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...where M is the gravitational mass, G is the universal constant of gravitation, and r is the absolute distance. Therefore, the masses can be expressed as functions of the other parameters: M=gr/G and m=F/g. From these, it is clear that if the local acceleration of gravity is zero, g=0, then M=0 ..
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*** Is 'r' constant? What if r^2 = infinity?
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...but m becomes infinity or undefined even if F is constant or zero....
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*** "undefined" means having a finite value.
I am just making these comments, not knowing where you are going with your arguments but making provisions for any eventualities or any deductions you might make.
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...If g is nonzero, M increases without bound with square of distance, ...
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*** It is difficult to see what you are aiming at but all your corollaries if I may call them that seem to be skewed and incorrect. The physical reality is that g varies with 1/r^2 so it is not M that increases with r^2 for a constant g but M is constant while g varies inversely with r^2.
You need to explain what physical reality you are referring to by your abstract reference to the mathematics of the equations.
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...while m remains practically a constant and m=0 if and only if F=0.
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*** Again this is twisted reality: if I apply 0 force to an object of mass 10 kg say will that mean that for the object m = 0 since F = 0? No it doesn't since g is also = 0 in this case => m = F/g = 0/0 which is NOT equal to zero.
Further, a force of 10 kN say can be theoretically applied to 0 mass giving infinite acceleration. Which means that m can be zero for cases other than F = 0 as you proclaim.
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In conclusion, these demonstrated that gravitational mass as a continuous field is directly proportional to the square of distance ...
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*** Flawed logic, flawed analysis and a flawed conclusion. The expression M = gr^2/G says that for a given object of mass M the acceleration due to gravity varies inversely with r^2.
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...while inertial mass as a quantum of particle remains unchanged...
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*** Again a meaningless conclusion in my view: when two particles combine mass is "lost". So what is the meaning of your statement in light of this fact? Mass is not as "constant" as you affirm.
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Since fields are difficult to detect unless they interact, for example: the Higgs field, gravitational mass are then the missing mass of the universe.
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*** You are trying to make a distinction between gravitational mass and inertial mass but there is really no difference. In your treatment of the subject you are using the equations for the [gravitation] force between two masses M and m. If you would carefully scrutinize the physics of the case you are considering you will see that what you are referring to as "gravitational mass" is the gravity field of the object of mass M at a distance away from its surface. And what you are considering as inertial mass is the entire gravity field of the small object of mass m.
In light of this "missing mass" would comprise the gravity field of all objects starting from their surface outward.
It would be interesting to know how you arrive at the concept that mass is "missing" from the universe.
Roger
Linear Mode
