Significant Findings

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Clock Second of an Atomic Clock

as function of the Gravitational Potential Gradient

 

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

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

T0 (sec) = 1.0000000000000

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

vorbit = 0     vescape = 0    vresultant = 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  Vescape  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 (m2s-2). Thus, the square of the escape velocity, v2escape (m2s-2), may be used as a gauge for the non-measurable gravitational potential (m2s-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 (m2s-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 v2resultant (m2s-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 (133Cs) 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 133Cs 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 (133Cs) 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(vres) = 1.0000000002507 sec

Clock Adjustment (sec): 1.0000000006990 - 1.0000000002507 = .0000000004483

 

At 2.694 Earth Radii a clock second is T(vres) = 1.0000000003886 sec

Clock Adjustment (sec): 1.0000000006990 - 1.0000000003886 = .0000000003104

 

Earth Looking Down on North Pole

At 1.000 Radii   vearth = 448 m/s,  vescape = 11189 m/s and vresultant = 11198 m/s

At 1.498 Radii    vorbit = 6465 m/s, vescape = 9143 m/s and vresultant = 11198 m/s

At 1.000 Radii and at 1.498 Radii the clock rates are exactly the same.

using equatorial motion vearth = 448 m/s, T(vresustant = 1.0000000006990 sec

using vorbit = 6465 m/s at 1.498 Radii,       T(vresultant)  = 1.0000000006990 sec

 Thus, from the above combinations of 1.000 Radii and 1.498 Radii

the instruments require absolutely no clock rate adjustments. 

 

Hyperfine Splitting of the 6s electron level of the 133Cs Atom

Figure Reference: www.hyperphysics.phy-astr.gsu.edu/hbase/images/csclock.gif 

 

Cesium (133Cs) 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 (m2s-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 (m2s-2) as follows:

 

(J/Kg)

from

Work W = F x s

 = M x A x s

(Kg ms-2 m/Kg)

or

(m2s-2)

energy per unit mass

energy per unit mass

velocity2

 
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) Vescape (m/s) Clock Error 133Cs 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 gsun > gearth.

Note: For ALL distances up to 14.2 AU's, the Gravitational Potential Vsun > Vearth

 At the distance of 14.2 AU's from the Sun the Gravitational Potential Vsun = Vearth.

 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.

Vsun is 14.14 times VEarth 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/s2, at 1 AU the Sun's g-field = 5.956E-03 m/s2

This clearly shows that the Cesium (133Cs) 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 Vescape  = 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 Vescape  = 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 (133Cs) atoms of the atomic clocks.

 

This is clearly confirms that the Cesium (133Cs) 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 Vsun of the sun is dominant over the earth's potential VE 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 133Cs 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 133Cs 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 133Cs atoms, a tidal effect causing the electron configuration of the 133Cs atoms to be slightly altered. The gravitational potential gradient of the Earth acting on the 133Cs atoms is effectively a lengthening of the pendulum of the atomic clocks by means of a radial displacement from the unperturbed configuration of the 133Cs 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

  1. 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. 

  2. 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

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

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

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

 

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