True; it was a nit pick. But a discussion worth having, I think, and it made
a nice change from dissembling on HLLs vs assemblers while disembowelling
their authors. 

-- 
Regards
Alex McDonald

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