**Mass-dependent gravitation -- unified force theory -- everything changes (except gravitation)**

**Introduction**When Isaac Newton discovered gravitation in the 17th century, he worked out the value of a gravitational constant, G, which defined the strength of the earth's gravitational field as observed by the motion of the Moon in its orbit.

That "constant" had a known value based on any recognized value of the earth's mass, since the product (GxM) was known from the values of GM/R available from any set of experiments measuring gravitational acceleration. Since this is an elementary foundation of modern physics, I will note in passing that the conventional mass of the earth, namely 6.0 x 10^27 gm, is accepted along with the density of 5.4 ... so this theory is about the cosmology of the rest of the universe and relationships of gravitation to the much stronger electro-magnetic force which apparently binds a single electron to a single proton (in a hydrogen atom) at much higher rates of force than gravitation at least as far as we observe it in the earth-moon system. The electro-magnetic force is on the order of 2.3 x 10^39 times as strong as gravitation. But the author noted that distance for distance in larger atoms, the binding force began to drop off when compared between atoms of increasing mass and radius of electron shells, until it was only about 10^38 times as strong as gravitation for complex and large atoms like uranium-238. The situation there suggests that perhaps the electro-magnetic force obeys some unarticulated principle in which the one unified "electro-gravitational" force slowly drops off with increasing mass.

The author then investigated the concept that this slow decline in the value of G' (the revised value of G to make it mass-dependent) would continue through the range of masses encountered in the human-scale physical world and the cosmological world. What might that mean for cosmology?

In general, the key point to remember here is that for every other object in the solar system, galaxy and universe, the mass of objects has been estimated by assuming that G is constant, and observing the pull that objects exert on other objects that orbit them. If G is constant, then these planetary or stellar objects will have known masses based on that constant G, when the different rates of observed gravitational pull are considered. Since the mass of orbiting satellites (or planets) does not matter in this calculation (it is based simply on GM'/R where M' is the mass of the planet or star at the centre of orbital radius), it was rapidly calculated that for example Jupiter was exerting 318 times the gravitational pull of the earth on its moons, Saturn 95 times as great, etc, so that each planet's mass could be estimated from the earth's assumed mass. Similarly, the Sun has a theoretical mass about 0.33 million times that of the earth. And in conventional cosmology, the mass of these objects when compared to their volumes relative to the earth would give an idea of their density.

The new theory of mass-dependent gravitation requires instead that G'M' be equal to the currently accepted product GM' which means that if G' is different from G, then M' for each object must be revised to keep the product constant.

This means in general that objects thought to be heavier than the earth (not denser) must be heavier still, while objects thought to be lighter than the earth must be lighter still. And that changes everything we think we know about the solar system, the galaxy, and the universe. As you will see in the detailed discussions that follow, we may have blown everything in cosmology except for Venus, the earth and the asteroids. In the case of the asteroids, they exert very little pull on anything so we assume they are snowballs, ice balls or loose agglomerations of stones and dust. This may still be the case. However, prepare to have your mind entirely blown away by what everything else actually is ... and then ask yourself how we could prove this (or disprove it).

**Further proof of the gradual reduction in scale of the unified force in larger atoms**The single hydrogen atom is very tightly bound together compared to the earth-moon system. If the earth were a proton and the Moon were an electron, then the Moon would have to whiz around the earth every few seconds to exhibit the same gravitational pull as the proton on the electron. But larger atoms have slightly weaker binding forces on their more numerous satellite electrons. Their nuclei weigh more in relative terms than hydrogen, so even if their electrons behaved exactly the same, the scale of the force would be weaker. However, the electrons are also slower in rotating around their orbits per unit distance, so it can be seen that by the time you get to the mid-range atoms like iron, the value of G' has dropped from 10^27 as with hydrogen, to 10^26. Out towards uranium, it drops further below 10^25. (at the mass of the earth, G is 6.67x10^-8..).

Consult the reference below for the relative ionization energies of the elements in the periodic table.

http://en.wikipedia....of_the_elements

Let's take a fairly straight-forward example. The energy to strip an electron from hydrogen is roughly equal to that required for oxygen. Now the oxygen atom has a mass (in most isotopes) 16 times that of hydrogen, but the electron to be captured is four times as far from the centre as it sits in ring 2 (there are minor variations in geometry which will, if this theory becomes generally accepted, become the field for detailed fine-tuning of the theory on the atomic scale, for now we are just concerned with a general indication of how the unified force is dropping off with increased mass.) So, getting back to the example, hydrogen is evidently requiring four times the unified force energy for escape, since its electron requires four times as much of a jolt to move it per unit of distance. Now if the geometry of the atoms is such that scales are also increasing slightly with greater mass and complexity, then our estimate of four times the value of G' is lowered somewhat towards 3.5 (because if the oxygen atom is wider in each ring, the energy required should be a bit less, so hydrogen is therefore not looking quite as strong relative to oxygen in its scaled gravitational field).

Looking further down the table in the reference above, one notes that after element 10, the values all go down considerably, and this is of course due to the fact that the elements now have three (or more) rings of electrons, so that now we are expecting the energy to be about one-ninth times the mass. Since these elements are generally 20-40 times the mass of hydrogen, their gravitational energy should be perhaps 3-5 times that of hydrogen, but it is only when we get to chlorine (17 Cl 35) with its mass of 35 times that of hydrogen that we find a roughly equal energy (a bit lower actually) potential. So this makes chlorine about 22% as strong a source as hydrogen per unit mass. Going on to the atoms with four rings, krypton (this makes me homesick) has roughly equal binding energy at presumably 16 times the distance for about 80 times the mass, so that this element is pulling at about 20% the rate of hydrogen. Then going down into the fifth ring, we find that xenon with about 130 times the mass of hydrogen needs about 80% of the energy to remove an electron at 25 times the distance. This works out to a gravitational potential in the vicinity of 16%. By the time you get to the most massive elements you are looking at values below 10 per cent.

Note that for hydrogen, if the unified force is 2.3 x 10*39 times as strong as G at earth's mass, then G' for hydrogen has exponent 32.2 (earth has exponent -7.2 from 6.67 x 10*-8..) and note all units are in the old c.g.s. system using grams not kgs (the ratios would be the same).

What does this imply about the scale of G' which we have come to call the "electro-magnetic force" in this mass range? The diagram below illustrates what happens, and how it extends towards the cosmological range of masses.

Below, in figure 1, you will see the gradual drop-off for G' from the mass of hydrogen (1 atomic mass unit or 1.67 x 10"-24 gm). Mass is arranged logarithmically from left to right, and the scaled value of G' is represented in the horizontal scale, also in logarithmic form.

*Fig. 1 -- Values of G' for selected atomic masses*

G'..... MASS >> -24.5 .... -24.0 .... -23.5 .... -23.0 .... -22.5 .... -22.0 .... -21.5

32.2 -----------------------------------H---------------------------------------------------------------------

32.0 ----------------------------------------------He---------------------------------------------------------

31.8 ---------------------------------------------------------O-----------------------------------------------

31.7 -------------------------------------------------------------Cl------------------------------------------

31.6 ------------------------------------------------------------------------Kr-------------------------------

31.4 ---------------------------------------------------------------------------------------------------------

31.2 ---------------------------------------------------------------------------------------Rn-----------------

31.0 -------------------------------------------------------------------------------------------------U--------

G'..... MASS >> -24.5 .... -24.0 .... -23.5 .... -23.0 .... -22.5 .... -22.0 .... -21.5

If all the other elements were plotted on a graph together with these examples, as I have done in my research notes, the curve would be a little uneven but would generally fall at the same pace throughout. Now, before we leave the atomic realm, how about the extension of this graph to the

*left*to smaller masses. These would include the sub-atomic particles, electrons, quarks, neutrinos etc. I have not done much work "over there" because this is not my area of expertise and there is nothing very obvious about the application of this theory other than perhaps to the strong and weak forces which must await the work of other, more qualified researchers in the future. I am more interested in the extension of this curve (line?) to the

*right*towards the mass range of familiar objects and then planets and stars (and satellites, asteroids, everything in space).

Also before we leave this section, I should point out that the curve or line that you might wish to draw over these points would fall at a slower rate for every increment that you imagined might exist in the expansion of scale of atoms as they get more massive and crowded with electrons. If uranium were to be proven ten times as spacious per electron ring as hydrogen, then there would be no real drop off at all. So if the increase in radius is on the order of 2-3 times this curve or line would drop off less precipitously. But for now we will go with the equal radius approach.

**Extending the Unified Force G' variable towards higher mass values**It is now relatively simple to visualize what happens as G' continues to drop off at about one exponent value every third mass exponent value, and possibly more like one every two after a while since the curve is apparently increasing in slope gradually. After traversing the 51.6 logarithmic units of mass between a hydrogen nucleus (the proton) and the earth, the value of G' (at that point G) has increased 39.2 exponents. So this can be sketched out in the graph below, figure 2.

*Fig. 2 -- Generalized connection between atomic scale G' and earth mass value of G*

G' ........MASS . -24 -20 -16 -12 -08 -04 -00 +04 +08 +12 +16 +20 +24 +28

32..................xx...............................................

30....................xxxx...........................................

28.........................x..........................................

26.............................x.......................................

24................................x.....................................

22....................................x..................................

20........................................x...............................

18............................................x............................

16................................................x........................

14....................................................x......................

12........................................................x..........

10..............................................................x........

08.................................................................x......

06.....................................................................x........

04.........................................................................x......

02............................................................................x.....

00................................................................................x.......

-2......................................................................................x..

-4...........................................................................................x.

-6.............................................................................................x.

-8..................................................................................................x.(G).

G' ........MASS . -24 -20 -16 -12 -08 -04 -00 +04 +08 +12 +16 +20 +24 +28

The reader will note that around mass exponent 5, the mass of a human adult roughly (100,000 gms or 100 kgs) the value of G' is about 10^8 which would suggest a rather powerful gravitational attraction held by ordinary sized objects in our everyday world. This, I would submit, is dispersed within the general field of the object that dominates the local gravitational environment (the earth in our case) but also within magnetism and other electical phenomena. In any case, this part of the theory has no particular relevance to cosmology, other than to suggest that perhaps all space objects are more massive than we thought in which case (let's say the earth had density 100) the value of G is lower and the values of G' for everyday objects would also be lower.

Now, before we move on to the real meat of this new theory, the revised cosmology, just take in the general slope of the values of G' through the range 24 to 28 and note that it is falling at a fairly steady pace now of about one exponent in G for every exponent in mass. What does that imply about the real nature of solar system objects, stars and galaxies?

more to follow ... please do not comment until a second post appears in a few minutes' time. thanks.

**Edited by Roger J Smith, 17 February 2011 - 12:14 .**