* (John Baez) schriebt:

Milgrom's solution is to say that Newton's laws are messed up.

Of course this is a drastic, dangerous step: the last guy who tried this
was named Einstein, and we all know what happened to him. Milgrom's theory
isn't even based on deep reasoning and beautiful math like Einstein's!
Instead, it's just a blatant attempt to fit the experimental data.
And it's not even elegant. In fact, it's downright ugly.

Here's what it says: the usual Newtonian formula for the acceleration
due to gravity is correct as long as the acceleration is bigger than

a = 2 x 10^{-10} m/sec^2

But, for accelerations less than this, you take the geometric mean
of the acceleration Newton would predict and this constant a.

Are you sure this is a correct description?

The geometric mean of this and that is just (this*that)^0.5, which if the
above is correct means essentially using the square root of the Newtonian
value, scaled by a constant.

I assume that by "acceleration" what is meant is not the acceleration of
an object in a given frame of reference, but the acceleration component due
to gravitational attraction to some other object or collection of objects.

And if so I assume further that this implies some distance between 'em, that
the other object(s) in question is the total gravitational attraction of the
galaxy hosting the object.

And if so isn't it possible that the effect that is attributed to weak
effective gravitational attraction above might instead be due to distance?

So, have anybody calculated the effect of accelerated Hubble expansion on the
apparent law of gravity over the distances involved?

It seems to provide the necessary non-square-distance-law to modify Newton's
law at sufficient distance. The questions I as a layman can see are (1)
whether it is of sufficient magnitude for the observed effects, and (2) (when
the math is done, and at least for some reasonable cosmological model) whether
it provides a sharp enough departure from Newton's law to appear as a
MOND-like sharply changed behavior in the effective law of gravity, and (3)
whether the particular form, namely apparent square root, is critical, and if
so whether Hubble law gives that or can approximate it.

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