Yes, I agree with you and Tobin Dax, that it doesn't matter what units of measuring mass are used (it could be stones), since mass is mass, always the same. Nothing changed as far as the physical properties of the object of mass is concerned, whether weighed or accelerated. What I had been trying to show, why this is a problem for me, is that a unit of measure for mass derived in one G is going to be different for the same unit of measure in another G. In other words, 1 kg doesn not equal 10 kg for the same mass. So this unit of measure chosen is dependent on G where it is derived.

Let me show it another way. As shown above, G can be defined as G = r^2 * a/ m. But then it must also be: 10G = r^2 * 10a/ m, so mass is still the same, only G' is ten times what we know. Now, if the Xians (per illustration above) think their 10G is merely Gx (one unit of G'), then of necessity their equation would be: Gx = r^2 * 10a/ (?m). This is the problem I'm trying to show. Should (?m) now not be, in Xian kilograms, 10m? So per "their" equivalence, kgx = 10kg in ours.

Why is this important, since it appears a rather mundane problem? I can see it as a problem when it comes to estimating the size and density of a foreign body should G there be different from ours. Back to planet X, if Gx = 10G, and we're using our kilograms, then Gx = r^2 * 10a/ m, but if our kilograms are used, then "mx", planet X's mass, is 10 kg in our terms, but one kgx in theirs. I interpret this as us thinking their planet X should be either 10 times the size of Earth (which it is not) or 10 times the density. Another way is to say that their planet, given its known size parameters, is actually ten times gravity denser than it should be. In fact, if Gx is ten times G, the density of the planet need not be affected, only the results of what things would weigh there, and by equivalence, how things would respond to acceleration (and perhaps also affect their centripetal force, so affect their planetary spin).

Can you see where this is taking me? If, for example, a neutron star (so called) has a great mass equivalent (in our G terms) to several solar masses, we of necessity must think it is very dense for the amount of gravity it displays (hence the resultant spin is very great), that its composition must of necessity be something we do not have here in our vicinity of space, though we know it is very small by comparrison to our Sun. But if it is the G of the neutron star that is so great that it "appears" as if it were several solar masses (I'll skip for now the reasoning why this might be), then its size may be even larger than we estimate (as if made of only neutrons), and density not necessarily so compact. In fact, it may be not too much denser than our own Sun, and perhaps only comparatively smaller if its internal radiation pressure is less, meaning it was a small star to start with.

Take another example. I read somewhere that Jupiter may have a rocky core about two or three Earth masses. Whether or not this is true, I can't confirm since I never saw how this was arrived at, whether through radar probing of Jupiter's interior, or derived from atmospheric occultation, or from ephemeris spin data(?). But if true, given a constant G, how could a small rocky core hold such a vast atmosphere? Unless the G is much greater than supposed, it is virtually impossible as a gas. (This may be another reason why speculations on Jupiter's atmosphere is that it has a liquid core?) I know all the arguments against why this cannot be true, how the springs on Huygens worked properly, etc. (in fact I have no way of knowing whether or not my hypothetical planetary G' calculations are right, as shown earlier), but if mass is measured in Earth's kg, then Jupiter's atmopshere cannot be possible for such a small rocky core. A small rocky core can hold a very large atmopshere only if the acceleration towards the center of mass, the gravity, is much greater for the size and density of the planet would otherwise allow. This is why I think the kilograms used is important, because if they are not adjusted for local G conditions, like in the neutron star example above, we may be overestimating density versus what it really is. A neutron star may not be so dense, only its mass (due to much higher G) acts as if it were.

There is also a practical side to this question (on hypothetical mass in a hypothetical variable G), and that has to do with how space probes will behave near any under-over estimated planetary body. If we can get that right, then we can have a more direct physics to plot flight paths without having to use adjustment tables, and then numerous inflight adjustments. In effect, it cleans up our engineering task for space flight with a better physics. It's not that we fail to get there, since using gravitational assist trajectories are of necessity self correcting (G * M as a product value is still the same, even if G and M are wrong), but that we may be handicapped with a constant G. A better way may be to use local kilograms (as opposed to Earth kilograms) to work out the dynamics of how a spaceprobe will behave in the vicinity of another planet, hypothetically.

So, can a (variable) measure of mass size and density improve on Newton's physics for a variable G? That ultimately is the question. Can we better understand very distant bodies, such as neutron stars with variable kg, adjusted for local G? Would our overall understanding of cosmology be improved, if G is found to be a variable (something we still do not know)? These were my reasons for bringing up this question. (At this point, however, I don't even want to get close to what this means for Einstein's General Relativity theory.) For this reason, I titled this question as "hypothetical" only, until such time that we find G to be otherwise than now postulated.

And I still do not know what the Xian's kilograms should be, ten fold or a hundred fold.

Sorry about the identity mixups, it may be due to a "multiple personality" syndrome. ops: I never like "Lunatik" anyway.

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