Re: Dark matter/energy - is it real?

:: Michael Ash <mike@xxxxxxxxxxx>
:: This is related to a more practical question wrt halos and solar
:: systems. In this thread, an analysis was given of the solar system,
:: where basically the Sun was at the center of the sphere, and d was
:: the theorized local density for dark matter. This gives a (small)
:: additional attractive force to all other bodies in the solar system
:: towards the Sun. Yet if you center the sphere on the galaxy, it's
:: clear that everything falls towards the center of the galaxy and
:: there is no force towards the Sun. Again, something here is
:: obviously wrong, but what is it?

: throopw@xxxxxxxxx (Wayne Throop)
: The analysis wrt the sun makes simplifying assumptions that turn out
: not to be the case; namely, that the gravity from the mass
: distribution outside the solar system cancels. It doesn't, because
: the distribution outside the solar system is not a sphere.

Or in more detail, take the solar-centered case.
Take shells centered on the sun, larger than your distance to the sun.
Once you've considered all such complete shells, you will have left
over a big ven-diagramy-like concave-thingie thicker on the other side of
the galaxy. And it will be offset just enough to cancel the sunward
force of the sun-centered sphere at your radius, and on top of that,
will supply a galactic-center-ward force. In short, you get the same
answer whether you decompose sun-centered or galaxy-centered; it's just
that the sun-centered deomposition is inconvenient because it has this
big piece left over that's neither the sun centered sphere, nor part of
any complete sun-centered shell. Which is not a problem you have with
the galaxy-centered decomposition; in that case, you account for all
the distributed mass as either in the sphere, or in a shell.


Wayne Throop throopw@xxxxxxxxx http://sheol.org/throopw
.

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