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Old November 27th 17, 10:06 PM posted to sci.astro.research
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Default Addition of grav'l potentials?

On Monday, November 20, 2017 at 4:33:30 PM UTC-5, wrote:
On Friday, November 17, 2017 at 2:27:13 AM UTC-5, stargene wrote:
An impossible question?

I would like to know if there is a straightforward way of calculating
the sum of two different gravitational potentials U and V at some point
x.

To simplify as much as possible, I imagine, say, that two neutron stars
n1 and n2 are in circular orbit around their mutual center of gravity
(*) and that the point x is always outside their orbit but on a line
joining their centers...Something roughly like:

x _ _ _ _ _ _(n1) _ _ _(*) _ _ _(n2)

and r1 is distance between x and n1; r2 is the distance between x and n2.

Separately and classically, U, for n1 might be:
U = -G M(n1)/r1 and V, for n2 might be: V = -GM(n2)/r2 . But
what would GR say about this?

So, assuming that r1 and r2 are easy to define, would the sum U+V be
analogous to SR's addition of velocities:

w=(u+v)/(1+uv) ,

..where U=-u^2 , V=-v^2 and their sum W = -w^2 ?

Or am I wildly off base? I just realized an added wrinkle he n1 and
n2 are possibly in relativistic motion and my `straight line' thinking
might be naive.

Thanks


I once posed this type of addition concerning a gravity anomaly
in Denver Colorado. One mass was to be a spheroid earth with
all of the Rocky Mountains removed. Basically a plain with a
sea level altitude of Denver's, about 5000 feet. This is Newtonian
geometry.

The Rocky Mountains were to be a type of planar disk as a first
approximation. So the equation will be non Newton's, but
approximately as a set of spheres inside the disk. Just add up
distance outcomes for the disk interior.

The intention was to interpret the anomaly as an disk asteroid sitting
on a plain.

If course I was ridiculed, only.

[[Mod. note -- Your proposal is in fact not implausible. Actual gravity
models need to consider lots of density variations in the solid Earth
as well (actual mountains also have "fundations" which project below the
spheroid-earth-with-all-mountains-removed). See
https://en.wikipedia.org/wiki/Gravity_anomaly
https://en.wikipedia.org/wiki/Bouguer_anomaly
for a bit more information.
-- jt]]


Thanks the issue is in the sciences. I forget the reference,
but around 1982 a researcher used a spinning top in an
aircraft to look at the gravity field along the New Jersey
cliff system. He saw a definite precession change in the
gyro.

This might be the only way to measure the Bouguer Anomaly
I suggest.

The NIST responded by making a top and measured the mass change
of it. They compared the mass at two altitudes and saw
no mass change. Implying no altitude gravity field. This
was done at the Boulder Lab of the NIST.

In my way of thinking the NIST was at fault for not defining
the lower limit of sensitivity of their answer. I would
demand the use of a spring lever balance equal to a gravity
survey detector system. They used a common electronic strain
gauge laboratory scale.