The path of gravity

[Bill Eshleman]

Gravity travels in straight lines, right?…NO.

When I first posed this to supposedly smart fellows,
they quickly conjectured, “Even though we know that
the speed of gravity is not infinity as Newton
suggested, gravity and electromagnetic waves travel
in straight lines anyway. Maybe the straight lines
are tilted due to delays caused by the finite speed
of radiations, but they are still straight.”

But look at it this way; light at the center of the face
of the Sun, destined for Earth, emanates from the Sun, always perpendicular to the Sun’s surface…always.

From the perspective of the Earth, our telescopes aimed
at the Sun, are always aimed where the Sun was approximately
8 minutes ago. So always, there are two angles that the
path must satisfy, and a straight line is not capable of
fulfilling these two requirements, so the path is a curve
in a dynamic system; not a tilted straight line.

Curves are longer than the straight line connecting the
source and destination, so I suspect that the 8 minute delay is augmented by a tiny delay due to the longer
path of the travel of gravity and electromagnetic waves.

A piece of a quadratic polynomial could satisfy the
required angles at the Sun and the Earth; but a higher
power polynomial can always be found that will match
the curve better, especially at the curve’s midpoint.

If the curve is approximated by ratios of polynomials,
there will always be remainders for every quotient.

So, armed with these conditions, what is the polynomial
representation for that curve?

Well, join the discussion, and maybe we will find out.
I’ve got some ideas up-my-sleeve, anybody else got any
ideas? Like maybe the introduction of gravitational
magnetism?

I’m hoping that this problem will be a nice armchair
exercise for the puzzle-solvers out there.

[Bill Eshleman]

The picture in this post is a page out of my “idea-book”.

This cardioid-like curve is constructed piecewise-linear,
with the equality,

(delta theta)/(delta R) = theta/R

For our Sun, theta is the angle between an imaginary line
to where the Sun really is, and an imaginary line to where
the Sun was about 500 seconds previously. R is the distance of separation of the Earth and Sun, a 500 second
trip for the light(and gravity).

We all know that light and gravity travel only in straight
lines if not interfered with somehow, but that cardioid-like
“path” is compelling to say the least. Could it be a real path? Please dash my hopes with some logical reason why
that cardioid-like curve is just a mathematical artifact.

I literally need to “straighten-out” out that curve so I can
discard it or optionally leave more folks confused, as
certainly am I.

Gyula, please put Picture004.jpg here:

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