The fundamental expansion of Newton’s gravitation law is to recognize that gravitational forces depend - in addition to the mass of matter - also upon the inertial velocity of that matter. It is derived that gravitational forces are of electrodynamic nature and have their origin in nuclear electric displacement charges due to inertial matter motion. It is also hypothesized that the gravitation constant G does not apply to determine masses of cosmic objects, which are provided instead by their own specific gravity factors G_Vi which are all different from each other. Gravitation constant and gravity factors are linked by the equation G=G_Vis_Vi. The specific mass correction factors s_Vi are the ratios of the "horizontal" gravitation constant to the "vertical" (central) gravitation factors. It is therefore claimed that - in opposition to current opinion - the direct application of G is a basic error in determining the correct masses of sun and planets including Earth presented here. They differ from present textbook values substantially.

Newton’s gravitation law focuses on mass of matter as the one decisive property for determining classic gravitational forces between any material bodies /1/. Einstein’s GRT introduced spacetime and curved space to theoretically explain observed cosmic effects /2/. Relativistic velocities have been considered to provide better access to the complex nature of gravitation.

Gravitation is, however, still not understood to the extent that it can be merged with quantum physics and integrated in a "grand unified theory" (GUT) /3/. While striking similarities of Newton’s gravitation law and Coulomb’s law for electric forces are obvious, a common origin has been denied generally /4/.

Since Newton it has been assumed that the gravitation constant G - which has been determined experimentally only on Earth and still is not very accurate without knowing its real theoretical background /5/ - is valid universally and applies to central gravitational forces between cosmic objects. All earlier and current cosmological models are based upon this assumption. Evidence appears to be in favour of it, since the grand successes of scientific and technical exploration of space as well as ist commercial utilization seem to be obvious proofs of the validity of present scientific opinions concerning G.

No thorough analysis is needed, however, to recognize that all experimental proof is derived only for the correctness of gravitational forces effecting any cosmic object, satellite, and spacecraft. These forces, as is well known, are determined (besides by the inverse of the squared distance) by the product of G and a (matter) mass M. Therefore any particular gravitational force would not change (at a given distance), if a false value of G would be used, since a cosmic mass cannot be measured directly, but only calculated using a force and the gravitation constant. A factor G not applicable would therefore lead to a false mass, despite a correct force.

This paper outlines the electrodynamic and nuclear origin of gravitation and considers the considerable influence of already non-relativistic matter velocities on it. In addition, it emphasises that the gravitation constant G is not directly applicable to determine correct masses of cosmic objects. Eventually, new mass values for sun, planets, Earth and its moon are presented.

These macrocosmic results, while being interesting as such, are derived via a general nuclear approach to gravitation, which provides the analytical tools for also evalutating nucleons and atoms of other cosmic objects than just Earth by utilizing astronomic and astrophysical observation data.

The denial of gravity’s electrodynamic origin is based upon the ratio of electric forces to gravitational ones in the order of 10⁴² /4/. But this ratio only applies to direct static electric forces. If second- and fourth-order nuclear electro-dynamic forces are considered then no such ratio results. In opposition, there is a clear link from nuclear and atomic electric forces to the macrocosmic gravitational ones. Classic electrodynamic laws can be used to describe gravitation perfectly, resulting in conclusions which lead far beyond what Newton’s gravitation law /6/ is capable to provide for. This statement applies also to the theory of general relativity (GRT).

The classic approach, which considers only the masses of two bodies at a distance, is expanded in ETG (Electrodynamic Theory of Gravitation /7/) by the assumption that also the inertial velocities of these (matter) masses with respect to a central reference body like the sun contribute to the gravitational forces between these bodies. The results are correction factors s_Vi which transform the gravitation constant G to specific gravity factors G_Vi=G/s_Vi and the present textbook masses M_i to the different values s_Vi M. Incidentally, also Earth has 5,4 % more mass than is assumed at present, which will be outlined later.

All gravitational forces can be interpreted as electric ones for which Coulomb’s law applies, as is illustrated in fig. 1a. A gravitational force always originates from an electric field effecting nuclear displacement charges. This electric field is generated by other nuclear displacement charges. This approach eventually also links the radius of any planet or star to the mean diameters of their nucleons, based upon their observable properties.

In fig. 1a two spherical bodies are sketched with their properties needed for gravitation analysis. They comprise a number n_i of nucleons and elementary charges e, a radius R_i, a distance r from each other, a free fall acceleration g_i, and a velocity v_i with respect to a reference body. Both spherical bodies carry external nuclear displacement charges and therefore also respective electric fields. The meaning of the symbols used is given in a list at the end of this paper.

The process of mutual attraction is as follows. The electric field of body 1, generated by the accumulated external nuclear displacement charge q₁, attracts the total internal nuclear displacement charge Q₂, and the electric field of body 2, generated by the accumulated external nuclear displacement charge q₂, attracts the total internal displacement charge Q₁ of body 1. The gravitational fields oscillate at frequencies in the order of 10²³ Hz.

The gravitational forces between both spheres are given by equation group 1. Both forces are symmetrical and determined by the electric field of one body at the location of the other body and the total internal nuclear displacement charge of that body. If the distance r is not considered, the result is that the respective displacement charge products qQ are equal, as is indicated.

The accumulated nuclear displacement charges q (external) and Q (internal) are given in the equation groups I and II. Combination of these groups with group 1 results in equation 2, which both contain the correction factors s_i. These factors have several definitions, three of which are given by equ. c of fig. 1a. It introduces the diameter of neutron, proton or atomic mass unit as a matter property decisive for the analysis of gravitation. This is sketched in fig.1b, which outlines that only motion generates the external nuclear displacement charge being effective as the very source of gravitation. A resting nuclear sphere becomes a moving ellipsoid, the eccentricity of which is , being the ratio of external to internal nuclear displacement charges which is very small (for Earth 10^-8). And so is the external nuclear displacement charge . The internal nuclear displacement charge is s²e. This analysis and emphasis of nuclear displacement charges leads to the conclusions given as equ. 3 in fig. 1a: Since s is a function of the square of velocity, as can be seen in equ. c, also the internal nuclear displacement charge s ²e and nuclear mass are functions of velocity, although in different orders. This means that neither nuclear displacement charge nor nuclear mass are constants, as will be discussed in more detail in the next chapter.

External forces and energy become available only through motion like indicated also in fig. 1b. Total mass of nucleon matter plus magnetic and electric fields connected to it remains constant through all velocities and is its rest mass, but mass distribution on matter and magnetic and electric fields changes with velocity (equ.4). While the magnetic field energy - which represents the kinetic energy of a moving matter mass - is proportional to the second order of ß, the electric (gravitational) field energy is proportional to the fourth order of ß. Only at light velocity, when matter mass disappears, the two field energies and their respective masses become equal. This concept seems to contradict, of course, all experimental results with accelerators, which generally are considered as proof of the mass increase with velocity postulated by SRT /8/. However, while the experimental results with accelerators are correct, their interpretation is not. Accelerators operate, like travelling wave tubes (TWTs), as amplifiers for EM fields. And since each moving matter particle generates such fields according to equ. 4 in fig. 1b, these are amplified and then mistaken, after analysis of the collision energies, as fundamental mass increase with velocity and therefore proof of a central SRT postulate. But the increased particle mass is technically added by the amplifying accelerator, and not generated by the moving particle itself.

Nuclear analysis of gravitation reqires a fundamental decision on nuclear energy and its internal rotational propagation velocity. Since nuclear energy depends upon nuclear frequency as well as upon nuclear mass and nuclear energy propagation velocity , the question to answer is whether nuclear energy is independent from translateral velocity and thus also independent from nuclear diameter , or if nuclear energy is changing with , while remains practically constant at non-relativistic velocities. In this paper it is assumed for a number of reasons that nuclear energy remains constant and independent from nuclear diameter , resulting in the conclusion that velocity of circular energy propagation within a nucleon is higher than c for nucleon diameters above . It also means that and therefore and .

This is discussed using fig. 1b. The two nuclear states assummed are rest and motion. In both states nuclear energy rotates with the always constant frequency n - equ. 1 - at a velocity which is higher than translateral light velocity c for diameters wider than .

When a nucleon moves, its energy orbits are no more circles but ellipses which lead to a charge polarization with a respective external electrical field having the frequency 2n (second order harmonic of n ).

Nuclear energy is rotating nearly circularly with the velocity on an elliptic orbit with the very small numerical eccentricity . Nuclear energy circulation velocity is determined by the nuclear refractive index as given in fig.1b, equ.7, and in fig. 2a, equ. 3. If is higher than c. The square of is higher than 1, then is lower than c. If is higher than c. The square of is smaller than 1, then is higher than c. The square of equals the mass correction factor s_i. Rotating energy is contained within a nucleon by total reflection. This is only possible if there is a negative step change of the refractive index at the nucleon surface, i.e. charge density within a nucleon is always higher than outside of it on its surface (by the ratio ß²). Thus total reflection of rotating energy is possible.

As a consequence of this model it is apparent that nuclear mass does change considerably already at small, non-relativistic velocities: Nuclear mass is determined by the frequency n and the factor , resulting in a variation of nuclear mass with the variation of the nuclear diameter , and of the nuclear frequency . Despite nucleat mass and frequency change nuclear energy remains unchanged for all nuclear diameters, namely .

A nuclear diameter can also be derived by the equations given in fig. 2b, where macrocosmic angular velocity is substituted by free fall acceleration g. With the knowledge of velocity and free fall surface acceleration of any cosmic object it is possible to derive the mean diameter of its nucleons. The nuclear diameter is determined by the ratio in combination with the factor 1/2J n * (equ.2 in fig. 2a) .

The nucleons of stars and planets have masses which are inversely proportional to the nucleon diameters. The refractive indeces for all diameters below are higher than 1. If, however, the nuclear diameter exceeds this value, then the refractive index falls below 1 and a nuclear energy propagation velocity above c results. This means that below the diameter f _c the nuclear mass is higher than u because of the reduction of nuclear energy circulation velocity, while for nuclear diameters above this value the nuclear mass is smaller than u as already explained before. The correction of macrocosmic masses of stars and planets derived in this paper is therefore due to changes of nuclear masses compared to that of the atomic mass unit u, as opposed to changed numbers of nucleons.

Reference to u is, of course, concerning always mean nuclear mass. Masses of individual nucleons are those of either neutrons or protons, which vary with inertial velocity and therefore are not universally constant. In any case, masses of nucleons change with the diameters of neutrons and protons, while the mass of u is a constant by definition. An important point is the respective inertial frame used for the description of internal and external effects of nucleons.

This is indicated in fig.2c, which shows two functions. One function concerns nuclear mass. From the considerations above the linear function results: The smaller the nuclear diameter, the higher is nuclear mass; and the wider the diameter, the smaller is nuclear mass. Nuclear energy, however, is constantly for all nuclear diameters.

The other function refers to the ratio of internal nuclear displacement charge to nuclear mass, which is also proportional to the inverse of .

There is a fundamental softspot in the direct applicability of G - traditionally determined on Earth via "horizontal" gravitation - to "vertical" (i.e. central) gravity for the determination of respective masses of cosmic objects. As will be shown, this inherent methodical error has been preventing the correct determination of cosmic masses.

While here is no place to deal with the details of G determination, it must be emphasized that the basic systematic error has been to eliminate the free fall acceleration of Earth with its respective electric field and to assume that "vertical" gravity would follow the same rules as "horizontal" gravitation. While this would be correct for an experimental setup in free space far away from any major matter mass, where such a discrimination would make not much sense anyway, this decision involves the fundamental error on Earth surface, where the electric field E_E exists. A detailed discussion of the difference between the "horizontal" gravitation constant G and the "vertical" gravitation factor G_VE=G/s_VE is beyond the scope of this paper. The general but fundamental explanation, however, is obvious considering the nuclear origin of gravitation and the location of external displacement charges on matter surfaces as sketched in fig 3.

This figure shows that for horizontal gravitational interaction other displacement charges are concerned than for vertical gravitational interaction. If both sets of displacement charges were equal, no difference would result. But due to the surface electric field E_i of a considered planet the "vertical" nuclear displacement charges have values different from those of the horizontal ones. While G is a universal constant it cannot be applied directly to central forces of cosmic objects like planets. However, it can be used for the calculation of the respective gravity factors via the correction factors s_Vi.

From the ratio of the critical nucleon diameter to Earth nucleon diameter, which is , it follows that the correction factor for Earth mass is s _VE=1.054, which leads to the gravity factor of Earth being 5,4% smaller than the gravitation constant G, with the consequence, that Earth mass is 5,4% higher than the present textbook values claim. The actual gravity factor valid for Earth mass derivation is G_VE=G/s _VE=6,33× 10^-11Nm²kg^-2. The refractive index of Earth nucleons is since the mass correction factor s is equal to the squared refractive index.

Before utilizing all needed equations for the analysis of gravitation factors and masses of our sun and its planets it is required to derive sun velocity with respect to the center of our galaxy. Sun velocity values given in literature /9/ are based upon observations which are neither reliable nor close to the real orbit velocity.

There are at least two approaches to determine the orbital velocity of our sun. One is to use equation 2 in fig. 1a. The second one is to consider our moon and Earth as a model for determining sun velocity. Both approaches should, of course, lead to the same result, and they do.

The derivation of the sun’s orbit velocity given here is based upon the model Moon-Earth. The task is to derive sun velocity with the knowledge of only the orbit velocity of Earth and the free fall surface accelerations of both sun and Earth. In order to find an appropriate approach Moon and Earth are considered. We know Moon velocity with respect to Earth as well as both free fall accelerations, and we wish to derive the velocity of the Earth. The "trick" is to consider at least two different velocities which our moon has as well as Earth. This is sketched in fig. 4. Moon has a velocity with respect to Earth, but it has also a velocity with respect to the sun. This velocity is - averaged - the same as that of Earth with respect to the sun. This fact can be used to determine the correction factor s_S of the sun, with which it is possible to derive the second velocity using the equation for v_sun shown in fig.4.

The unexpected result is that sun velocity referred to our galaxy center is only slightly higher than Earth velocity with respect to the sun, namely by about 2,4%. If this small difference has a meaning for the development of the unique conditions on Earth for life is unknown. But there may be a relation.

The universal gravitation constant G determined experimentally on Earth by using horizontal gravitational forces is claimed (as already mentioned) to be not applicable directly for the determination of any cosmic mass, since cosmic objects have all different velocities with respect to their central bodies. Their resulting different gravity factors lead to also their masses being different from present textbook values. In this section the quantitative analysis is limited to the planets, including Earth, of our solar system and the sun itself. Also our moon is covered.

Present textbook mass values are listed in fig. 5a, together with other observed data (of course, orbit velocity of the sun is not yet a textbook value). Applying the equations derived for G_V, M and s , the new values for these properties of sun and planets are given in fig. 5b together with nuclear diameter f_i, electric field strength E_i and correction factor s_Vi. Absolute values are given for Earth only, while the values for the other planets and the sun are given as relative values. Fig. 5c shows the relative mass differences not in numbers but in bars.

Mass of the sun is more than twice of what is still assumed. And also our moon has about only 67% of the mass attributed to it currently. As was mentioned already, even Earth has 5,4% more mass than has been assumed. The biggest mass correction concerns Neptune which has about 2,6 times the mass allocated to it now. In general it can be said that those cosmic objects with have less mass than the classic gravitation law suggests, while bodies with own more mass than is classically calculated.

Fig. 5a  Astronomic Textbook Values

Note: Relative mass derived by the assumption that G as a universal constant is directly applicable to derive correct masses (which is not valid).

The known gravitation constant G is hypothesized to be not applicable directly to analyse central gravity forces for deriving masses of cosmic objects. For determining correct masses of these objects their gravity factors G_Vi=G/s_Vi have to be applied instead. Gravity and Gravitation have both the same nuclear electro-dynamic origin due to inertial matter velocity, but the gravity factors G_Vi vary and are different for all planets and the sun. Respectively, also the masses of sun and planets – and those of Earth and Moon, too - are different from present textbook values. Gravitation and gravity can both be explained as electrodynamic forces. While "horizontal" gravitation - which cannot be applied directly to derive masses via "vertical" central attractive forces - is independent of velocity, "vertical" gravity does not depend upon matter mass alone, but also upon inertial matter velocity.

Fig. 5b  Corrected Values for G_Vi and M_Vi

Three sets of conclusions are given in figures 6 to 8. The set of conclusions I refers to macrocosmic and cosmic relations, the set of conclusions II refers to nuclear and atomic relations, and finally the set of conclusions III refers to general relations.

As was mentioned already, the number of particles of given matter does not change with velocity, while nuclear diameter and with it nuclear mass and charge are depending on it. Energy, however, remains always constant. But the famous equation E=mc² should read , with nuclear mass and nuclear energy rotation velocity both being variables depending upon translateral inertial velocity v_i. This does mean that hn equals . h, which physically means energy per oscillation, changes with if it is not referred to external space, but to the interior of a nucleon. Because of system change a transformation is then required. The transformation factor is the refractive index .

1. E. Segrè: Die großen Physiker und ihre Entdeckungen S. 411 ff., München, 1986
2. Allgemeine Relativitätstheorie: Physik Bd.1, S. 22 ff., Leipzig, 1989
3. GUT-Modelle: Physik Bd.1, S.348 ff., Leipzig, 1989
4. R.F. Feynman: Vom Wesen physikalischer Gesetze, S. 44, München 1990
5. H. Ch. v. Baeyer: Die Schwäche der Anziehung, Die Zeit, 31.05.1996, S. 29-30
6. Newtonsches Gravitationsgesetz: Physik Bd.1, S.342, Leipzig, 1989
7. M.F. Böhm:An Electrodynamic Model of Gravity, Politechnika, St. Petersburg, 1997
8. Spezielle Relativitätstheorie: Physik Bd.2, S. 907 ff., Leipzig 1989
9. P. Moore: Der große Atlas des Universums, München 1990

e	elementary charge
E	electric field strength
u	atomic mass unit
q	external displacement charge of cosmic object
G	gravitation constant
Gv	gravity factor
Q	internal displacement charge of cosmic object
vi	inertial velocity of object i
	ratio v/c
c	translateral light velocity
	velocity of rotating nuclear energy
h	Planck constant
	elementary voltage
	transformed Planck constant
r	distance between cosmic objects
si	correction factor of object i
R	radius of cosmic object
	diameter of nucleon i
R*
	diameter of atomic mass unit
g	free fall surface acceleration
	corrected nucleon mass
n *	n /Hz
D	displacement charge
	angular velocity of cosmic object
M, m	Newton mass
	angular velocity of energy within nucleon with mass u
	ctg of rotation axis angle
	refractive index of nucleon
ni	number of particles
	nuclear electric field strength
	nucleon surface
	nuclear frequency

Gravitation is interpreted as an electrodynamic phenomenon originated by external nuclear displacement charges. External nuclear charge displacement is caused by lateral motion velocity v of any nucleon, both proton and neutron. Charge displacement is generated by v being either subtracted from or added to the velocity with which nuclear energy and charge are assumed to rotate within each nucleon. Thus the circular charge "orbits" of a resting nucleon are transformed into elliptical ones of a cucleon in motion, which results in a negative displacement charge at orbit aphelions and in a positive displacement charge at orbit perihelions. Each nucleon thus becomes a very weak and oscillating electric dipole the field of which is postulated to be the basic element of any gravitational field.

Each cosmic object has a surface layer of atoms and nucleons, where the accumulated external nuclear displacement charge generates a field which reaches out into vacuum (Fig. A1). This field is hypothesized to be the gravitational field. It cannot be screened since it is not generated by free electrons, but by displacement charges linked to the nucleons of matter. And it has a frequency of . is the magnitude of the gravitational field strength of Earth.

The total charge of any cosmic object is Coulomb. Each nucleon of such an object, either proton or neutron, contributes to it. Due to the inertial motion of a body there is a very small external displacement charge on the surface of each nucleon. This displacement charge generates a respective electric field, which connects each nucleon to the closest neighboured ones (fig. A1). The external nuclear surface charge is proportional to the square of ß (the ratio v/c), i.e. . This external nuclear displacement charge generates the field . In a stable state the electric force has to be equal to the accelerating force (: nuclear mass), which leads to . The macrocosmic surface acceleration is the same as the nuclear acceleration given by the ratio of second-order nuclear electric force to nuclear mass.

There are two kinds of permittivities, and . The nuclear permittivity determines the magnitude of a specific gravity factor G_Vi. The macrocosmic permittivity is determined by total mass and radius of a cosmic object, in addition to velocity v_i, which means that all external cuclear dispalcement charges are accumulated on the surface of each cosmic object. then determines the overall permittivity of any cosmic object.

The internal nuclear displacement charge is:

with and

The nuclear diameter is different for every cosmic object, while is universally constant. The length is equivalent to the transformed nuclear frequency:

since:

An internal nuclear displacement charge generates - if subject to translateral motion - an external displacement charge:

Because of vacuum transmission properties interaction of external and internal displacement charges of different particles is proportional to (combining equations (1) and (5)):

The external nuclear displacement charge is:

which results in the external nuclear electric field:

The total external displacement charge on a planet’s surface is:

and the resulting electric field is:

, and are derived by these considerations:

With nucleon diameter and an alternate expression for is:

which allows for expressing nuclear energy as:

The attractive force of one nucleon on another neighboured one is:

which delivers, considering equ. 11:

It appears that this nuclear acceleration is identical with the gravitational acceleration on any cosmic body’s surface. The nuclear permittivity can now be determined via equ. (8):

The planet permittivity can be derived via equ. (10) and (15), since both provide the same electric field values, with being the number of nucleons:

The electric forces are always attractive, which means that the interacting displacement charges must have different signs. This is ensured by the external second-order displacement charges, which have always a positive sign. The resulting electric field therefore attracts the negative total internal nuclear displacement charge .

In fig. A2 and fig. A3 essential equations for analyzing correct cosmic gravity factors and masses are summarized. In fig. A2 the equations which describe the respective nuclear and atomic environments are listed, while in fig. A3 the respective equations for the macrocosmic environments are given.

The first part of equ. 1 in fig. A2 is the essential one for gravitational acceleration, and it leads to the second part by considering equ.4. Equ. 6 puts h into an electric context and postulates the existence of an elementary voltage. Considering this, equ. 1 can be transformed into equ. 2, which shows the relation of gravitational acceleration to velocity v, nucleon diameter and the constant factor n * . Equ. 5 indicates the variability of nuclear mass due to inertial motion velocity and the resulting variation of the nuclear refractive index .

It is apparent from these short considerations that Maxwell’s laws are the tools for a detailed analysis of the electromagnetic fields of moving nucleons and their mutual electromagnetic interactions. Also the principles of planet motions can be applied to nucleonic masses. Last not least ETG (Electrodynamic Theory of Gravitation) provides a straightforward approach to link gravitation and quantum physics, which can, however, not be treated in this paper.

In Fig.A3 the essential equations for deriving the correct masses of cosmic objects are given.

Fig. A3 Essential Equations

b) Macrocosmic Environment

Equ.1 shows that a given gravitational surface acceleration of any cosmic object is independent from the correction factor s_i. Mass s_i M_i and gravity factor G/s_i, however, change with it. Equ.2 considers the distance r to a second object and gives the gravitational acceleration with which one object is effecting a second one at its location gravitationally.

Equ. 3 shows, how the ratio of two uncorrected "Newton masses" can be used to calulate the correction factor of the second mass if the correction factor of the first mass is known. If, for instance, Earth with its correction factor 1,054 is used as the reference, then the correct mass of any other planet or the sun can be determined provided velocities and radii are known. This equation can be used also to derive the velocity of the sun. It is the slightly modified version of equ. 2 in fig. 1a of the main text.

Equ.4 is a modification of equ.3 and gives the ratio of correct masses of two cosmic objects within the same cosmic system.