Re: Why the 3rd skyscraper came freefalling down on 9/11

["Paul J Kriha" <paul.nospam.kriha@xxxxxxxxxxxxxxx>]

Bryan Olson <fakeaddress@xxxxxxxxxxx> wrote in message
news:B6Clh.41303$wc5.20894@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> John E. Hadstate wrote:
> > "Woody Brison" wrote:
> >> Gravity
> >>
> >> Consider two objects floating in space, each being small
> >> compared to their separation.  Each object experiences a
> >> force directed toward the other object.  The force is
> >> equal in magnitude to
> >>
> >>   F = G m1 m2 / r^2
> >>
> >> where G = the gravitational constant
> >>      m1 = mass of the first object
> >>      m2 = mass of the second object
> >>      r = distance between them
> >>
> >
> > Sort of;  r is actually the distance between their centers
> > of mass.
>
> It's yet more complicated. Picture a light but rigid rod with two
> dense masses at the ends. The center of mass is at the center of the
> rod. Now I bring a small and dense object just a little ways from the
> center of the rod, in the plane that is normal to the rod and bisects
> it. What is the force of the rod's gravity on my small object? If you
> consider the rod to be equivalent to a point mass at the rod's center
> of gravity, I think you get a wrong answer.

With highly irregularly shaped objects one cannot use
the center-of-mass approximation. To get a (more) precise
answer, one would have to calculate the vectors of
gravitational acceleration caused by each molecule of
the irregular object individually and then add them all up.

I remember measuring g with a standard 1m pendulum
in my student years. A measurable difference was
noted between two different rooms in the same building.
It was probably due to irregular deposits of heavy ore
near the surface of Earth and the irregular shape of the
building itself. So even Earth is irregular enough not to
be regarded as a single point in space.
pjk

> > The acceleration of gravity (courtesy the CRC
> > Handbook of Chemistry and Physics, 49th Edition, Page F144)
> > at sea level is:
> >
> > Latitude 0: 9.78039 m/s/s
> > Latitude 45: 9.80621 m/s/s
> > Latitude 90: 9.83217 m/s/s
> >
> > The variation due to latitude stems from the fact that the
> > Earth is not spherical.  Sea Level at the poles is closer to
> > the center than it is at the Equator.
>
> Not really. The larger part is because the acceleration figures
> they cite are the apparent acceleration if we consider the Earth
> to be stationary and not rotating.
>
>    http://en.wikipedia.org/wiki/Equatorial_bulge
>
>
> --
> --Bryan
>