as
function of the Gravitational Potential
Gradient

In
deep space
where the gravitational potential is near zero the natural frequency of
cesium ^{133}Cs would be at a maximum.

In a
zero gravity space (V = 0) a clock second
could be defined as

T_{0 }(sec) =
1.0000000000000

In
this space
there can be little or no sources of gravitation from gravitating matter, and hence,
no escape velocity (v_{escape}=0).

v_{orbit} =
0 v_{escape} =
0 v_{resultant} = 0

…………………………………………..…………..…………….

The
gravitational potential

usually
expressed in
units of (J/Kg) is found to
act directly on the time keeping instrument, namely, the clock. As there
can be no direct measurement on the gravitational potential
itself, especially in
space at the site of the orbiting time keeping instrument, the escape velocity
V_{escape} in units of (m/s) may be squared and used as a
gauge for the gravitational potential, both of which are in the units of (m^{2}s^{-2}).
Thus, the square of the escape velocity, v^{2}_{escape}
(m^{2}s^{-2}), may be used as a gauge for the
non-measurable gravitational potential (m^{2}s^{-2}).
See Reference 1.

An observer in the frame of reference of a clock in
orbit hypothetically sees the effects of an
aberrational effect of a gravitational potential gradient of the very
same units (m^{2}s^{-2}) acting on the Cesium
atoms of the atomic clock.
Because of the orbital motion of the clock, the gravitational potential
gradient acting on it may be expressed mathematically using the square of the escape velocity,
namely v^{2}_{resultant}
(m^{2}s^{-2}). Thus, a clock second may
be easily defined as:

and
from

a clock second
is simply given as

The gravitational forces acting on
an atomic clock in orbit is cancelled by the centrifugal forces
acting on it. However, there is always a gravitational potential
gradient acting on the Cesium (^{133}Cs) atoms of an
orbiting atomic clock that cannot be cancelled by any known
technical means. Thus, the escape velocity squared is shown to be
a gauge for the gravitational potential gradient that is acting on
the clocks. The evidence shows there is always a gravitational
potential gradient that acts on the ^{133}Cs atoms of an
orbiting atomic clock in much of the same manner in which the
gravitational potential gradient of the moon causes the tidal
effects on Earth. The findings presented here convincingly show
that the gravitation does not interact directly with
broadcast information or the electromagnetic waves that are
transmitted from the satellites bearing the atomic clocks.

Observational
evidence consistently shows that the gravitational phenomenon that
is actually causing the slowing of the atomic clocks is directly
linked to the gradient of the gravitational potential, not
the gravitational potential itself.

In
Reference 2 a very similar principle employing the Galilean
transformation of velocities to add the orbital velocity of planet
Mercury and the velocity of the propagation of the gravitational
field, exchanged between the Sun and the planet Mercury, obtains
the precise perihelion rotation of the planet Mercury of 42.988
arcsec/century. Similarly for the PSR1913+16 binary neutron pulsar
star system, a perihelion rotation of 4.2265 degrees per year was
obtained. See pages 63 - 65 in Reference 2.

Important:
It is also to be noted that both here in this work and also in
Reference 2, a direct interaction between gravitation and
electromagnetism need not be assumed. The gravitational light
bending phenomenon taking place at the Sun bears convincing
observational evidence that this is the case. It is
convincingly apparent that the gravitation acts directly on the Cesium (^{133}Cs) atoms
of the clocks, not the transmitted electromagnetic signals or the
waves that convey the time signals from the orbiting atomic
clocks.

At 4.175 Earth Radii a
clock second is T(v_{res}) =
1.0000000002507
sec

Cesium (^{133}Cs) Frequency as Function of
Distance R (Radii) or

as Function of a Decreasing
Gravitational Potential of Earth

(J/Kg)

This is the work required to move a
unit of mass from R to infinity. It is also the kinetic
energy that a unit mass acquires when falling from infinity to R.

The Gravitational Potential of Earth expressed in units
of (J/Kg) is also expressible in units of (m^{2}s^{-2})
and thus in the same units as the square of the escape velocity.

The potential V(r) at a distance r from the mass M is
defined as the work W done by the gravitational field bringing the mass
M from infinity to the point r.

The potential is

The units (J/Kg) can be expressed
directly as (m^{2}s^{-2}) as follows:

(J/Kg)

from

Work W =F x s

= M x A x s

(Kg ms^{-2 }m/Kg)

or

(m^{2}s^{-2})

energy per unit mass

energy per unit mass

velocity^{2}

The measurement of the Gravitational Potential at the
site of the orbiting atomic clocks is a very challenging task and is
perhaps currently a technically unfeasible task. Determining the escape
velocity is well at hand and is easily determinable and is a direct
measurement for the non-measurable gravitational potential. Some clock
errors as a function of the orbital radii of Earth are summarized as in
Table 1.

Table
1

Clock
Errors Due
to Earth Gravitational Potential Alone

Dist (Earth Radii)

V_{escape (m/s)}

Clock Error

^{133}Cs Frequency (Hz)

1.00000

11189

1.0000000006990

9192631770

1.49800

9143

1.0000000004659

9192631772

2.69480

6824

1.0000000002590

9192631774

4.17500

5481

1.0000000001672

9192631775

6.61500

4354

1.0000000001055

9192631775

8.00000

3959

1.0000000000872

9192631776

40.7000

1756

1.0000000000086

9192631776

beyond Pluto orbit

12

1.0000000000000

9192631776

It is important to note that the tabulated results from
the orbiting atomic clock data
shows a summary of recorded clock errors as a functions of the Earth's
gravitational potential only, not considering the effects of the
gravitational potential of the sun. It is a well known fact that the Earth's
gravitational acceleration exceeds that of the sun for distances up to
40.7 Earth Radii.

We shall conduct a thought experiment, ein Gedankenexperiment,
a favorite tool of Dr. Albert Einstein, briefly describes in a Nutshell
the essential point of the problem.

Ein
Gedankenexperiment

Note: For
distances beyond 40.7 Earth Radii the Solar Gravitational Acceleration g_{sun}
> g_{earth}.

Note: For ALL distances
up to 14.2 AU's, the Gravitational Potential V_{sun} > V_{earth}.

At the
distance of 14.2 AU's from the Sun the Gravitational Potential V_{sun}
= V_{earth}.

Given that the
gravitational potential is a 1/r-effect,
at 1 AU and along the orbital path of Earth,

the Sun's
gravitational potential is a factor of 14.2 times that of the Earth.

V_{sun} is
14.14 times V_{Earth} all along Earth orbit

Most Importantly Note that the Escape Velocity from the Sun at the Earth's position
of 1 AU

a distance of
1.496E+11 m from the sun is 42127.9 m/sec, a clock error of
1.0000000098714

At 40.7 Earth Radii
in any direction from the Earth the Gravitational Acceleration g of
Earth

and Gravitational Acceleration
g the Sun at 1 AU are
equal.

At 40.7 Earth Radii
the Earth's g-field = 5.956E-03 m/s^{2}, at 1 AU the Sun's g-field =
5.956E-03 m/s^{2}

This clearly
shows that the Cesium (^{133}Cs) atoms of the atomic clocks in
Earth orbit have to be

predominantly
effected by the gravitational
potential gradient of
the Earth alone.

From Table 1, the
escape velocity from the Earth's surface is V_{escape
}= 11189 m/sec,

corresponding to a clock
error on Earth of 1.0000000006990
sec.

However,
it would be totally incorrect to assume that the escape velocity
of V_{escape
}= 42127.9 m/sec,
required to escape from the gravitational grip of the Sun and
clear from the Solar System, starting from any place along
Earth's orbit at 1 AU, would actually
correspond
to a clock error of
1.0000000098714 sec. This would be fundamental flawed because
understandably the Sun's gravitational potential has very little
or negligible tidal effects on the Cesium (^{133}Cs) atoms of the atomic clocks.

This is clearly
confirms that the Cesium (^{133}Cs) atoms of the atomic clocks

are slowed by the
gravitational potential gradient of the Earth

On the Gravitational Potential Gradient of
Earth

The gravitational potential V_{sun} of the sun is
dominant over the earth's potential V_{E} for all r less than 14.2
AU's.

The
gravitational potential of the earth and of the sun are given as

and

It is also to be noted that the potential gradient
of the sun along the orbital path of the earth (at r = 1AU) is
much less than that of the earth's potential gradient for all
points along the earth's orbital path.

where by definition, examining the region
from r to r+z

For satellites in a near earth
orbital path, the gravitational potential gradient of the earth is
over three
orders of magnitude greater than that of the sun's gravitational
potential gradient. This is understandable because in proximity to
the earth, the gravitational potential
lines of force diverge much more rapidly than those of the much more
distant sun. Examining the gradient of the
gravitational potential the earth and that of the sun, we can make
the
following comparison:

This clearly explains why the
atomic clocks appear to be predominantly effected by the earth's
gravitational potential gradient for distances well beyond the moon.
This is well understood due to the fact that in proximity to the
earth the gravitational potential of the earth gives rise to
gradient lines of force that all point towards the center of the
mass of Earth while those
of the much
more distant mass of the sun will be more parallel, less converging and
consequently cause weaker or non-measurable tidal effects on the ^{133}Cs atoms
of the clocks. It should be interesting to
note that the tidal effect of the Moon acting on Earth is a
factor of 2.177 times the tidal effect of the Sun acting on Earth.
Also, note that the gravitational
force of the Sun on Earth is a factor of 178.74 times the
gravitational force of the Moon on Earth.

This means that, from the above
calculation, the Moon has a greater tidal effect on the near Earth
orbiting atomic clocks by a factor of 2.177 times that of the
tidal effect of the more distant Sun.

In
all near Earth orbits there is always a

gravitational
gradient potential that is offset

by
a centrifugal acceleration gradient

The evidence clearly shows that it
is the gravitational
potential gradient of the earth itself that predominantly acts on the ^{133}Cs atoms of
orbiting atomic clocks in much of the same manner as the
gravitational potential gradient of the moon causes the tidal
effects on the Earth.

Radial
Tidal Effect

of
Gravitational Gradient

The gravitational
potential gradient introduces a deformation of the ^{133}Cs atoms,
a tidal effect causing the electron configuration of the ^{133}Cs atoms
to be slightly altered. The gravitational potential gradient of
the Earth acting on the ^{133}Cs atoms is effectively a lengthening
of the pendulum of the atomic clocks by means of a radial
displacement from the unperturbed configuration of the ^{133}Cs atoms.
It is this effect alone that is largely responsible for the
gravitational slowing of the atomic clocks that are operating
above the surface of the Earth and in near Earth orbit. The
gravitational tidal effects of the Sun are at least 3 orders of
magnitude less than those of the Earth.

The findings show this has nothing at all to due with Relativity.

References

James Carter, "The
True Direction of Gravitational Force", Proceedings of
the Natural Philosophy Alliance, 18th Conference of the NPA, 6-9
July 2011, University of Maryland, College Park, USA, vol.8, pp
107-109.

Dowdye,
Jr., E.H., "Extinction
Shift Principle: A Pure Classical Alternative to General and
Special Relativity", Physics Essays,
Volume 20, 56 (2007) (11 pages); DOI: 10.4006/1.3073809

Neil Ashby, University of
Colorado, http://vishnu.nirvana.phys.psu.edu/mog/mog9/node9.html

Peter H. Dana, Global
Positioning System (GPS) Time Dissemination
for Real-Time Applications, Department
of Geography, University of Texas at Austin

Donald E. Simanek, Lock Haven
University, "Tidal Misconceptions",
www.lhup.edu/~dsimanek/scenario/tides.htm