Ratio of electrostatic to gravitational forces:
Fc = ce2/(4*pi*e0*r2), This is the electrostatic force between two charges with a charge ce at a separation of r meters. ce is the charge of the electron or proton. e0 is the permittivity of vacuum.
Fg = G*me*mp/r2, This is the gravitational force between an electron and a proton at a separation of r meters. G is the gravitational constant. me and mp are the mass of the electron and proton.
Fc/Fg = ce2/(4*pi*e0*G*me*mp) = 2.269E39, This is the huge ratio of electrostatic to gravitational forces. Small charges produce big forces.
Balancing electrostatic and gravitational forces:
ce2/(4*pi*e0*r2) = G*kg2/r2, the electrostatic force between two opposite charges equals the gravitational force between two masses.
(a*s)2/(4*pi*e0) = G*kg2, The forces are equal at any distance. They are both inverse square forces. The r2 cancel. Replace ce with the more general (a*s), amps*seconds for the charge, for any charge and mass.
(4*pi*e0*G).5 = a*s/kg = 8.617E-11_a*s/kg, this is the gravitational charge per kilogram, coulombs/kg .
a*s = kg*(4*pi*e0*G).5, the gravitational charge equals the mass *(4*pi*e0*G).5
Gravitational charges:
msun = 1.9884E30_kg, mass of the sun.
mearth = 5.9722E24_kg, mass of the earth.
a*s = kg*(4*pi*e0*G).5, the gravitational charge equals the mass *(4*pi*e0*G).5
gcsun = msun*(4*pi*e0*G).5 = 1.713E20_a*s, the gravitational charge of the sun.
gcearth = mearth*(4*pi*e0*G).5 = 5.146E14_a*s, the gravitational charge of the earth.
Sun and earth gravitation:
msun*mearth*G/au2 = gcsun*gcearth/(4*pi*e0*au2), the gravitational force using mass and the the electrostatic force using gravitational charge are equal. An au astronomical unit is the distance from the earth to the sun.
msun*mearth*G/au2, the gravitational force between the sun and earth.
msun*mearth*(4*pi*e0*G) /(4*pi*e0*au2), multiplied by 4*pi*e0/(4*pi*e0)
msun*(4*pi*e0*G).5 *mearth*(4*pi*e0*G).5 /(4*pi*e0*au2), factored (4*pi*e0*G) into two square roots.
gcsun*gcearth/(4*pi*e0*au2), electrostatic force using gravitational charge.
1.713E20_a*s *5.146E14_a*s/(4*pi*e0*(149.598E9_m)2) = 3.5401E22_kg*m/s2
1.98843E30_kg *5.9722E24_kg *G/(149.598E9_m)2 = 3.5414E22
_kg*m/s2,
The Coulomb forces calculated using gravitational charge and Newtonian gravity calculated with masses are the same. Gravitational charge and mass are equivalent. The force is the same only the units used to calculate the force change.
Sun and earth centrifugal force:
mearth*vearth2/dbcearth =
msun*vsun2/dbcsun = 3.55E22_kg*m/s2, there are two equal centrifugal forces unchanged by using gravitational charge instead of mass. dbc is the distance to the barycenter, the center of mass of the earth-sun system
mearth*vearth2/dbcearth =
mearth *(4*pi*e0*G).5 *vearth2/(dbcearth*(4*pi*e0*G).5), multiplied by (4*pi*e0*G).5/(4*pi*e0*G).5
gcearth *vearth2/(dbcearth*(4*pi*e0*G).5), gcearth = mearth*(4*pi*e0*G).5
msun *vsun2/dbcsun =
msun *(4*pi*e0*G).5 *vsun2/(dbcsun*(4*pi*e0*G).5), multiplied by (4*pi*e0*G).5/(4*pi*e0*G).5
gcsun *vsun2/(dbcsun*(4*pi*e0*G).5), gcsun = msun*(4*pi*e0*G).5
Gravitational acceleration:
mearth*G/rearth2 = gcearth/(rearth2)*(G/(4*pi*e0)).5, the gravitational acceleration using mass and electrostatic acceleration using gravitational charge are equal.
mearth*G/rearth2 = 9.79822007_m/s2, gravitational acceleration at the surface of the earth, using mass.
mearth*(4*pi*e0*G) /(4*pi*e0*rearth2), multiplied by 4*pi*e0/(4*pi*e0)
mearth*(4*pi*e0*G).5*(4*pi*e0*G).5 /(4*pi*e0*rearth2), factored (4*pi*e0*G) into two square roots.
gcearth*(4*pi*e0*G).5/(4*pi*e0*rearth2) = 9.79822007_m/s2, substituted gcearth for mearth*(4*pi*e0*G).5.
gcearth/(rearth2)*(G/(4*pi*e0)).5, collected terms.
gcearth/(rearth2)*.77448_m3/(a*s3) = 9.7979_m/s2, since (G/(4*pi*e0)).5 = .77448_m3/(a*s3),
The electrostatic acceleration of the earth at the surface of the earth, using gravitational charge is the same as the gravitational acceleration using mass. Calculations using charge or mass produce the same gravitational accelerations.
The number of electron charges required to keep the earth in orbit:
gcearth/charge per electron = charges
5.146E14_a*s/(1.602E-19_a*s/charge) = 3.212E33_charges, number of electron charges required for the earth.
charges * mass/charge = mass of electrons
3.212E33_charges * 9.109E-31_kg/charge = 2926_kg of electrons
The surprisingly small charge of 2926_kg of electrons when balanced by the same amount of opposite proton charge in the sun will provide the tensile force to keep the earth in orbit without any ongoing power requirements. Small charges produce big forces. Compare this charge disparity of 2926_kg of electrons that is required for electrostatic gravity with the solar output.
Alternate source of charge imbalance:
The solar output or solar wind could provide the slight charge imbalance necessary for gravity, but we will look at it from another perspective. All the electrons in the sun and earth repell each other. All the protons in the sun and earth repell each other. All the electrons in the sun and earth attract all the protons in the sun and earth. All the atoms in the sun and earth are polarized in this way which simulates a charge imbalance attractive force which we call gravity. There is also charge imbalance in bonding of atoms in chemistry or in dielectric and deformable dielectric materials. We will look for the charge imbalance in the atoms themselves. This is a search for the polarized atom. We seek the geometry of Bohr's planetary atom that allows it to store charge and act like a capacitor when pulled and pushed by the charges in other masses or when accelerated.
Click figure to animate!
Electron and proton binary atom with circular orbits:
The dipole of the electron and proton in their orbits make rings of charge. These orbiting charges constitute electron and proton toroidal currents which loop around as rings and helical poloidal magnetic fields which orbit around the toroidal currents. The magnetic fields point out of the page along the axis of rotation. The red electron ring should be at a radius 1836 times bigger than the blue proton ring when drawn to scale. The orbiting charges constitute electron and proton torroidal currents which orbit the long way around the torus or ring. Looping the short way around a torus, through the hole like the wires on torroidal transformers, we have poloidal magnetic fields. Tokamks and spheromaks and ring electrons have torroidal currents and poloidal magnetic fields with resultant helical magnetic fields as does this atom. The density of the electron and proton charge in this atom, along their orbital path around the center of mass, is uniform. There is a uniform charge density. The charge per radian of the electron and proton on their binary orbital path are constant and equal since they have the same angular velocity. The velocity of the electron is 1836 times the velocity of the proton since the mass of the proton is 1836 times that of the electron and the momentum of the electron and proton are equal. The distance between the charges is constant. This is a charge neutral binary atom confined to orbit in a plane. It is not a sphere.
Click figure to animate! Electron and proton binary atom with elliptical orbits:
The dipole of the electron and proton in their orbits make elliptical rings of charge. The red electron ring should be 1836 time bigger than the blue proton ring when drawn to scale. The barycenter, the center of mass, is at one focus of the ellipse. The density of the electron and proton charge, along their orbital path around the center of mass, is not uniform. The charge per radian is not uniform. Since these are elliptical orbits they slow down as they get farther out from the center of mass. Since they spend more time farther out at a slower speed the charge density is greater farther out. There is a non-uniform charge density. The leftside is electronegative. The rightside is electropositive. This ellipse is very polarized. The charges are separated. Its poles would attract the opposite poles of similarly polarized ellipses, like the ones below. The long axis of the ellipse is the dipole moment of the ellipse.
Precession outputWhy are atoms spheres? Dipoles, rotation, torque and precession:
Gyroscopes precess when subject to torques. The elliptical electron and proton orbital rings in atoms must precess like gyroscopes into spheres for us to see them as atoms.
How is that? It might seem that these rings need some tensile strength or viscosity to be spun into spheres. Rings can be gyroscopes. Rotating dipoles can also be gyroscopes. A twirling baton is airborn and rotating.
Precession in atoms is common. It is seen in microwave ovens and medical scanners. When you apply a tilting torque to a gyroscope it precesses in a direction perpendicular to both the axis of the tilting torque and perpendicular to the axis of rotation.
Dipoles in the presense of charge experience a tilting torque around the short axis of the ellipsoid or dipole which tries to align the north and south poles of the dipole with the charge like a compass aligns with a magnet. This tilting torque which is perpendicular to the long dipole axis of the ellipse and perpendicular to the axis of rotation produces a rolling precession around the long north-south axis of the ellipse. The ellipse rolls around its longest axis. A polarized elliptical ring precesses into a rolling polarized ellipsoid in the presense of a charge. We see them as polarized atoms. The atom, which is a bipolar ellipsoid, prolate spheroid and dipole, aligns with charges. The opposite charges on each end of the atoms attract so the atoms stack in rows.
The atoms precess like beads rolling on a string. The poloidal magnetic field is parallel to the axis of rotation of the electron and proton. The magnetic field rotates with the precession and is blurred by the precession, to a blinking north-south-north-south. This requires more thought. This is similar to the description of helical electromagnetic waves. They both can be described by Euler's equations.
Source of the dipoles: This is a quote from a chapter on dipoles by Tatum; "But what if the molecules do not have a permanent dipole moment, or what if they do,
but they cannot easily rotate (as may well be the case in a solid material)? The bulk
material can still become polarized, because a dipole moment is induced in the individual
molecules, the electrons inside the molecule tending to be pushed towards one end of the
molecule.
Thus, one way or another, the imposition of an electric field may induce a dipole moment
in most material, whether they are conductors of electricity or not, or whether or not their
molecules have permanent dipole moments.
If two molecules approach each other in a gas, the electrons in one molecule repel the
electrons in the other, so that each molecule induces a dipole moment in the other. The
two molecules then attract each other, because each dipolar molecule finds itself in the
inhomogeneous electric field of the other. This is the origin of the van der Waal's forces."
Quantum silliness has attributed the van der Waal's forces and the Casimir forces to the Heisenberg uncertainty principle. The more certain we are of where something is, the less certain we are about where it is heading. Quantum field theory holds that empty space, the vacuum, is fizzing with short-lived particle-anti-particle pairs according to the uncertainty principle. The shorter the time the pair exists, the greater energy the pair may impart to the vaccuum. Very short lived pairs have near infinite energy. This means that one calculates the energy density of the vacuum as near infinite, which some do, which is silly, of course.
The polarization and separation of charge considered as the origin of van der Waal's forces is also here considered as the origin of gravitational, centrifugal and inertial forces.
Circles to ellipses:
A positive charge, to the right of an atom, is like an increase in the orbital centrifugal force, to the right, for the electron. The atom responds by taking on an elliptical shape by increasing its radius to the right. Isn't this like the tidal bulge of the earth being caused by the moon?
Iron filings and bar magnets: When you look at the pattern of iron filings on a glass or plastic over a bar magnet, you see lines of magnetized iron filings stuck together by magnetism. The iron filings have become lines of tiny series magnets, lines of tiny series dipoles, curving around to the opposite poles of the bar magnet. The lines of tiny series magnets repell each other which accounts for their spacing. The lines repell each other because their poles point in the same direction and like poles repell. The lines may stick together when they are close to each other and and their centers are offset.
Shielding: Magnetic forces are not shielded or reduced by a copper plate between magnets. I didn't speculate about photons. I tried two magnets and a penny. Magnets are related to electricity. Electromagnetic waves could not go through a penny but forces do. Are the forces between two charges shielded by a conductive foil?
I haven't heard of any experimental evidence of gravitational shielding being evaluated from the July 22, 2009 solar eclipse in Asia. The sun and earth interaction are blocked by the moon, during the eclipse, over a tiny area of the earth.
A copper or aluminium foil might be used to demonstrate shielding of electrostatic repulsion or attraction forces, if any shielding exists, if you can figure a way to avoid interaction of the charges with the plate. I tried a simple experiment. An electroscope works by the deflection of charges by electrostatic repulsion. Two styrofoam balls are supended by threads making a crude electroscope. They are charged with a "Fun-fly-stick" battery powered portable toy van de Graff generator. Having the same charge, the styrofoam balls repell. Then I tried to insert an aluminum foil between the balls. The aluminum foil attracts the balls because it has less charge. The balls touch and loose their charge. With sufficient charge, I speculate, the foil would become a neutral surface in an electrical gradient. It would be charged to the local gradient. The forces would be unaffected. There are simple experiments here somewhere but I have yet to find an experimental answer. The force between charged plates can be measured with Kelvin's absolute electrometer. It can be nearly as easily measured with a digital scale as was the force between magnets in the appendix. We know the insertion of a dielectric between charged plates should decrease the force between the plates at low frequencies. What is the measurable effect? What measurable effect does the insertion of a conducting foil have on the force between the plates?
The atoms are bipolar ellipsoids. They stick together in clumps, rows, columns, loops and rings. They experience tensile and compressive forces. There are linear polarizations perpendicular to an axis of rotation as in the centrifugal force of an orbiting planet or a rotating planet. There are circular polarization as in gravity. Polarizations of planets are the vector sum of these polarizations.
Loop forces and gravity are perpendicular to the dipoles: Atoms demonstrate the flattening of gravity and circular polarizations in the figure on the right. There are no open ends on the closed dipole loops. They are loops that wrap around a planet. The loops apply an obvious compressive force. The ends of the individual atomic dipoles tend to line up, opposite charge to opposite charge, around the planet in long dipole loops of latitude. The two planets on the right attract each other in the same way as oppositely directed columns of bar magnets. Loops of magnets attract each other in this same way in the previous figure. They attract each other when their north poles point in opposite directions. Opposite poles attract. Like poles repell. Loops can attract and repell.
Centrifugal force is parallel to the dipoles: Atoms respond to orbital or planetary rotation with a centrifugal force which is perpendicular to the axis of rotation. It is always directed away from the axis and is proportional to the square of the tangent velocity at a distance from that axis. The force of rotation moves the proton slightly away from the center of the atom. The electron and proton orbits in the atom become elliptical. The atom becomes polarized. The polarized atom is attracted to its neighbors and the background charge of the cosmos.
Along the orbit of the planet, near the axis of rotation and the day-night line of the planet, the orbital centrifugal force equals the sun-planet gravitational force. This is a neutral axis of equilibrium. The atoms on the night side of the planet, facing away from the sun, have a bipolar positive polarity. This raises many questions about the solar wind and the plasmasphere of the earth and any part they might play in electrostatic gravity. The orbital centrifugal force exceeds the orbital gravitational force on the dark, night side of the planet. This polarization extends across the planet in a very long series dipole so that the sun side of the planet has a weak slightly negative polarity.
The gravity on the surface of the planet far exceeds the the gravity imposed by the sun. The centrifugal force of rotation usually exceeds the orbital centrifugal force. See planetary data. There is a superposition of solar gravitation and orbital centrifugal force on top of the larger local gravitational force and local rotational centrifugal force.
On a planetary scale looking only at orbital forces: G>C, gravity is greater than centrifugal force. G=C, orbital gravitational force equals orbital centrifugal force along the orbit. C>G, centrifugal force is greater than gravity. This is more complex than our original simple hypothesis of opposite charge in the sun and planets causing gravity. The polarized atoms stick together in long rows, rather like magnetic beads making long dipoles. The suns atoms are polarized in the same direction as the planets. The positive end of a row of atoms in the sun is attracted to the negative end of a row of atoms in the first planet. The positive end of the row of atoms in the first planet is attracted to the negative end of a row of atoms in the second planet and so on to the other planets. These are series dipoles the width of the planets. These long series dipoles have large q*d products and proportionally large forces. The force on dipoles is proportional to the q*d product, the charge on the end of the dipole times the length of the dipole, and dE/dx the inhomogeneous electric field caused by similar dipoles in other planetary bodies.
Atoms modeled as bipolar ellipsoids and spheres:
Centrifugal force stretches the atom. Gravity flattens the atom. When the centrifugal force equals the gravitational force the atoms are spherical. When there are no accelerations the atoms are spherical.
Inertial centrifugal force pulls the proton away from the center of its atom which polarizes the atom proton out facing away from the sun. This stretches the atom into a bipolar ellipsoid which may be called a bipolar prolate spheroid but this conceals its important elliptical roots. The inhomogeneous charge density of the elliptical orbit traced out by the electron and proton within the atom leaves the atom with pointed ends with opposite charges. These opposite charges attract each other into long rows with charged ends.
In a similar but perpendicular argument, gravity causes atoms to become flattened into bipolar ellipsoids. Their charged ends are perpendicular to the force and parallel to the surface of the planet. They are the result of being flattened not stretched. One might think the atoms would be flattened into a squashed sphere, an oblate spheroid, the figure of the earth due to its rotation. How particles might orbit, present bipolar charge or precess into oblate spheroids is unknown. Orbits do however, make ellipses as discovered by Kepler. Atomic scale ellipses with oppositely charged ends may precess into ellipsoids. The electrostatic torque imposed on the elliptical dipoles, of the atoms, along their length causes a perpendicular precession of the elliptical orbits of the electron and proton into ellipsoids.
The oppositely charged ends of atoms flattened by gravity attract their neighbors and they assemble into concentric rings of atoms. The rings are like lines of latitude which wrap around the planet. The rings are parallel to the surface of the planet. These rings have no exposed ends. Their charge is mostly hidden in the rings. When there is an equilibrium between the orbital centrifugal and gravitational forces, along the orbital path, like the astronauts in freefall in space, their polarizations cancel and they become unpolarized spherical atoms. They are free of both gravity and centrifugal force. They are still always subject to inertia, force = mass*acceleration, because any acceleration polarizes their atoms with respect to the background universe. Does this mean the background universe is charged? Indubitably. This is a charged example of Mach's principle.
Memories:
Do you have memories of centrifugal force as a child? Of being slung out from the center of a merry-go-round, while you held on for dear life? Centrifugal force polarized your atoms. It was the charge of the cosmos that tried to throw you from the merry-go-round. Our polarized atoms holds us to the earth. This is a profoundly small polarization of charge in each atom. Small charges produce big forces.
What does this mean? Does this answer the big questions? See the paper by Assis which describes his work and Faraday's experiments along these lines.
Is mass due to gravitational charge?
Is inertia due to gravitational charge? When atoms are accelerated, are they polarized proportional to the acceleration, with this acceleration polarization opposed by the gravitational charge of the universe?
Is centifugal force the pull of the background universe on the atoms polarized by the acceleration of rotation?
It does seem possible. Inertia and mass are related to gravity. Linking charge, gravitation and centrifugal force together is particularly important. These three bedrocks of physics were previously unrelated. Can this be proved?
Insulators: "Electronic processes in materials" by Azaroff and Brophy; "Another way of describing an insulator is to note that the electrons are so tightly bound to the atoms that at ordinary temperatures they cannot be dislodged either by thermal vibrations or with ordinary electric fields. The negative and positive charges in each part of the crystal can be considered to be centered at some point, and since no conductivity is possible, the localized charges remain that way essentially forever. When an electric field is applied to the crystal, the centers of positive charge in the crystal are slightly displaced in the direction of the applied field and the centers of negative charge are slightly displaced in the opposite direction. This produces local dipoles throughout the crystal, and the process of inducing such dipoles in the crystal is called polarization. The ratio of the induced dipole moment to the effective field is called the polarizability of the atom, and the dipole moment induced in a unit volume of a polarized insulator can be considered as the average of the dipole moments of all the atoms in that unit volume. It is possible that certain groups of atoms (complex ions or molecules) already possess permanent dipole moments. In crystals containing such atomic groups, an external field tends to orient the dipoles parallel to the field direction. In the absence of an external field, the dipoles are randomly oriented because of their thermal motion, so that the crystal has a zero net moment. The polarization of such polar crystals is strongly temperature-dependent since, even in the presence of an applied field, thermal motion tends to randomize the dipole orientation. On the other hand, the polarization of nonpolar crystals is independent of temperature since, in the absence of an external field, no dipoles exist in the crystal. The temperature dependence of polarization, therefore, can be used to distinguish polar insulators from nonpolar insulators." We will follow nonpolar insulators and the separation of charge mentioned above.
Origins of flux: Thomas L. Martin Jr. in the "Physical basis for Electrical Engineering"; "It now becomes convenient to assign a synthetic reality to the flux lines, although they are a creation of the mind only and do not exist physically, it is convenient to assume that flux lines do exist and to use them to describe the regions about charged bodies. Thus, we assume the following statements are true:
(1) Charged bodies are the sources of lines of electric flux. (a) Flux lines emanate from bodies carrying positive charge. (b) Flux lines terminate on bodies carrying negative charge.
(2) The flux lines are directed parallel to the force exerted on a positive test charge.
(3) The total number of flux lines associated with a charged body is proportional to the flux density and test charge.
The flux lines are used to represent systematically the flux about a charged body. The flux and charge are really just two different ways to describing the same phenomenon. The charge q describes the properties at a point. The flux and flux density describe the properties some distance away from the point occupied by q. Thus flux and q are just different manifestations of the same physical quantity, so flux = q."
In the figure above: "a charge of +q coulombs is produced on one plate in vacuum, and a charge of -q coulombs on the other plate when a potential difference of V volts is established. If the potential difference is doubled it is found that the number of charges on each metal plate doubles.
It appears that the ratio of the charge q to the potential difference V is a constant of the system. This constant is defined as the capacitance C. A physical structure having capacitance is called a capacitor."
C = q/V, charge2/energy, farads, coulombs/volt, a2*s4/(kg*m2),
Adding a dielectric: "When some insulating material is included between the plates of a capacitor, the situation depicted above results. It is convenient to picture the insulator as being full of dipoles randomly oriented under normal conditions. When an electric field is applied, we assume that it causes the dipoles to rotate until they come into alignment with the electric field by an amount sufficient to bring them into alignment with the electric field. In so doing they produce new lines of flux, and induce additional charges on the capacitor plates. This causes the total accumlated charge q' on each plate to be larger than the vacuum case without the dielectric even though the potential difference remains the same. We spoke of dipoles rotating when the electric field was applied. Actually, all of the dipoles in the material may be induced and present only when the electric field is applied.
qi = induced charges
q' = q + qi, the new value of the charge.
C' = q'/V = (q + qi)/V, the new value of the capacitance.
This capacitance is larger than that obtained with vacuum between the plates.
You can easily see that the extent of increase of the capacitance is controlled by the character of the insulating material between the plates. The capacitance increases as the density of dipoles increase because this raises the number of induced charges.
P = n*p/v, the flux density added by dipoles, dielectric polarization, dipole moment per unit volume, coulombs per meter2, charge/area.
n is the number of dipoles in the material between the plates. n*p is the total dipole moment in coulombs*meters. v denotes the volume of the insulating material.
D = charge/area = q1/(4*pi*r2), the flux density imposed by q1, coulombs/meter2, a*s/m2, on the surface of a sphere which surrounds the charge q1.
F ~ q2*D, Force is proportional to the test charge q2 times the flux density,
F = q2*D/e0, force is proportional to the flux density imposed by q1 on q2, e0 is the dielectric constant of vacuum or the permittivity of vacuum.
F = q1*q2/(4*pi*e0*r2), substituted for D, this is Coulomb's law.
E = F/q2 = D/e0, force/charge, electric field intensity
Dv = e0*E, flux density in vacuum, charge/area = charge2/(force*area) *force/charge.
Dm = em*E, flux density in dielectric, em = dielectric constant of the material between plates.
flux density in dielectric = flux density in vacuum + flux density from dipoles
Dm = Dv + P,
em*E = e0*E + P,
em = e0 + P/E, divide through by E the electric field intensity.
kr = em/e0 = 1 + P/Dv, divide through by e0, dimensionless relative dielectric constant."
The ratio of the capacitance obtained with some insulating material between plates to the capacitance with vacuum insulation is the relative dielectric constant kr."
kr = C'/C = (q + qi)/q = 1 + qi/q = em/e0 = 1 + P/D
For vacuum the relative dielectric constant kr is equal to one. For water the relative dielectric constant kr is 78. The force between capacitor plates is divided by kr is 78 when the space between the plates is filled with water at zero frequency. At optical frequencies of 10E14 to 10E15 hertz the kr of water is 2. Conductors are infinitely polarizable so their kr approaches infinity at zero frequency. At the high frequencies of the atomic dipoles, 6E15 hertz, there is a force between the charges. Dielectric constants have no obvious relationship to mass.
We take from this that charge is induced by the presence of a dielectric in a potential field and that a dielectric induces these charges as the dielectric becomes polarized with dipoles. Some of these induced charges, those that are caused by the polarization of gravity, are the gravitational charges we have been looking for. Dipoles have an attractive force proportional to the inverse forth power of distance so dipoles can not be the source of gravity. Charges induced by dipoles have an attractive force proportional to the inverse square of distance and can therefore be the source of gravity.
Tidal bulges: Tidal bulge equations and exposition, tides and other interesting items are at Johnson's website.
We calculate the tidal bulge of the earth using accelerations. We calculate the accelerations both using mass and using gravitational charge. The accelerations have the same values. Tidal bulges in atoms, caused by charges, may use the same procedure.
mearth = 5.972E24_kg, the mass of the earth.
rearth = 6.378E6_m, the radius of the earth.
mmoon = 7.348E22_kg, the mass of the moon.
dmoon = 384.4E6_m, the distance from the center of the earth to the center of the moon.
gcearth = mearth*(4*pi*e0*G).5 = 5.146E14_a*s, the gravitational charge of the earth.
gcmoon = mmoon*(4*pi*e0*G).5 = 6.3317E12_a*s, the gravitational charge of the moon.
Accelerations using mass:
ge = G*mearth/rearth2 = 9.79822007_m/s2, the gravitational acceleration of the earth at the surface of the earth, using mass.
ged = G*mearth/(rearth+Δr)2 = 9.79821898_m/s2, the gravitational acceleration of the earth at the surface of the earth +Δr.
gmd = G*mmoon/(dmoon-rearth-Δr)2 = 3.431742494E-5_m/s2, the gravitational acceleration of the moon at the surface of the earth +Δr.
gms = G*mmoon/(dmoon-rearth)2 = 3.341742487E-5_m/s2, the gravitational acceleration of the moon at the surface of the earth.
Accelerations using gravitational charge:
ge = gcearth/(rearth2 )*(G/(4*pi*e0)).5, the gravitational acceleration of the earth at the surface of the earth, using gravitational charge.
ge = gcearth/(rearth2)*.77448_m3/(a*s3) = 9.7979_m/s2, since (4*pi*e0*G).5/(4*pi*e0) = (G/(4*pi*e0)).5 = .77448_m3/(a*s3), using gravitational charge.
ged = gcearth/(rearth+Δr)2*(G/(4*pi*e0)).5, the gravitational acceleration of the earth at the surface of the earth +Δr, using gravitational charge.
gmd = gcmoon/(dmoon-rearth-Δr)2*(G/(4*pi*e0)).5, the gravitational acceleration of the moon at the surface of the earth +Δr, using gravitational charge.
gms = gcmoon/(dmoon-rearth)2*(G/(4*pi*e0)).5, the gravitational acceleration of the moon at the surface of the earth, using gravitational charge.
ge - Δg = G*mearth/(rearth + Δrearth)2, the gravitational acceleration of the earth and the pull of the moon above the surface of the earth.
ge - Δg = gcearth/(rearth + Δrearth)2*.77448_m3/(a*s3), using gravitational charge.
(ge - Δg)/ge = G*mearth/(rearth + Δrearth)2*rearth2 /G*mearth, divided by ge.
(ge - Δg)/ge = gcearth/(rearth + Δrearth)2*.77448_m3/(a*s3)*rearth2 /(gcearth*.77448_m3/(a*s3)), using gravitational charge.
1 - Δg/ge = rearth2/(rearth + Δrearth)2, canceled mass or gravitational mass.
1 + Δg/ge = (rearth+ Δrearth)2/rearth2, inverted.
1 + Δg/ge = (rearth/rearth+ Δrearth/rearth)2,
1 + Δg/(2*ge) = 1+ Δrearth/rearth, square root.
_ We just used these two handy approximations which I discovered by accident.
_ Check these with your calculator.
_ (1.00008)-1 = 1+(.00008*-1) = 1-.00008, inverted
_ (1.00008).5 = 1+(.00008*0.5) = 1.00004, square root
_ The integer and fractional parts are separated which simplified this problem.
Δg*rearth/(2*ge) = Δrearth, canceled the ones.
Tidal bulge = Δrearth = 0.3570_m, This is the amount of the tidal bulge. The earth is egg shaped or ellipsoid shaped by the pull of the moon. It is so small because the acceleration imposed by the moon, Δg is so small, 1.096E-6_m/s2. The earth is also shaped by its spin on its axis producing a much larger equatorial bulge.
Tidal bulge ratio:
Δg/(2*ge) = Δrearth/rearth = 5.59750E-8 = Δratom/ratom,
5.59750E-8 *ratom = Δratom = 2.962E-18_m, tidal bulge, on each side of the atom. The atoms have a radius of about 5.292E-11_m so the tidal bulge of the earth or atom is,
1/17.285E6, one part in 17 million. The earth is ellipsoidal under the gravitational effects of the sun and moon. The earths atoms are ellipsoidal under the gravitational effects of the sun and moon and their neighbor atoms and any other accelerations. This bulge in the atoms is too small to be seen with a scanning tunneling microscope. The atoms still appear spherical because they are egg shapped by only one part in 17 million. Both the atom and earth are bulged a similar small proportional amount by the same external forces.
Eccentricity of atoms and ellipses:
a = ratom+Δratom = 5.292E-11_m +2.962E-18_m = 5.2920002962E-11_m, x radius of the elliptical atom,
b = ratom-Δratom = 5.292E-11_m - 2.962E-18_m = 5.2919997038E-11_m, y radius of the elliptical atom,
e = (a2-b2).5/a = 4.7316E-4, eccentricity or,
e = ((r+Δr)2-(r-Δr)2).5/(r+Δr), eccentricity or,
e = (4*Δr/r).5 = 4.7318E-4,
e = rapogee-rperigee/(rapogee+rperigee), 2*a*e/(2*a) = e
We can move on to discover the charge density at the ellipsoid ends of the atoms. This might relate to the gravitational charge of the atoms.
Charge separation:
The red electron and blue proton ellipses share a common focus and eccentricity.
The radius of the Bohr atom is re + rp.
The center of the red ellipse of the electron from the focus is re. The center of the blue ellipse of the proton from the focus is rp. The amount of charge separation is proportional to the eccentricity as is the amount of opposite charge on each end of the atom. e is the eccentricity of both ellipses but the electron ellipse is much bigger. e*(re + rp), is the separation of the centers of the electron and proton ellipses. If the eccentricity is zero then the atom is spherical and free of bipolar end charges.
Click figure to animate! Electron and proton binary atom with elliptical orbits:
r = a*(1-e2)/(1+cos(angle)*e), the polar form of the ellipse equation.
rapogee = a*(1-e2)/(1-e) = a*(1+e), when the angle is pi, r is maximum, at apogee, at its farthest from the center of mass focus.
rperigee = a*(1-e2)/(1+e) = a*(1-e), when the angle is 0, r is minimum, at perigee, at its nearest to the center of mass.
Kepler tells us planets sweep out equal areas in equal time. Their velocities must vary in elliptical orbits.
area = r2*angle/2, the area of each wedge of the ellipse is defined by r and angle.
angle = 2*area/r2, the angle advanced for a fixed area of wedge. A constant equal to 2*area can be used with the r from the ellipse equation to calculate an angular increment to trace out equal areas in equal times. This traces out the ellipse as it shows the changes in velocity along its orbit. See the figure above. This change in velocity as the proton and electron pair move around their elliptical orbits is what interest us with respect to polarized atoms. As the velocity varies so does the charge density. The positive and negative atomic charges are visible at the opposite ends of the atom. The atom is polarized.
See Orbit 101 for several methods of predicting future orbital locations.
Charge per radian:
Planets and electrons trace out equal areas in equal times in their orbits. Electrons on elliptical orbits tracing out equal areas in equal times have a variable velocity which leads to a variable charge density and polarization of the atom. The area is,
Δareaapogee = Δangleapogee*a2*rapogee2/2 = Δangleapogee*a2*(1+e)2/2, on the electron end of the atom.
Δareaperigee = Δangleperigee*a2*rperigee2/2 = Δangleperigee*a2*(1-e)2/2, on the proton end of the atom.
Δareaapogee = Δareaperigee
Δangleapogee*a2*(1+e)2/2 = Δangleperigee*a2*(1-e)2/2,
Δangleapogee*(1+e)2 = Δangleperigee*(1-e)2,
Δangleapogee*(1+e)2/(1-e)2 = Δangleperigee, e = 0.0004732 for the tidal bulge of the earth or the atom.
Δangleapogee*(1.001894) = Δangleperigee,
Δangleapogee*(1+e*4) = Δangleperigee, The electron traces out equal areas in equal time, but the angle the electron traces out at the proton end of the elliptical atom is bigger. The velocity is greater and the charge per angle or charge per radian is less. The charge per radian is greater where the electrons move slower, as they do, at the extended portions of the elliptical orbit where the electron radius is greater.
Circle to ellipse: An electron in an circular orbit goes to an elliptical orbit by a change of velocity, Δv. This is an increase in momentum and energy as well as velocity.
rcircle = rperigee = a*(1-e), the minimum radius, closest to the center of mass focus.
rapogee = a*(1+e), the maximum radius, farthest from the center of mass focus.
vcircle*(1-e)/(1+e) = vapogee, isolated vapogee.
vcircle*(1-2*e) = vapogee, or
vcircle/vapogee = (1+2*e),
vcircle/vapogee = (1+Δv), substituted.
Δv = 2*e,
Another clue: Atomic mass is measured in AMU, atomic mass units, 1.660E-27 kilograms, about the mass of a proton and electron dipole. Mass is proportional to the number of dipoles. Gravity is proportional to mass.
AMU: one atomic mass unit = 1.66053886E-27 kilograms
Wiki says it is one twelfth of the mass of an isolated atom of carbon-12 (12C) at rest and in its ground state.
1 AMU or U = 1.660538782E-27 kg = 931.494028 MeV/cē
electron plus proton, (1.0078 amu) 1.6735E-27_kg = (1.0073 amu) 9.1094E-31_kg + (0.0005 amu) 1.6726E-27_kg
hydrogen atom, (1.00794 amu)*1.66054E-27_kg/amu = 1.67372E-27_kg,
neutron, (1.0087 amu), 1.6749E-27_kg,
1 amu or u = 1_gram/(Avogaodro's number) = 1_kg/ (1000*(Avogadro's number))
We noticed before that (c3*e0/hp).5 = 6.000359E23_a*s/(kg*m)
is very close to Avogadro's number. Using it as Avogadro's number,
1_kg/ (1000*(Avogadro's number)) = 1.66656E-27_m/(A*s) = 1_AMU * 1_kg*m/(A*s)
This is at least an odd and interesting coincidence which links Avogadro's number, AMU and meters per charge.
The gravitational charge per AMU is,
1.66656E-27_kg * (4*pi*e0*G).5 = 1.4361E-37_A*s, or
1.66656E-27_kg*m/(A*s) * (4*pi*e0*G).5 = 1.4361E-37_m,
Earth in Bohr atoms:
ratom = rc/(alpha2) = 5.292E-11_m, the minimum radius of the Bohr atom.
ratom*2 = 1.058E-10_m, the diameter of the atom or,
9.448E9_Bohr atoms/meter, if the atoms are cheek to jowl.
9.448E9_atoms/meter * 6.37E6_m (radius of the earth) = rearth*alpha2/(2*rc) = 6.026E16_atoms, the radius of the earth in diameters of series atoms or capacitors.
4/3*pi*6.018E163 = 9.133E50 atoms, the volume of the earth in Bohr atoms.
What is the composition of the Earth?
Wiki and Google say, Earth's solid mass is about
32% iron * 55.845 amu = 17.8704 amu.
30% oxygen * 15.9994 amu = 4.79982 amu.
15% silicon * 28.0855 amu = 4.212825 amu.
14% magnesium * 24.305 amu = 3.4027 amu.
3% sulfur * 32.066 amu = 0.96198 amu.
2% nickel * 58.6934 amu = 1.173868 amu.
1.5% calcium * 40.078 amu = 0.60117 amu.
1.4% aluminum * 26.9815 amu = 0.377741 amu.
98.9% at 33.400 amu or
100% at an average of 33.7719 amu per atom for the earth.
9.133E50 atoms at 33.7719 amu = 3.08438E52_amu or dipoles, the volume of the earth in amu or dipoles.
Gravitational charge per atom:
gcearth = mearth*(4*pi*e0*G).5 = 5.146E14_a*s, the gravitational charge of the earth.
gcamu = mamu*(4*pi*e0*G).5 = 1.430929E-37_a*s, the gravitational charge per AMU or dipole.
ce/gcamu = 1.6021E-19_a*s /1.430929E-37_a*s = 1.11962E18, The gravitational charge of the dipole is much, much smaller than the charge of the electron. Were does this tiny charge reside?
gcearth/gcamu = 5.146E14_a*s/1.430929E-37_a*s = 3.59626E51 gravitational charges or dipoles.
mearth*(4*pi*e0*G).5/(mamu*(4*pi*e0*G).5) =
mearth/(mamu)
= 3.59626E51, but this is only a ratio of masses.
3.08438E52 /3.5956E51 = 8.5782067, ratio of amu from volume to amu from gravitational charge. This is of the right magnitude.
Atomic dipoles:
An electric dipole consists of two charges of equal magnitude separated by a distance.
q*d = electric dipole moment, q is one of the two charges. d is the distance between the charges. d is constant in a circular orbit. d varies in an elliptical orbit.
Torque = q*d*sin(angle)*E, a torque is created by the dipole as it tries to align itself with an external charge or electric field. This is the cross product of q*d and E. This torque is why objects tend to orbit in a plane and why solar systems and some galaxies form disks.
Ey = q*d/(4*pi*e0*y3), the electric field perpendicular to the dipole. y is the perpendicular distance far from the dipole.
Ex = 2*q*d/(4*pi*e0*x3), the electric field along the axis of the dipole. x is the distance far from the dipole. The electric field along this axis is twice that which is perpendicular to the axis. See Tatum.
Ex = 2*a/(b*x3), substituted a = q*d. b = 4*pi*e0.
dEx/dx = -(2*a*(b*(3*x2))/(b*x3)2,
dEx/dx = -(6*a/(b*x4),
q*d *dEx/dx = -(6*q2*d2/(4*pi*e0*x4), the force on a dipole in the x direction is proportional to q*d.
q*d *dEy/dy = -(3*q2*d2/(4*pi*e0*y4), the force on a dipole in the y direction is proportional to q*d.
The force between dipoles decreases with the inverse forth power of the distance between the dipoles. Gravitational force decreases with the inverse square of the distance between the masses. The interaction of solitary dipoles can not explain gravity. Long series of dipoles have large q*d products and proportionally large forces.
Calculations using inverse square force:
force1 = m*m*k/x2 = m2*k/x2,
for the force between two magnets. One m is a magnet on a scale. The other m is a magnet in a stack of magnets on a platform above the magnet on the scale. k is the constant of proportionality. x is the distance between the magnet on the scale and the first magnet on the platform. All the magnets appear the same but they vary somewhat in strength.
force2 = m2*k/(x)2 + m2*k/(x+d)2, for the first two magnets on the stack. d is the distance between the magnets on the stack. Each additional magnet is stacked and added at a greater distance in multiples of d from the scale as it is stacked onto the previous magnet. Each addition identical magnet adds a decreasing incremental force at the scale because it is at an increasing distance from the scale.
force4 = m2*k/(x+0*d)2 + m2*k/(x+1*d)2 +
m2*k/(x+2*d)2 +
m2*k/(x+3*d)2, for the first four magnets on the stack.
Using 4/4 inches: one inch for the distance between the magnet on the scale and the stack of magnets.
force4 = m2*k/(4/4)2 + m2*k/(4/4+1/4)2 +
m2*k/(4/4+2/4)2 +
m2*k/(4/4+3/4)2, x = 4/4 and d = 1/4 for quarter inch magnets, for the first four magnets on the stack.
force4 = m2*k/(4/4)2 + m2*k/(5/4)2 +
m2*k/(6/4)2 +
m2*k/(7/4)2, collect terms.
force4 = m2*k*(4/4)2 + m2*k*(4/5)2 +
m2*k*(4/6)2 +
m2*k*(4/7)2, inverted the denominator and multiplied.
force4 = m2*k*16*( (1/4)2 +
(1/5)2 +
(1/6)2) +
(1/7)2),
force10 = m2*k*16*(1/16 +1/25 +1/36 +1/49 +1/64 +1/81 +1/100 +1/121 +1/144 +1/169),
force10 = m2*k*16*0.20978 = m2*k*3.3565, collected terms for a calculated series, for a ten magnets stack with x=4/4.
Weighing magnetic force: A gram scale may be used to determine the attractive and repulsive force between series magnets. Within the scale, a steel screw which supports a reference magnet is threaded into the small aluminum beam which measures forces by its deflection. When the small aluminum beams deflects it stretches a strain gage. The strain gage operates a digital display. The results are non-linear increases in force with increasing numbers of series magnets. First, put one magnet on the scale. Second, zero the scale with this magnet. Then, measure the force of attraction or repulsion, of a series of magnets stacked on a platform which is at a fixed distance above the magnet on the scale. Each additional magnet adds a decreasing force as it is stacked farther from the scale as they are stacked higher on the platform.
The internal batteries were wired and moved to a distance. The interaction of their steel ruined careful measurements of forces between magnets.
We measured the force between two magnets as 10.68_g using x = 4/4 = one inch.
The force between one magnet and a ten magnet stack equals 21.77_g.
force10 = 21.77_g = m2*k*3.3565, The total force is now correct but we seek the increment added by each magnet.
m2*k = 6.4859_g
m2*k*16 = 103.77_g
103.77_g *(1/16 +1/25 +1/36 +1/49 +1/64 +1/81 +1/100 +1/121 +1/144 +1/169),
103.77_g/16 +103.77_g/25 +103.77_g/36, for the first three terms in the series calculated.
6.48_g +4.15_g +2.88_g, for the three terms in the inverse square series calculated versus,
10.68_g +4.94_g +2.09_g, for the first three terms of the series measured with 4/4 as the distance between the magnets and the scale. Measurements enforce some reality in any process. The inverse square calculation does have pretty math but it does not seem to be a good fit to the measured reality. We must look for a better fit to the measurements.
Using a binary fraction:
When you look at a binary number such as,
0.1111111111b, an integer which is zero, a "decimal point" and a fractional part in binary notation with ten ones, or
0. +1/2 +1/4 +1/8 +1/16 +1/32 +1/64 +1/128 +1/256 +1/512 +1/1024 = 1023/1024 = 210-1 /210, in decimal notation. The fractional part adds up to a little less than one depending on how close you want to go to one with a decreasing increment of the fraction by adding more ones on the right of the binary fraction.
We seek a simple rule to estimate the increment of force added by each magnet so that we might know the total force of a series of n magnets from the force between the first few magnets in the long series. The force on a series of magnets can be considered like a weight multiplied by a binary fraction which adds up to a little less than one.
21.77_g*(1/2 +1/4 +1/8 +1/16 +1/32 +1/64 +1/128 +1/256 +1/512 +1/1024) =
21.77_g *1023/1024,
21.77_g/2 +21.77_g/4 +21.77_g/8, for the first three terms of the series calculated using the binary procedure.
10.88_g +5.44_g +2.72_g, for the first three terms of the series calculated.
10.68_g +4.94_g +2.09_g, for the first three terms of the series measured with 4/4 as the distance between the magnets and the scale.
The first magnet had a force of 10.68_g. The first ten magnet stack had a force of 21.77_g. The force with a twenty magnet stack equals 22.74_g. The force with a forty magnet stack equals 22.92_g. The second ten magnets only added 0.97_g. The second twenty magnets only added 0.18_g.
This is only a start in research by weighing magnetic repulsion using quarter inch cube magnets. I also have eighth inch cube magnets. Cylinder magnets may be better. This is a series with decreasing increments which too quickly become too small for my 0.01_g display scale and non-uniform neodymium magnets which vary by more than 0.25_g in force when separated by one inch.
Twenty magnets makes a dipole twenty times longer than a dipole made with one magnet. The first dipole had 10.68_g on one end and -10.68_g on the other end separated by one magnet and 6.35_mm. The dipole moment of one magnet q*d is 67.82_g*mm. Twenty magnets makes a dipole with a force of 22.74_g on one end and -22.74_g on the other end separated by twenty magnets and 127_mm. The dipole moment of twenty magnets q*d is 2888_g*mm. This force is more complex than the analysis of isolated dipoles would suggest. A long series of dipoles has an accumulated force on their oppositely charged ends and a lot of distance between their ends for a large q*d.
A circuit is not necessary for electrostatic gravity:
Polarized atoms storing their tiny gravitational charge do not need to be wired together. If there is a conductive path their electrostatic gravity is unimpeded. The bipolar atoms are like capacitors and are arranged in series, along each row, so
Qseries = Q1 = Q2 = Q3, they all have the same small gravitational charge.
Cseries = 1/(1/C1 + 1/C2 + 1/C3), 1/(n*(1/C)) = C/n, since n, the number of capacitors is very large, the capacitance of the row is very low.
Vseries = V1 + V2 + V3, This is a voltage divider over a very large number of capacitors where there is a conductive path.
The capacitors are arranged in parallel rows, so
Qparallel = Q1 + Q2 + Q3, is the sum of the charge in all the rows, which is the sum of all the charge. The total charge is undiluted by series or parallel effects. All the individual atomic gravitational charges participate in the gravitational effect if there is a conductive path or not.
Cparallel = C1 + C2 + C3, this is the sum of the capacitance of the rows. A large sum of small capacitance is what? The capacitance is unknown.
Vparallel = V1 = V2 = V3, The voltage drop along the parallel rows is the same where there is a conductive path.
Spherical capacitor:
Q*E = Q2/(4*pi*e0*r2), the electrical force equals the Coulomb force.
E = Q/(4*pi*e0*r2) = volts/meter = force/charge = kg*m/(a*s3), divided by Q.
V/r = Q/(4*pi*e0*r2), substituted V/r for E.
V = Q/(4*pi*e0*r) = volts = energy/charge = kg*m2/(a*s3), multiplied by r.
Q/V = 4*pi*e0*r = C = Farads = charge2/energy = a2*s4/(kg*m2), this is the capacitance of a isolated sphere with a radius r. As r increases the capacitance goes up.
Parallel plate capacitor using force and charge:
Q = C*V, charge = charge2/energy * energy/charge, energy = Q*V
Q = C*E*d, substituted E*d for V, V = E*d, E = V/d, charge = charge2/energy * force/charge * distance, energy = Q*E*d
Q = C*d*Q/(area*e0), substituted Q/(area*e0) for E, E = D/e0 = charge density/permittivity: D = charge density = Q/area: E = Q/(area*e0), so force/charge = charge/(area)* force*area/(charge2), so e0 = charge2/(force*area) = a2*s4/(kg*m3)
C = e0*area/d, cancelled Q, charge2/energy = charge2/(force*area) *area/(distance), capacitance in a plate capacitor. If the area goes up, or the distance between the plates decreases, the capacitance goes up.
Q = e0*area *V/d, substituted e0*area/d for C, in Q = C*V, charge = charge2/(force*area) *area *energy/(charge)*1/(distance), Combined the above equations. Even something as complex as the capacitor can be understood in terms of charge, force, energy, distance and action-at-a-distance without any reference to electric fields.
Atoms as capacitors: Two oppositely charged ellipsoid ends of polarized bipolar atoms, work the same as the parallel plate capacitors. If the voltage (energy/charge) is constant, while the area of the plates or the charged area of the ellipsoid ends increases, then the charge goes up. As an atom becomes more polarized the opposite charges at each end of the ellipsoid increases as the atoms charges become more separated. The charged area increases. The distance between the ends of neighbor atoms decreases as the atoms become more ellipsoid. An increase in the area of the charge or a decrease in the distance apart of the charges on neighbor atoms both increase the capacitance. The energy required is converted to additional charge stored between the plates or ellipsoids. Where we see forces or accelerations we see charge. Charge is starting to look like a placeholder for force on the plates. Energy is conserved.
Charged concentric spherical shell atoms:
Binary orbits in a plane are stable in isolation. Stable atoms, which we see in photos, require the spherical symmetry which they aquire by the precession of their orbits out of the plane. The electrons and protons are not confined to the two dimensions of a plane. They orbit in three dimensions. Atoms are spherical spinning precessing dipoles. This is how medical scanners and microwave ovens work. In a proton-electron binary atom, the proton is close to the center of mass where it orbits and precesses. This is seen as a charge spread over a spherical surface traced out by the orbiting and precessing proton. The electron across the center of mass from the proton and farther out but orbiting with the same angular velocity as the proton is also like a charge spread over a spherical surface traced out by the orbiting and precessing electron. Is this an electron cloud? How can a cloud-like electron become a negative ion particle? What you see depends on the metaphors you use. The surface of the atom, the electron orbit, is negative for circular orbits. Negative spherical surfaces of atoms repell each other and do not clump together without being polarized. The positive surface of a positive ion would be attracted and pulled into the negative surface of an atom. They would merge until the ion and atom were at equilibrium, until the ion reached the region of charge neutrality within the atom which is halfway between the electron spherical surface and the much smaller proton spherical surface. The positive ion would be repelled by the proton within the atom beyond the region of charge neutrality. This leaves us with the familiar image of bonding as overlapping spherical atoms.
An atom as a concentric spherical capacitor: This is another approach to charge separation. Aren't the electron and proton in the Bohr atom somewhat like the oppositely charged parallel plates of a capacitor? Or the oppositely charged concentric spherical plates of a capacitor? The proton orbit is like a sphere of charge surrounded by the much larger sphere of charge of the electron orbit. While they are neutral they are spherical and concentric. As the charges separate the spheres become ellipsoids. The ellipsoid ends become oppositely charged. Their area increases. Their capacitance increases.
The electron orbit is considered as a negatively charged sphere with a radius of re = 5.2889E-11_m.
The proton orbit is considered as a positivly charged sphere with a radius of rp = re*me/mp = 2.8804E-14_m.
The distance between the spheres is re-rp = 5.28602E-11_m apart.
Q/V = C = Farads = 4*pi*e0*r = charge2/energy = a2*s4/(kg*m2), This is the capacitance of a isolated spherical capacitor. We can use this formula for a concentric spherical capacitor with r defined in a special way. Here,
r = 1/(1/(rp) - 1/(re)) = re*rp/(re-rp) = re*me/(mp-me) = 2.88159E-14_m, this r is only slightly larger than the proton sphere rp.
C = 4*pi*e0*r = 4*pi*e0*2.88159E-14_m = 3.2061E-24_Farads, additional charge could be imposed by electrostatic gravity with or without a change in geometry.
Charged ends of atoms:
The positive end of an atom has a positive _a*s charge and the negative end of an atom has a negative _a*s charge. This is the very small polarized charge of the atom. This is the slight separation of the much larger charges of the electron and proton in the atom.
Force between the ends of the polarized atom:
Q*E = Q2/(4*pi*e0*d2) = _kg*m/s2,
E = Q*E/Q = _kg*m/s2/(_a*s) = _volts/meter,
Gravitational energy stored between the ends of the polarized atom:
Q2/(4*pi*e0*D) = _kg*m2/s2,
Voltage drop across the gravitational capacitor:
Q = e0*a *V/d, formula for a plate capacitor.
V = Q*d/(e0*A), isolate V. We are solving for the voltage drop across each gravitational capacitor.
Q = _a*s, gravitational charge of an atom.
d = ratom*e = 2 *5.292E-11_m * e = _m, spacing of the capacitor plates is the distance between the foci. This is the separation between the centers of the electron and proton ellipses. The centers are no longer concentric.
ratom2*pi/2 = 5.292E-11_m2*pi/2 = 4.3987E-21_m2, area of a ellipsoid end or plate is half the surface of the Bohr atom.
V = Q*d/(e0*A) = _kg*m2/(a*s3), volts/atom
Binary atoms in circular orbits:
periode = periodp, the orbital period of the electron and proton are equal. They are a binary system.
2*pi*re/ve = 2*pi*rp/vp,
re and rp are the distances to the center of mass of the system for an electron and a proton. ve and vp are the tangent velocities of the electron and proton.
re/ve = rp/vp, multiplied by 1/(2*pi)
re*vp = rp*ve,
re = rp*ve/vp, isolated re for later use
ve = vp*re/rp, isolated ve
ve2 = vp2*re2/rp2, calculated ve2 for later use
The centrifugal force equals the coulomb force in binary atoms.
centrifugal forcee = centrifugal forcep = coulomb force
me*ae = mp*ap, force equals mass times acceleration
me and mp are the mass of the electron and proton. ae and ap are the centrifugal accelerations as are ve2/re and vp2/rp
me*ve2/re = mp*vp2/rp = ce2/(4*pi*e0*(re+ rp)2) = 8.2436E-8_kg*m/s2
The centrifugal force of the electron at its distance from the common center of mass equals the centrifugal force of the proton at its distance from the common center of mass equals the electrostatic force between the electron and proton.
me*{vp2*re2/rp2}/re = mp*vp2/rp, substituted for ve2
me*{re2/rp2}/re = mp/rp
me*re = mp*rp, collected terms. This is the balance equation used in scales.
re = rp*mp/me, calculate re for later use
me*re = mp*rp,We can calculate the distance to the center of mass of the particles.
re + rp = center distance
{rp*mp/me} + rp = center distance, substituted for re.
rp*(mp+me)/me = center distance,
rp = center distance*me/(mp+me), the distance from the center of mass to the proton.
This example uses the electron and proton masses and their circular orbit center distance. The closest center distance from the Bohr atom is,
center distance = classical radius of an electron/alpha2 = rc/alpha2 = rp+re
rc/alpha2 = 2.8179E-15_m/(7.297E-3)2 = 5.292E-11_m,
mp = 1.6726E-27_kg,
me = 9.1093E-31_kg
rp = center distance*me/(mp+me) = rc/alpha2 *me/(mp+me) = 2.880E-14_m
rp = 5.292E-11_m*9.1093E-31_kg/(1.6726E-27_kg+9.1093E-31_kg)
rp = 5.292E-11_m/(1836.1526+1) = 2.880E-14_m, is the distance from the center of the proton to the center of mass of the proton-electron system. The proton is close to the center of mass. The electron is 1836 times farther out.
re = rp*mp/me = rc/alpha2 *mp/(mp+me) = 5.2889E-11_m,
Bohr calculated the electron tangent velocity as,
ve = c*alpha = c/137.036 = 2.1877E6_m/s, the electron tangent velocity.
vp = c*alpha*me/mp = 1191.4_m/s, the proton tangent velocity. Since their their momentums are equal, vp/ve = me/mp.
ve/(2*pi*center distance) = 6.579E15_hertz, the frequency at which the electron and proton orbit.
Electron magnetic moment:
The current flowing around a loop times the area enclosed by the loop is the magnetic moment.
current *area,
charge *frequency *area,
ce *v/(2*pi*r) *pi*r2,
1/2 *ce *v *r, 1/2 *charge *velocity *radius
1/2 *ce *c *r = hp/(4*pi) *ce/me
Spin is constant at hp/(4*pi). The magnetic moment is spin times ce/me, hp/(4*pi) *ce/me. The magnetic moment decreases with increasing mass of the electron.
r = hp /(2*pi*me*c) = rc/alpha
The magnetic moment also implies that the radius of the electron is rc/alpha.
The Bohr magneton is, 1/2 *ce *c *rc/alpha = 9.27E-24_A*m2.
The accepted value of the magnetic moment, mm = 9.284770E-24_A*m2, is about (1+1/862) or (1+alpha/(2*pi)) times bigger than the Bohr magneton. Where do all those decimal places come from? We paint with a broad brush omitting small corrections. We will see that alpha/pi is the ratio of the radii of the ring electron.
Useful equations:
me = 9.1094E-31_kg, mass of the electron
ce = 1.6021E-19_a*s, charge of the electron
mp = 1.6726E-27_kg, mass of the protron
c = 299792458_m/s, speed of light
alpha = .007297 or 1/137.036, fine structure constant
hp = 2*pi*me*c*rc/alpha = 6.626E-34 _kg*m2/s, Plank's constant
e0 = 1E7/(4*pi*c2)_a2*s2/(kg*m) = 8.854E-12_a2*s4/(kg*m3), e0 = charge2/(force*area) , permittivity of vacuum.
Avogadro's number? = (c/(u0*hp)).5 = (c3*e0/hp).5 = 6.000359E23_a*s/(kg*m)
G = 6.6739 E-11_m3/(kg*s2) is the gravitational constant.
rc = ce2/(4*pi*e0*me*c2) = 2.82E-15_m, the classical radius of the electron or
me*c2 = ce2/(4*pi *e0 *rc), The rest energy of the electron equals the energy associated with the charge of the electron of ce and a radius of rc. If the rest energy increases then rc decreases.
These papers go some way in the right direction___________
Accelerating superconducting disk produces reversing pulses of gravitation:
Spinning super conductors - Gravitational attraction when accelerated in one direction and repulsion when accelerated in the other has been experimentally detected by
Tajmar.
Electromagnetic drive:
emDrive - This looks like the drive which will be used in space craft of the future.
http://www.emdrive.com/
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