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Force of Objects
According to the conventional theory of the nuclear strong force all nucleons attract each other with a force that is an inverse function of distance. This is essentially the same as gravity. But at nuclear distances the nuclear strong force is something like 1040 times the strength of gravity. It however drops off more rapidly with distance than does gravity and becomes insignificant compared to gravity at distances greater than the nuclear scale. This is plausible enough but there is not a shred of empirical measurement to support it.
The magnitude of the strong force due to an object would be proportional to the number nucleons and hence to its mass. Hence the force between two objects of masses m and M would be
where G is the gravitational constant and r is the separation distance between the two objects. The function H(r) may be very small but not zero. This would be the law governing the motion of the planets rather than the simple Newtonian law. Although the function H(r) may be small there is the possibility that over a period of several billion years it would have its effect.
However consider the situation with electrostatic force. It is 1040 times more powerful than gravity and has the same distance dependence as gravity. But generally objects have equal numbers of positive and negative charges and thus no net charge.
What comes out of the analysis of the empirically measured binding energies of nuclides is that nuclei are largely held together by the spin pairing of nucleons. This spin pairing is exclusive in the sense that a neutron can spin pair with one other neutron and with a proton and likewise for a proton. This spin pairing does not involve a field and cannot be properly termed a force.
There is an interactive force between nucleons that is not exclusive. It can be explained by nucleons having a nucleonic charge that is of opposite sign for neutrons and protons. Thus nucleons of like type are repelled from each other and unlike types are attracted. But the net nucleonic charge of a nucleus is the result of the cancellation of the charges of the two types of nucleons. If the nucleonic charge of a proton is taken to be +1 then the nucleon charge of a neutron is −2/3. Thus for bodies like planets the nuclear force has negligible effect not because of the distances but also because of the net cancellations.
Most of the mass of Earth is in the iron of its core. Over ninety percent of iron is the isotope Fe-56 which contains 26 protons and 30 neutrons. It is not an exact cancellation; 26−(2/3)(30)=6. The stable isotope of lead, Pb-204 contains 82 protons and 122 neutrons. This nuclide has a near perfect cancellation; 82&mins;(2/3)122=2/3. For uranium 238 it is 92-(2/3)146=−5.33. Because the two-thirds ratio for the nucleonic charge of the neutron compared to that of the proton there is definite tendency for the stable isotopes of the heavier elements to have 3/2 as many neutrons as protons so there is a cancellation of net nucleonic charge.
Conclusion: The conventional theory of the strong force is erroneous. The nuclear strong force has no or negligible effect beyond a nucleus because of the exclusivity of nucleonic spin pairing and the net cancellation of nucleonic charges.
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