theory it is thought that electrons are a string of electrons that can be thought of as a rope. The rope oscillates at tremendously low frequency. It has an up and down motion, nonetheless. This gives the electron a centripetal force as well as a gravitational potential energy. It is this gravitational potential energy that physicists call a gravity wave. There is very little gravity or g in space, but there is always some, and the electron has mass. The gravitational potential energy is equal to the electrostatic force and both are very small, but a part of the equation nonetheless. The mechanical portion of the wave can be shown or represented as follows (Figure 13):

Requiredcentripetalforce = m v 2 r

At the top the minimum speed to maintain a circle is the speed which gives a downward centripetal acceleration a = g. So, the minimum speed at the top is given by

v top ( minimum ) = g r

Conservation of energy relates the velocities at the top and bottom of the circle:

1 2 m v top 2 + m g 2 r = 1 2 m v bottom 2

Substitutions give the relationship between the tensions at the top and bottom.

T bottom = T top + 6 m g

This finding will require a change to the Lorentz equation from F = qE + qvB to the following:

F g + F c = q E + q v B

This is a significant finding because it also redefines the radio wave and the

Figure 13. Centripetal and gravitational force.

power wave. The implication is that all electromagnetic waves are electrically and mechanically balanced. Observations of high current arc furnace transformers confirm this finding by way of the physical movement of the primary leads connecting the transformer. Arc furnace transformers operate effectively as short circuit and currents of tens of thousands of amps are not uncommon. Bolted short circuit faults are also known to have violent physical movements that are attributed to the Lorentz force. Given that the Earth requires over a billion amps for its normal operation, it is not a stretch of the imagination to visualize giant electromagnetic waves emanating from the Sun as plasma like conductors oscillating mechanically, as well as electrically. These are magnificent power waves propagating through space at the speed of light transferring much needed life sustaining energy to the planet’s antenna. Planets are thus the most powerful of antennas, which convert electromagnetic energy to a billion amps of electric current which causes rotation and generate the planets own electromagnetic field. The receiver then becomes the transmitter. The solar system, and the universe, is envisioned as a vast network operating as a tremendously low frequency power system network. The size and immensity of the interconnected network of stars in the universe make it extremely stable and predictable.

We know that there is an electromagnetic wave that is E and B, and opposite that is a mechanical wave, which would be F centripetal and F gravitational. The wave is thus four dimensional and F can be shown to be two components, Fc and Fg, which correlate proportionally to E and B (Figure 14).

Another way to view Lorentz force is to view it on a particle basis in an electromagnetic field with a rotational force.

In the case where the charged particle q moves in both electric field E and magnetic field B, that is an electromagnetic field (Figure 15), the combined

Figure 14. Lorentz force vectors.

Figure 15. Lorentz electromagnetic force vectors.

force F that acts on the particle becomes the electromagnetic force that is the vectoral sum of Fe and Fm:

F = F e + F m = q E + q v × B

11. Ground Waves

Ground wave propagation uses the area between the surface of the Earth and the ionosphere for transmission. The ground wave can propagate a considerable distance over the Earth’s surface particularly in the tremendously low frequency. Typically, a ground wave signal is made up of a number of reflected waves. Since the Sun and the Earth are in the line of sight, there will be a direct wave as well as a reflected signal. There will be a number of reflected signals as the transmission will be reflected by a number of objects including the Earth’s surface and any hills, or large objects or buildings that may be present. In addition to this there is a surface wave. This tends to follow the curvature of the Earth and enables coverage beyond the horizon. It is the sum of all these components that is known as the ground wave. Beyond the horizon the direct and reflected waves are blocked by the curvature of the Earth, and the signal is purely made up of the diffracted surface wave. It is for this reason that the surface wave is commonly called ground wave propagation. The surface wave is also very dependent upon the nature of the ground over which the signal travels. Ground conductivity, terrain roughness or roughness of the sea, and the dielectric constant all affect the signal attenuation. In addition to this the ground penetration varies, becoming greater at lower frequencies, and this means that it is not just the surface conductivity that is of interest. At lower frequencies penetration means that ground strata down to hundreds of meters may have an effect. The tremendously low frequency gives us an idea of how deep the currents of the Earth are from the surface [56] .

Despite all these variables, it is not surprising that the terrain with good conductivity gives the best result. Current prefers the least path of resistance. Thus, soil type and the moisture content are of importance. Salty sea water is the best, and rich agricultural, or Marshy land is also good. Dry sandy terrain and city centers are by far the worst. This means sea paths are optimum, although even these are subject to variations due to the roughness of the sea, resulting in path losses being slightly dependent upon the weather. It should also be noted that in view of the fact that signal penetration has an effect, the oceans seawater table may have an effect dependent upon the frequency [57] .

12. Cosmic String Theory and Maxwell’s Equations

Maxwell’s equations are a set of equations that, together with the Lorentz force law, form the bedrock of classical electromagnetism and optics. The famous equations describe how electric and magnetic fields are generated by charges, currents, and changes of each other. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Electromagnetic waves in vacuum travel at the speed of light according to Maxwell. When passing through a material medium, they slow down according to that object’s permeability and permittivity. Dark matter is thin enough that in space waves travel very close to the speed of light. The wavelength is the distance from one peak of the wave’s electric field to the next and is inversely proportional to the frequency of the wave. The distance an electromagnetic wave travels in one second, in vacuum, is 299,792,458 meters.

The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. Figure 16 shows a plane linearly polarized electromagnetic radiation

Figure 16. Electromagnetic wave.

wave propagating from left to right (X-axis). The electric field is in a vertical plane (Z-axis) and the magnetic field in a horizontal plane (Y-axis). The electric and magnetic fields in electromagnetic radiation waves are always in phase and at 90 degrees to each other.

Maxwell’s equations have two major variants. The microscopic Maxwell equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The macroscopic Maxwell equations define two new auxiliary fields that describe the large-scale behavior of matter without having to consider atomic scale details. However, their use requires experimental determined parameters for a useful description of the electromagnetic response of materials.

When considering cosmic electromagnetic waves macroscopic dominates the conversation, but even macroscopic is not sufficient to comprehend the size and immensity of cosmic waves. Maxwell, when formulating his equations in the 1800’s would have never considered electromagnetic wavelengths billions of meters long and tremendously low frequency (TLF). There is no indication in the writings of Maxwell or JJ Thompson that they or anyone else of the time period used the Biot Savart law to calculate the current draw of the Earth at 1.7 billion A. It is doubtful that in the early stages of the development of these fundamental equations that the ampacity of lightning was understood. Today we know that lightning can range from several thousand amps up to 200,000 A.

Lightning is perhaps the best example we have of the grandeur of cosmic electromagnetic waves emanating from the Sun to power planets. Lightning as we know is a short circuit to ground whereas cosmic waves are traveling through space not connected to anything. But the size and power are similar and give us a clue as to the characteristics of cosmic electromagnetic waves. It is the characteristics of lightning that leads one to percolate thoughts on the possible expansion of Maxwell’s equations. For we know that lightning is not just an electromagnetic wave. The phenomena of lightning include much more than just propagating waves of magnetic and electric fields. Lightning is accompanied with thunderous sound waves, intense light waves, explosive pressure waves and high energy convective radiant heat waves. Combined with the Lorentz forces of centripetal and gravitational waves we begin to see that on the grand scale of lightning, or even on the scale of an arc flash we have a wave that it is multi-dimensional. When we add up all the dimensions―magnetic, electric, centripetal, gravitation, sound, light, pressure, convective and radiant heat―we have nine dimensions plus wave time.

It is postulated that lightning waves may be cosmic superstrings with ten dimensions. To extend this theory, we then begin to consider that cosmic waves are also ten dimensional super strings traveling through space. At over a billion amps and billions of miles long it is visualized that these cosmic super strings are moving through time and space as gigantic twisting bending snakes of energy. Since the cosmic waves are unground and unconnected, the current flow in the super string itself is contained when compared to when it reaches its planetary destination. Many of the dimensions of the snake are suppressed or stored like a coiled spring. The electrical and mechanical dimensions are propagating and vibrating through space waiting to connect and spring. The mechanical movement of the string produces a low frequency sound and gives space its normalized pressure and warms the space as well. Very little light is generated by the superstring in space as little change of state is occurring.

When we expand the electromagnetic wave to a cosmic scale the wave looks different than what we imagine emanating from our 20-amp wall outlet. But, then the question becomes, what is the nature of the electromagnetic wave when it is scaled down from the cosmos? We know that at a commercial or industrial service 5000 and 6000 A are not uncommon. Even at this magnitude, we have mechanical bracing to counteract the mechanical forces, and we hear the hum of vibration in the switchyard along with the smell of ozone due to pressure. When walking gingerly through a 345,000 V high voltage substation there is a sense of foreboding that should something go amiss, there are more dimensions to Maxwell’s equations than just the magnetic and electric fields. One feels that beneath the surface of the electromagnetic wave are the other dimensions traveling with the electromagnetic weave. Just as voltage and current are stepped up and stepped down by transformers, it is theorized that sound, pressure, heat and light can be stepped up or stepped down based on the energy and demands of the wave. Arc flashes resemble lightning strikes and give us an example where sound, pressure, heat and light are instantly stepped up, and voltage and current stepped down. In a sense electromagnetic waves have their own built-in transformer action where nine of the dimension can be stepped up or down based on their relations and interactions with one another. It may even be possible that the timewave stands still, speeds up or slows down, when a catastrophic event such as an arc flash occurs.

Since its beginnings superstring theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics. Superstring theory is shorthand for supersymmetric string theory. Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of micro supersymmetric strings. It is thought that cosmic waves in the form of electrical, mechanical, pressure, sound, heat, etc. can be used to expand the theory to the macro physics world. It is hypothesized that at low energy levels and low frequency, such as 60 Hz, normal running condition of a power system, the electromagnetic vibrations dominate the spectrum and the other dimensions of the waveform―heat, pressure, sound, and light all lay dormant or suppressed. As the energy levels increase due to increase in current and voltage the other dimensions start to become noticeable. At high currents of 5000 or 6000 A or high voltage of 345,000 V these other dimensions become even more noticeable. At fault levels, or arc flash, or even lightning, there is a significant change in energy levels, and the frequency is raised substantially. This change in frequency and energy causes the dormant dimension of heat, pressure, sound and light to increase in amplitude and strength such that they become the dominant forces involved and the electromagnetic wave becomes negligible. Effectively a change in energy and frequency changes the characteristic of the waveform from an electromagnetic and mechanical force to waveform of heat, pressure, sound and light force. This concept or theory of waveform shape shifting due to frequency would be consistent with ten-dimensional super string theory.

Maxwell himself stated to the Royal Society that he dropped the mechanical portion of his equations due to the complexity of integrating mechanical forces with the electromagnetic and electrostatic equations. This complexity grows even greater when nine or ten dimensions are considered to be part of Maxwell’s equations. But it might be that Maxwell’s equations represent only a small portion of the ten-dimensional superstring we call an electromagnetic wave. Adding the seven other dimensions to make it a nine-dimension wave (Figure 17) with time as the tenth wave form would meet the super string theory for asymmetry.

13. Pattern of a Spherical Antenna

It is a property of antennas that the transmitting pattern of an antenna when used for transmitting is identical to the radiation pattern of the antenna when used for receiving. This is a function of the reciprocity theorem of electromagnetics. Therefore, in relation to planetary spherical patterns the antenna can be viewed as either receiving or transmitting, whether it is the Sun, the Earth or another of the planets. The spherical antenna is thus generalized for all large bodies in our solar system.

The far-field radiation pattern of a planet may be represented graphically as a

Figure 17. Artist depiction of nine-dimensional wave with time wave.

plot of one of several related variables, including; the field strength at a large radius, amplitude pattern or field pattern, the power output pattern and the directive gain. The plotted quantity for the total gain is typically plotted in dB. The plot is typically represented as a three-dimensional graph (as at right), or as separate graphs in the vertical plane and horizontal plane. This is often known as a polar diagram. A radiation pattern defines the variation of the power radiated by an antenna as a function of the direction away from the antenna. This power variation as a function of the arrival angle is observed in the antenna’s far-field. As an example, consider the 3-dimensional radiation pattern in Figure 18, plotted in decibels (dB) [58] .

Figure 19 is an example of a spherical radiation pattern that may represent a sun or planet. In this case, along the z-axis, which would correspond to the radiation directly overhead the antenna, there is very little power transmitted. In the X-Y plane (perpendicular to the Z-axis), the radiation is maximum. These plots are useful for visualizing which directions the antenna radiates. Typically, because it is simpler, the radiation patterns are plotted in 2-d. In this case, the patterns are given as “slices” through the 3D plane. The same pattern in Figure 19 (left) is plotted in Figure 19 (right). Standard spherical coordinates are used, where θ is the angle measured off the Z-axis, and ϕ is the angle measured counterclockwise off the X-axis [59] [60] .

The radiation pattern on the left in Figure 19 is a typical elevation pattern, which represents the plot of the radiation pattern as a function of the angle measured off the Z-axis. Observing Figure 19, we see that the radiation pattern is minimum at 0 and 180 degrees and becomes maximum broadside to the antenna 90 degrees off the Z-axis. This corresponds to the plot on the left in Figure 19. The radiation pattern on the right in Figure 19 is the azimuthal plot. It is a function of the azimuthal angle for fixed polar angle 90 degrees off the z-axis in this case. Since the radiation pattern is symmetrical around the Z-axis, this plot appears as a constant. A pattern is isotropic if the radiation pattern is the same in all directions. Antennas with isotropic radiation patterns are thought not to exist, and it is probable that planet poles are no different in this regard.

Figure 18. Spherical radiation pattern.

Figure 19. Two-dimensional radiation pattern.

14. Reflection Coefficient

In electrical engineering, the reflection coefficient is a parameter that describes how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium. Since dark matter is an evolving science it is theoretical conjecture that reflected waves are present in the solar system. It does seem probable from what we know about transmission systems and wave theory. In the case of planets, the Sun is delivering electrical power to the Earth and other planets though a near vacuum transmission line. If the impedance of the stellar line does not match the impedance of the planets, a reflection will take place and some of the power is reflected to the Sun. When both a forward and a reflected wave travel simultaneously in opposite directions on a transmission line, the resulting wave, being the superposition of the two, is called a standing wave. A low amplitude standing wave on a transmission line is not unusual, but transmitters usually do not receive back part of the power they deliver, and so they reflect it back to the receiver or planet.

The reflection coefficient is equal to the ratio of the amplitude of the reflected wave to the fundamental wave; expressed as phasors. It is common in electrical engineering to calculate how much of the electromagnetic wave is reflected by an impedance. The reflection coefficient is closely related to the transmission line coefficient [61] . Typical reflection coefficient versus frequency is shown in Figure 20.

15. Extremely Low Frequency (ELF) Waves

Extremely low frequency (ELF) in atmospheric science is usually given, from 3 Hz to 3 kHz. In the related magnetosphere science oscillations 0~3 Hz are considered to lie in the tremendously low frequency range (TLF).

Naturally occurring ELF waves are present on Earth, resonating in the region between ionosphere and surface seen in lightning strikes that make electrons in

Figure 20. Reflection coefficient vs. frequency.

the atmosphere oscillate. The fundamental mode of the Earth-ionosphere cavity has a wavelength equal to the circumference of the Earth, which gives a resonance frequency of 7.8 Hz. This frequency, and higher resonance modes of 14, 20, 26 and 32 Hz appear as peaks in the ELF spectrum and are called Schumann resonance (Figure 21). Lightning strikes cause the cavity to resonate, causing peaks in the noise spectrum. The sharp peak at 50 Hz is caused by radiation from global electric power grids [62] [63] . The rise of the amplitude at low frequencies, shown on the left side, is the tremendously low frequency (TLF) waves caused by slow processes in the Earth’s magnetosphere and Flux Transfer Events.

Due to their extremely long wavelengths, ELF waves can diffract around large obstacles, and are not blocked by mountain ranges or the horizon and can travel around the curve of the Earth. ELF waves propagate long distances by an Earth-ionosphere waveguide mechanism. The Earth is surrounded by a layer of charged particles in the atmosphere at an altitude of about 60 km at the bottom of the ionosphere, called the D layer which reflects ELF waves. The space between the conductive Earth’s surface and the conductive D layer acts as a parallel-plate waveguide which confines ELF waves, allowing them to propagate long distances without escaping into space [64] .

ELF and TLF waves can travel considerable distances through high impedance media like Earth and seawater, which would absorb or reflect higher frequency radio waves. The attenuation of ELF waves is so low that they can travel completely around the Earth several times before decaying to negligible amplitude, and thus waves radiated from a source in opposite directions circumnavigating the Earth on a great circular path interfere with each other. At certain frequencies these oppositely directed waves are in phase and reinforce, causing standing waves. In other words, the closed spherical Earth-ionosphere cavity acts as a huge cavity resonator, enhancing ELF radiation at its resonant frequencies.

Figure 21. Schumann resonance spectrum.

16. Calculate the Period of Electromagnetic Waves

In free space, the propagation speed of cosmic electromagnetic waves is the same as that of light, at approximately 300,000 km (Figure 22), so they would arrive there in about 1.3 seconds. The speed falls slightly when passing through a conductor such as an antenna or cable. The wave length λ (lambda) of radio waves is as follows: If the frequency of the radio wave is f, and the speed of the radio wave in a vacuum is c, then:

λ [ m ] = C [ m ] f [ Hz ]

Using the distance between Earth and Moon as the wavelength (Figure 20),

FrequencyofMoon = 300000000 / 390000000 = 0.769 Hz

PeriodofMoon = 1 f = 1.3 s

Table 3 shows the flux transfer periods of planets calculated using the distance between the Sun and planets.

We point out that the electromagnetic period for the earth is the same as that reported by Satellite data [26] , yet half of what was calculated in my earlier Cosmic String Theory paper, which was 16.6 minutes [65] . This is not unexpected and is consistent with cosmic string whereby changes of state or being is frequency dependent. Further research should show that in the cosmic wave there

Figure 22. Earth and moon wavelength.

Table 3. Flux transfer periods of planets.

is also pressure, sound, heat and light all operating at different frequencies yet traveling from the Sun to the planets. The cosmic wave is thought to be a multi-faceted wave with harmonic frequency corresponding to each change of state. The fundamental is the electromagnetic frequency of 0.002 Hz. Underneath it all is the time wave counting off seconds, minutes, days and years.

17. Cosmic Resonant Circuit

In such an astronomical application as the Sun and the Earth, electrical engineers are interested in effects where the distance from the Sun to the Earth is less than the dimension of the transmitting antenna of the Sun (Figure 23). The equations describing the fields created about the antenna can be simplified by realizing a large separation between planets and dropping all terms that provide only minor contributions to the final field. These simplified distributions have been termed the near-field and usually have the property that the angular distribution of energy change with distance, is according to the inverse square law. The angular energy distribution is known as the antenna pattern. When viewed to scale we see that the Sun acts as an electrical dynamo and as a gigantic inductive coupler transmitting electrical power to the planets which act dually as receivers and motors at the same time. Once powered the planets also act as self-excited dynamos and produce their own electromagnetic field.

Figure 23. Cosmic antenna’s to scale.

the LIGO detectors are spaced a mere 3000 meters apart. Tesla’s patent filings and experimental work in Colorado Springs give credence to his claims of millions of available horsepower to transfer wirelessly. Tesla’s calculation is 1/1000 of my calculation suggesting that cosmic power can be tapped from the universe at higher resonant frequencies of the fundamental tremendously low frequency (TLF).

Absorption of electromagnetic power in the reactive near-field region by another planet has effects that feedback to the Sun, increasing the load on the Sun that feeds the planet by decreasing the impedance that the Sun sees. Thus, the Sun can sense when power is being absorbed in the magnetic near-field zone by another planet and is forced to supply extra power to its own antenna circuit, and to draw extra power from its own nuclear power supply. Conversely if no additional power is being absorbed by a planet the transmitter does not have to supply extra power. The solar system acts as a power grid with a closed loop power sensing circuit that mimics antenna theory.

It is thus theorized that the Sun and Earth use primarily resonant inductive coupling to transfer power wirelessly across space. Resonant inductive coupling is also called magnetic phase synchronous coupling. The Sun and planets are conceptualized as resonant spherical Tesla coils harmonized for efficient power transfer with minimal losses. Electrostatic coupling and far-field radiation also contribute to the power transfer equation, but it is thought, to a lesser degree.

Resonance, such as resonant inductive coupling of a Tesla coil, can increase the coupling between the transmitter and receiver greatly, allowing efficient transmission at somewhat greater distances, although the fields still decrease exponentially. Resonant transfer works by making a coil ring like a bell with an oscillating current. This creates an oscillating magnetic field. Because the coil is highly resonant, any energy placed in the coil dies away relatively slowly over very many cycles; but if a second coil is brought near it, the coil can pick up most of the energy before it is lost. The energy will transfer back and forth between the magnetic field in the inductor and the electric field across the capacitor at the resonant frequency. Each winding has a capacitance across it and functions as an LC circuit, storing oscillating electrical energy.

When the voltage across the capacitor reaches the breakdown voltage of the spark gap a spark starts ionizing the air and lowering the spark gap resistance. This completes the primary circuit and current from the capacitor flows to the primary coil. The current flows rapidly back and forth between the plates of the capacitor through the coil, generating radio frequency oscillating current in the primary circuit at the circuit’s resonant frequency. It is theorized that lightning is a form of spark gap oscillating at Schumann Resonance to charge the capacitor around the Earth and discharge into the Earth’s spherical inductive coil.

This oscillation will die away at a rate determined by the gain-bandwidth, mainly due to resistive and radiative losses. Because the gain can be very high, even when low power is fed into the transmitter coil, a relatively intense field builds up over multiple cycles, which increases the power that can be received. At resonance, far more power is in the oscillating field than is being fed into the coil, and the receiver coil receives a percentage of that. However, provided the secondary coil cuts enough of the field, such that it absorbs more energy than is lost in each cycle of the primary, then most of the energy can still be transferred. The loose coupling slows the exchange of energy between the primary and secondary coils, which allows the oscillating energy to stay in the secondary circuit longer before it returns to the primary and begins dissipating in the spark. The secondary receiver coils are similar designs to the primary sending coils. Running the secondary at the same resonant frequency as the primary ensures that the secondary has a low impedance at the transmitter’s frequency and that the energy is optimally absorbed [67] . The range of resonant capacitive or inductive coupling using solenoid design for practical transfer of power is 10 times the antenna diameter. If we multiply the Sun’s diameter by 10, we obtain high efficient power transfer at a distance of 14 × 109 m. The Earth would also have a similar multiplying effect based on its diameter.

Since the two planets are separate the resonant frequencies of the two circuits, f1 and f2 would be determined by the inductance and capacitance in each circuit [68] :

f 1 = 1 1 L 1 C 1

f 2 = 1 1 L 2 C 2

L 2 = 1 4 π 2 C 2 ( f 2 ) 2

L 2 = 1 4 π 2 ( 7.83 ) 2 ( 710 × 10 6 )

L 2 = 0.582 Henry

However, because the Sun and planets are coupled together, the frequency at which the planet resonates is affected by the Sun’s electrical circuit and the coupling coefficient k and occurs at its anti-resonant frequency while the original resonant frequency acts as a resonant frequency. The frequency at which the planet’s spherical coil has to be driven is the resonant frequency.

f 2 = 1 1 ( 1 k 2 ) L 2 C 2 [68]

Our Sun to Earth calculations indicate that f 2 = 0.002 Hz . Therefore, we can solve k, the coupling coefficient:

k = 1 4 π 2 L 2 C 2 f 2 2 1

k = 1 4 π 2 ( 0.582 ) ( 710 × 10 6 ) ( 0.002 ) 2 1

k = 1 1.0001487447 1

k = 0.000255

The condition for planetary resonance can also be expressed as [68] ,

L 1 C 1 = ( 1 k 2 ) L 2 C 2

Calculating the Sun’s value of L1C1:

L 1 C 1 = ( 1 0.000255 2 ) ( 0.586 ) ( 710 × 10 6 )

L 1 C 1 = 0.000413

The capacitance of the Sun is approximately 73,000 microfarads [67] . The inductance of the Sun is approximately:

L 1 = 0.000413 73 , 000 × 10 6

L 1 = 0.00565 H

Inserting this value back into the frequency equation we calculate the equivalent Schumann Resonant, or resonant frequency of the Sun (f1) [68] :

f 1 = 1 1 L 1 C 1

f 2 = 1 1 L 2 C 2

f 1 = 1 1 0.000413

f 1 = 7.83 Hz

The Sun has an identical resonant frequency, or Schumann Frequency, as the Earth. The Tesla transformer is very loosely coupled, and the coupling is extremely small. Hence, the factor 1 k 2 is close to unity, while the two resonant frequencies differ by 2%, at most. Therefore, the transformer is resonant when the resonant frequencies of primary and secondary are equal. This implies that the Sun and all eight planets operate at the same Schumann Resonance of 7.83 Hz. Calculating the characteristics of all the planets is simply a matter of repeating the same calculations for each planet.

In a resonant planet coil, the high voltage is produced by resonance. The output voltage can be calculated approximately from conservation of energy. At the beginning of the cycle all the energy in the primary circuit, W1, is stored in the Sun’s capacitor. If C1 is the capacitance and V1 is the voltage at which the voltage gap breaks down, which is thought to be the peak output voltage of the Sun, this energy is [68] :

W 1 = 1 2 C 1 V 1 2

The total energy of a flux transfer events from the Sun to Earth is expected to be 3 × 1018 J, which equates to 3 × 1018 W. The voltage of the Sun is calculated [68] [69] [70] :

V 1 = 2 × W 1 C 1

V 1 = 2 × 3 × 10 18 73000 × 10 6

V 1 = 9 × 10 9 V

During the “ring up” this energy is transferred to the planet. At the peak V2 of the secondary sinusoidal voltage waveform, all the energy in the secondary W2 is stored in the spherical capacitance C2 between the poles of the planet [68] :

W 2 = 1 2 C 2 V 2 2

Solving the equation for voltage of the Earth we obtain,

V 2 = 2 × W 2 C 2

V 2 = 2 × 3 × 10 18 710 × 10 6

V 2 = 92 × 10 9 V

Assuming resonance and no energy losses, the peak voltage of the Sun and the planets can be calculated using the following equation [68] :

V 2 = V 1 C 1 C 2 = V 1 L 2 L 1

Confirming our results, we obtain,

V 2 = V 1 × 10

The value of N compares favorably with my calculation of N = 9.8 in previous work [44] . Indications are that the transformer turns ratio, N, for the wireless power system from the Sun to the Earth is equal to 9.8 or 10. Previously the Earth’s current had been calculated to be 1,730,000,000 A. The Sun therefore has a current of 17,300,000,000 A, or approximately 17 Billion A. Given the eight planetary loads the Sun is powering, a turn ratio of 9.8 to 10 appears realistic, as does the high reactive current.

I am concerned about the accuracy of the calculated voltages due to the small capacitance values used for the Sun and the Earth. As an alternative we can use the equation for energy for an inductor. We can solve for L using our solar energy source of 3.13 × 1018,

W 2 = 1 2 × L I 2

L 2 = 2 W 2 I 2

L 2 = 2 × 3.13 × 10 18 ( 1.73 × 10 9 ) 2

L 2 = 2.0 H

Solving for C2 we obtain,

C 2 = 1 4 π 2 L 2 ( f 2 ) 2

C 2 = 0.000206 F

Inserting the values of capacitance and inductance, and assuming R = 100 Ω for the Earth, we calculate the operating flux transfer frequency of 0.002 Hz and Schumann Resonant frequency. This confirms our model of the Earth.

Defining the parallel resonant frequency as the frequency at which the voltage and current are in phase, unity power factor, gives the following expression for the resonant frequency:

ω o = 1 L C [ R L 2 C L R C 2 C L ] 1 2

The above resonant frequency expression is obtained by taking the impedance expression for the parallel RLC circuit (Figure 24) and setting the expression for Xeq equal to zero to force the phase to zero.

C = 206 μ F

L = 2 H

f = 0.002 Hz ( solarsystemfrequency )

R C = 100 Ω

R L = 100 Ω

Z = 100 Ω

PhaseAngle = 0.05 degree

The Resonant Condition of the Earth is calculated to be 7.84 Hz.

Solving for V1 and V2 a second time we obtain,

V 2 = 2 W 2 C 2

Figure 24. Parallel RLC circuit of Earth.

V 2 = 170.6 × 10 9 V

V 1 = 17 × 10 9 V

Solving for C1 and L1 we now have,

L 1 C 1 = L 2 C 2

L 1 C 1 = 0.000412

Solving for C1 using voltages,

C 1 = ( V 2 V 1 ) 2 C 2

C 1 = 0.02 F

L 1 = L 2 ( V 2 V 1 ) 2

L 1 = 0.02 H

Inserting the capacitance and inductance into our RLC model, and assuming R = 100 Ω for the Sun, we again calculate the operating flux transfer frequency at 0.002 Hz and the Sun at Schuman Resonance. This confirms our model of the Sun (Figure 25).

C = 0.02 F

L = 0.02 H

f = 0.002 Hz ( SolarSystemFrequency )

R C = 100 Ω

R L = 100 Ω

Z = 100 Ω

Figure 25. Parallel RLC circuit of Sun.

The resonant condition of the Sun is calculated to be

f = 7.95 Hz

These Inductance and Capacitance values for the Sun are asymmetrical at 0.02 F and 0.02 H. The current and voltage for the Sun are also symmetrical at 17 Billion A and 17 Billion V, respectively. The power of the Sun is 2.89 × 1020. The Earth’s values differ due to the turns ratio of 10 but are tuned to match the same frequency as the Sun and the resonant frequency as well. The power of the Earth is 2.89 × 1017 W. Using another version for power, P = I2R, the ideal resistance of the Earth is approximately 1.0 Ω. It is concluded that these are the most accurate values for the Sun and Earth to date. My previous paper stands corrected based on what is presented in this manuscript [44] . We now have an electrical model for the Sun and Earth based on resonant tuning. Using the same approach, we can calculate all the values for the other 7 planets and model the entire solar system as electrical one-line diagram fairly easily.

Modeling the Earth as an RLC Series Impedance to determine the spark value of the Earth, we insert our calculated voltage of 170 Billion V/10 turns = 17 Billion V, and a surface resistance of R = 6.7 MΩ. The average lightning strike is then calculated to be 25,000 A. A value with the range of 10,000 to 50,000 A often cited. Figure 26 shows an RLC series circuit.

X c = 1 ω C

X L = 1 ω L

Z = R 2 + ( X L X C ) 2

Phase = ϕ = tan 1 [ X L X C R ]

At series resonance:

Figure 26. RLC series impedance.

Z = R

X C = X L

ω = 1 L C

Phase = ϕ = 0


C = 206 × 10 6 F

L = 2 H

At angular frequency

ω = 49 rad / s

Frequency = 7.82 Hz

Resistance ( R ) = 6.7 M Ω

Z = 6.7 M Ω

at Phase ϕ = 0.0016 degrees

The resonant condition is

Angularfrequency ω = 0.493 × 10 2 rad / s

Frequency ( f ) = 7.84 Hz

Z = R = 6.7 M Ω

Phase ϕ = 0.0

For an applied RMS voltage

V = 170 × 10 9 V

the RMS current will be

I = 25000 A [63]

The component voltages can be obtained by multiplying the current times the component impedances (Figure 27).

Capacitor : V c = I X c = 123170 V

Inductance : V L = I X L = 50746266 V

Resistor : V R = I R = 169 × 10 9 V

Since we use 3 × 1018 as our source of energy in our electrical equations, the Equation for Everything is now extended for Power, Energy in an Inductor and Energy in a Capacitor.

E = m c 2 = v c 2 60 = a 3 T 2 = G ( M 1 + M 2 ) 4 π 2 = K E + P E 1.0 × 10 15 = Q = P A F = λ h c = 1 2 q = V I = 1 2 L I 2 = 1 2 C V 2 = I 2 R =

18. Lightning and Current Path of Earth

By modelling the planets as Tesla coils, we have gained a new understanding of how lightning around the Earth acts as a spark gap. Energy is stored in the Earth’s atmosphere, which is a capacitor until the voltage level is crested at which time a spark, or lightning occurs from Earth to the sky. The bolts range anywhere from 10,000 A to 200,000 A. These strikes hit the Earth at a rate of 100 per second. This gives us a total current range of 1,000,000 to 200,000,000 A per second. Research by NASA shows that they emanate in one hemisphere, and then land in the other hemisphere thus creating a path through the Earth and then up into the high altitude to complete the path back around to the Earth [68] . We also know that lightning concentrates around the equator and travels around the globe. With this new discovery of the spark gap and our analogy to lightning we revisit the Toroid and update our model to get a visual of how current is discharged from the capacitive atmosphere to the Earth’s inductor.

In our Earth toroid model, we are using 10 turns, which based on NI gives us an I of 173,000,000 A. The relative permeability near the surface of the Earth is 1.

Finding the magnetic field inside a toroid is a good example of the power of Ampere’s law. In Figure 28, the current enclosed by the blue line is just the number of loops times the current in each loop. Ampere’s law then gives the magnetic field by

B 2 π r = μ N I

Figure 27. Phasor diagram.

Figure 28. Magnetic field of a toroid.

B = μ N I 2 π r

The toroid is a useful device used in everything from tape heads to tokamaks.

Magneticfield = permeability × turndensity × current

For a solenoid of radius

r = 6.38 × 10 6 m


N = 10 turns

The turn density is

n = N 2 π r = 2.5 turns / m

If the current in the solenoid is

I = 1.73 × 10 8 A

And the relative permeability of the core is

k = 1

Then the magnetic field at the center of the solenoid is

B = 0.542 G

The Earth’s magnetic field is about half a gauss.

The inductance can be calculated in a manner similar to that for any coil of wire. The application of Faraday’s law to calculate the voltage induced in the toroid is of the form:

E m f = N Δ Φ Δ t = N A Δ B Δ t

This can be used with the magnetic field express above to obtain an expression for the inductance.

L μ N 2 A 2 π r

where A = cross-sectional area;

r = toroid radius to center line.

Toroidal radius

r = 6.38 × 10 6 cm with N = 10 turns

Coilradius = 4.51 × 10 6 cmgivesarea A = 6.38 × 10 9 cm

Relative permeability of the core

k = 1

Then the inductance of the toroid is approximately

L = 2 H

The radius of the toroid coil radius is calculated using an inductance of L = 2 H. The coil radius is approximately 45,000 meters, of which we surmise roughly half travels through the Earth and the other half travel through the air, which has known relative permeability of 1. Heights of 15 to 20 km for lightning strikes are not unusual, so the model seems reasonable. The cross-sectional area of the toroid is approximately 6378 × 109 m2―another coincidental, yet curious number in view of the radius of the Earth being so similar.

We can also calculate the frequency of the toroid using the circumference of the Earth as the wavelength, 40,075,000 meters.

f = 3 E 8 / 40075000 = 7.48 Hz

If we assume a speed of light slightly faster than c = 3 × 109; yet proportional by 1 × 1010 with our constant of the solar system, we obtain the desired frequency.

f = 3.14 × 10 8 40075000 = 7.83 Hz

Our work raises the question regarding the current reference standard for the speed of light. We also note that 7.83 Hz is equivalent to a period of 0.1277 seconds, a coincidental number matching 0.1277 Ωm∙h2, a cosmological parameter pertaining to dark matter and dark energy, inflation and the structure of the universe [71] . It is postulated that all stars and planets operate at a frequency of 7.83 Hz determined by a universal constant of 0.1277 Ωm∙h2. It is thought the universal frequency of the cosmos is 7.83 Hz. Just as the power grid operates at 50 Hz in Europe or 60 Hz in the US, it is thought the galactic grid operates at 7.83 Hz. It should be stressed however that dark matter and dark energy problems are not the thrust of this paper and they can be, in principle, solved thru extended theories of gravity [72] .

19. Updated Model of the Earth

The new discovery of the spark gap or lightning circuit has given us fresh information to provide a more accurate view of the Earth’s electrical current paths (Figure 29). Like any electrical motor the Earth has two windings, a stator and an armature circuit. Our current thinking is that the stator winding is a ten-turn toroid Tesla coil, and the spherical coil is the Earth’s armature circuit. To make a transformer analogy the toroid is the primary of the transformer, and the armature spherical coil is the secondary of the transformer. The ratio of the Sun to toroid is 10, the ratio of the toroid to the armature is 1. It is thought that telomeric currents which flow on the outside of the Earth are represented by the spherical coil. J.J. Thompson’s original calculations for an earthly spherical coil will be consulted in the future with this new understanding of our planet. Below is our updated drawing showing how the Earth is wired with a primary resonant LC toroid coil acting as a motor stator. Planets are the most complex and peculiar of electrical machines imaginable.

However, it is important to note that the Sun is 150 billion meters away. It is so far away that the Sun does not “see” a tesla toroid coil or a spherical coil. The wiring diagram or motoring effect of planets is immaterial to the transmitter. To

Figure 29. Updated model of the Earth.

the Sun it is just an inductive load that can be lumped into one current sink. What the Sun or transmitter “sees”, or how it is modelled based on antenna theory, is a simple dipole antenna that receives energy. Therefore, our earlier calculation of frequency, or Schumann Resonance, of the Earth is deemed to be correct.

20. Conclusions

In the context of cosmic wireless power, energy harvesting or power harvesting, it is the conversion of energy from the electromagnetic field to electric power. The ambient electromagnetic energy may come from the Earth or the Sun’s electromagnetic field. Although the power gathering techniques are theoretical, and efficiency of conversion is yet to be determined, it is believed that one day cosmic wireless power transfer will be sufficient to power man’s needs, and the source of energy as limitless as the Sun itself. New technology such as piezoelectric and resonant Tesla coils tuned to comic frequencies, should be developed to eliminate the need for batteries in cars, allowing them to operate completely autonomously. Tapping the inexhaustible supply of cosmic power would put an end to world dependence on fossil fuels and nuclear energy. Greenhouse gases and nuclear waste will make these power plants obsolete. Solar and wind will have its place in the future, but it will be inefficient and costly when compared to a resonant electrical coil tuned to the cosmic power frequency. Other than the initial cost of the electrical coil, the energy will be free and simple to operate.

During research, the solar system’s atomic time clock has been discovered. Three equations of wave impedance have been related to seconds, minutes, days and years. Due to the nature of the equations it is concluded that time is also a wave and thus expected to have standing and reflect waves. Reflected waves may be the mechanism for understanding the concept of time moving forward or backwards. It may also be the doorway to time travel and teleportation. This discovery is a radical breakthrough in physics. Further investigation into the theory of timewaves and how best to model an analogous cosmic time machine using control theory is recommended. Time and time travel is one of the great contemplations of science and the wave impedance equations identified might be used to solve one of the great paradoxes in physics.

A new law of the Sun has been discovered 400 years after Kepler’s laws of motion were introduced. The new equation has been equated to the inverse of Kepler’s third law with the accuracy of a time piece. The solar system for the first time has been described as an acoustic system with the ratio of vibratory acceleration divided by volume acceleration then equated to pressure divided by force. The acoustic analogy fits well with my previous paper on Cosmic String Theory: Tension and Gravity, whereby the Sun and Earth were modeled as a violin in space [50] . A second law of cosmic efficiency is proposed that incorporates acceleration and volume expansion of the solar system. Two new measures of energy efficiency can now be considered for our solar system.

In addition, a velocity-energy equivalence equation has been developed and equated to mass-energy equivalence. E = vc2/60 is believed to be the missing law of electromagnetism that ties the nuclear world with the Newtonian/Kepler world. It sets the time clock of the solar system, synchronizes the Sun with the planets, and transmits the power of the nuclear fusion Sun to the solar system. The law applies to macro physics as we have seen but like Einstein’s mass-energy equivalence applies to quantum physics as well. By viewing the solar system as a wireless electrical power system and solving the problem of how the Sun is synchronized to the planets the author has uncovered a treasure trove of equations and new concepts about the solar system and the universe. Fusion, free electromagnetic energy, anti-gravity and time travel all seem theoretically and realistically achievable with this new insight. If a scientist could paint the heaven by the numbers, then the equation of everything will start with colorful symbols and letters that look something like this:

E = m c 2 = v c 2 60 = a 3 T 2 = G ( M 1 + M 2 ) 4 π 2 = K E + P E 1.0 × 10 15 = Q = P A F = λ h c = 1 2 q = V I = 1 2 L I 2 = 1 2 C V 2 = I 2 R =

The Earth’s energy constant is 3.13 × 1018 J. This is the energy that can be received by the capacitance and inductance of the Earth, which is a physical limitation based on the size of the Earth. The limitation is the rate at which the Sun rotates and transmits energy, and the capacity of the Earth to absorb energy. The rate of transmission is based on the velocity of the Sun. The size of the Earth’s capacitor is the capacity. The Sun and Earth work in conjunction to deliver and receive a constant amount of energy during fixed periodic flux transfer events. This energy constant becomes the fundamental constant by which all other constants and equations are set. The limitation to energy is how much can be transmitted and received via the planetary antennas. And, how much is being used up by the Earth. Once the Earth receives the energy it is divided up and used to perform a litany of tasks all of which can be modeled by laws and equations. The equation of everything states that everything is energy and energy is everything. If eternal life is rooted in the conservation of energy, might the story of the resurrection be a demonstration in the physics of transformation?

Ancient philosophers as far back as Thales of Miletus c. 550 BCE had inklings of the conservation of some underlying substance of which everything is made. Conservation of energy states that the total energy of an isolated system remains constant, it is said to be conserved over time. This law means that energy can neither be created nor destroyed; rather, it can only be transformed from one form to another. Special relativity showed that mass could be converted to energy and vice versa by E = mc2, and science now takes the view that mass-energy is conserved. Scientifically speaking, conservation of energy can be rigorously proven by the Noether theorem because of continuous time translation symmetry; that is, from the fact that the laws of physics do not change over time. Since our equation has a time translation symmetry it is possible to define conservation of energy for the solar system. A perpetual motion machine of the first kind cannot exist; no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. The Sun and stars have an abundant yet finite amount of nuclear energy.

The equation starts with nuclear energy of the Sun, which equates to wireless electrical power which equates to orbital energy of the planets, which equates to cosmic string theory, and so on. Additional equations will be added on the right-hand side as we define cosmic string theory for vibratory pressure, acceleration and force. The equation begins with the macroscopic on the left side and, overtime, will end with the microscopic on the rights side. This equation tells us that energy, not only can be exchanged with mass, it can take many different forms and shape itself to whatever needs the universe requires. Energy is the inverse of the electron and the proton, a most provocative of discoveries. The theory of everything will be realized through a progression of Euclidean equations that will be solved by equating to 3 × 1018 J. New units and constants will be required. The theory of everything now has form and function. The theory of everything is no longer a theory; it is an equation for everything. We have only scratched the surface with the first handful of laws.

It is believed that over time all equations and all constants will find their way into the equation of everything. The equation will be the longest equation in existence when completed. The equation of everything will describe the relationship between all things and make sense of the entire cosmos. All the electromagnetic constants will be redefined in terms of the equation, as well as atomic and nuclear constants. The equation will even extend to chemical constants eventually.

The Sun and the Earth have been modeled with resonant Tesla coils with interesting results. Using Schumann Resonance, the period of flux transfer events of the Earth and energy consumption of the Earth, we have been able to calculate exact values of inductance, capacitance, frequency, voltage and currents for the Earth and the Sun. Our understanding of how the solar system works electrically has been significantly enhanced by modeling the system as a wireless power transfer system tuned for resonance. It is now possible to model the Sun and all eight planets using the techniques presented. The modeling of the planets as resonating coils and values of inductance, capacitance and voltages in this manuscript are valid and considered a correction over my first paper [44] . Our understanding and ability to calculate lightning strikes is greatly enhanced through electrical modeling.

In its simplest form, the Earth can be viewed as a rotating current transformer (Figure 30) connected to a resonant capacitor with a dipole antenna acting as a conductor. Using the frequency of the Earth and a slower 1/3 speed of light due to media, we can calculate the wavelength of the Earth dipole antenna λ = (1 × 108)/7.83 Hz = 12.77 × 106, or approximately the diameter of the Earth. By

Figure 30. The current transformer―current transformers produce an output in proportion to the current flowing through the primary winding as a result of a constant potential on the primary conductor.

building replica Earth like devices to small scale and using known techniques for energy harvesting of resonant current transformers [65] , the potential for unlimited renewable energy from electromagnetism is a distinct possibility. We may be able to realize Thomas Edison’s vision of harnessing the electromotive power of the Earth using Tesla like know how.

The biggest electrical machines in the solar system are being conquered one calculation at a time. We have modeled the Earth’s stator winding as a toroid Tesla coil, or a loosely wound current transformer, and the armature as a spherical coil. One day we will map the universe and electrically model the entire galactic grid. Stars will be seen as sources of electrical energy to be harnessed and controlled by man using equations and constants. Man will learn to reshape the universe by transforming energy to suit his needs.


Author wishes to acknowledge ASK Scientific ( for formatting assistance and help with illustrations. Heartfelt thanks to JHEPGC and their editorial staff for giving me the opportunity to publish my papers. Much of the background radio theory content in this paper is relied upon, and cited, from a public domain document published by Occupational Safety and Health Administration, Cincinnati Technical Center, “Electromagnetic Radiation and How It Affects Your Instruments. Near-field vs. Far-field”, Department of Labor-Public Domain content, U.S. Dept of Labor, May 20, 1990.

Conflicts of Interest

The authors declare no conflicts of interest.


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