On Tue, Apr 26, 2022 at 11:33 AM Brent Meeker <meekerbr...@gmail.com> wrote:

> If all mass were scaled down by the same factor the gravitational
> interactions, like orbits and pendulums, would seem unchanged.

You might want to rethink that! At the surface of the earth (radius r)
Newton's law of gravitation states that the force on a particle of mass m is

       F = GMm/r^2,

where G is Newton's constant, and M is the mass of the earth. Then using
Newton's first law of motion, F = mg,
where g is the acceleration due to gravity at the surface of the earth, we
find by equating the two expressions for F:

       g = GM/r^2.

So, when all masses decrease by 50%, the value of g also decreases by 50%.
This leads to an obvious change in the period of the simple pendulum:

      T = 2pi sqrt(L/g),

for a pendulum of length L. Note that the period of a pendulum does not
depend on the mass suspended at the end of the string, but it does depend
on the mass of the earth,

But what about the natural frequency of spring-mass systems?  Halving the
> mass while the EM forces between molecules of the spring stay the same
> means the frequency will go up.   So must all interaction constants change
> to save the appearance?

JKC seems to think so. But that is obviously absurd. Any change in the
overall energy of a branch leads to immediately apparent effects.


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