Re: Impact of Spheroidicity

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Leigh's final question:

> As a parting shot, does the gravitational force of the Sun
> on the Earth point to the center of the Sun as we see it on
> Earth?

This is a trick question.  But the answer is no.  The direction the force
the Earth experiences due to the Sun is very close to the direction in
space where we will see the Sun's center in about 8 minutes into the
future.  Within experimental error that gravitational force is directed
toward the current instantaneous position of the Sun rather than the 8-
minute time-delayed visually *observed* location of the Sun.  But in
principle, the direction of that force is not *quite* exactly toward the
current instantaneous location of the Sun; but the difference is between
the actual direction of the force and the true direction of the current
location of the center of the Sun is too close to experimentally measure
(I think).  This does not mean that gravitational forces propagate
instantaneously, however.  Rather, it means that in the near field they
have a built-in compensation for the crudest lower order (in 1/c^2)
effects of the actual retardation in the propagation of gravitational
effects.  The resolution of this is seeming paradox is related to my
comment in my last post where I wrote (concerning Newton's 3rd law):

> In the case of gravitation it is an even better
> approximation than it is for electromagnetism because gravitational
> interactions tend to have the effect of their actual retarded interaction
> cancel out in the near field to a higher order in 1/c^2 than they do for
> electromagnetic forces.

When two separated charges interact (close enough to each other so that
the near field approximation is almost correct), the part of the force
that they experience due to each other (not counting the radiation
reaction force from the acceleration caused by that interaction) is
strictly causal in that the force on each object depends only on the
state of the other object one light-travel time ago.  *But* the direction
of the force does *not* point back to the location of the other charge at
that retarded time.  Rather the force is directed ahead of that location
by projecting the trajectory of that charge ahead to where it would be
expected to be at the current instantaneous time assuming that other
charge would continue to move at a uniform velocity and not accelerate
during the light travel time.  IOW, the EM force depends on old
light-travel-time-delayed information about the other particle, but it
extrapolates that info ahead to the current time assuming the other
particle moves with a uniform motion.  The effect is sort of like how a
hunter leads the position of a running deer in order to hit it with a
finite speed bullet or arrow.

Thus, if both charges were in uniform unaccelerated motion then the EM
force exerted on each one due to the other one *would* point to the
correct instantaneous location of that charge.  The effect of the time
delay would be cancelled out.  If the charges *do* accelerate then this
'leading' effect doesn't quite cancel out and the direction of the
EM force is not quite toward the exact current location of the other
charge.

As I understand it, for gravitation a similar effect holds, but it is
even *more* sophisticated.  The gravitational interaction in the near
field includes a built in compensation which projects the current
location of the other mass (based on that mass's light-time-retarded
position, velocity, *and* acceleration). This leading/projection effect
gets the current location of the other mass assuming that during the
light-travel time between the masses that other mass doesn't have a very
wild time-variable acceleration with a huge jerk rate.  This is why
within experimental error the gravitational force the that the Earth
feels due to the Sun is essentially toward the current actual location
of the Sun even though the gravitational interaction only propagates at
speed c.  This leading/projection/cancellation effect makes it look like
the gravitational interaction is instantaneous.  This also makes Newton's
3rd law hold to a remarkable degree of precision for gravitation even
though that interaction doesn't propagate locally any faster than c.
Part of the reason why this cancellation effect is so good for
gravitation is related to the fact that gravitational radiation is
not produced by uniformly accelerating masses.  The gravitational
radiation depends on the square of the jerk rate.  The reason for this
is related to the fact the lowest order source of gravitational
radiation is a fluctuating mass quadrupole moment.  For charges
they radiate EM radiation at a rate proportional to the square of
their acceleration and this is related to the fact that the lowest order
source of EM radiation is a fluctuating charge dipole moment.

David Bowman
David_Bowman@georgetowncollege.edu