return to homepage A RECALCULATION OF THE ROCHE LIMIT
Abstract: I will show that the current Roche limit is a myth. It is achieved by faulty postulates as well as faulty math. I will then calculate a new Roche limit, defined as that distance at which the charge field balances the gravity field. This will give us a useful equation to explain how bodies avoid collision. I will apply it to the great inequality between Jupiter and Saturn, showing how they create the resonance and showing the distance at which they passed millions of years ago.
Now let us calculate the first new Roche limit, where the E/M field balances the gravity field. Using the equations from my UFT paper, we just set the two fields to equal one another:
8(A + a) For the Moon, that would be R = 4,023km In my math, the orbital velocity doesn't make much difference. You will say, "Well, that is why it doesn't make any difference to the current Roche limit!" But, again, that is false, since the current Roche limit is dependent on tidal effects. The tidal effect of circular motion is always half the tidal effect of straight-line gravity, and therefore cannot be excised from the equations. This is according to the current rules of tidal math. You will say that my Roche limit is very small, but it isn't much smaller than the current Roche limit. The current Roche limit for the Moon is d = r(2M/m) ^{1/3}d = 9,488km In either case, the Moon would have to be very near the Earth, as you see. Now you will say, “I thought your orbit was already a balancing of the two fields. Shouldn't you have found the current orbital distance of the Moon, instead of 4,000km?” No, that is a big oversimplification. Yes, I have said that orbits are a balancing of both fields, but the Moon's orbital distance is caused by both Earth and Sun. We therefore have to balance six fields, not four. In my paper on Mercury, you may have seen me balance only four fields, but that is because Mercury is a simpler case than the Moon. Besides, you can see in these equations that even at the current distance of the Moon, the two fields are very near balance. We find a precise balance at around 4,000 km, but at 384,400 km, the balance is only slightly off. Just insert that last number into the first equations, with no orbital velocity. You will find that the unified field (represented by Newton's equation) is 4,580 times smaller than the solo gravity field (represented by [m(A + a)]). This means that only about 1/4,580 of the field is out of balance at that distance. The orbital velocity makes up a small part of that difference, and the Sun makes up the rest. In fact, the new Roche limit for the Moon I just calculated is still an oversimplification, for the same reason. If the Moon were bumped into a vastly lower orbit by some phenomenon, it would matter whether the Moon neared the Earth on the day side or the night side. All the fields present would have to be monitored mathematically, and I have left the Sun out of it. You see, the Sun tends to increase orbits of satellites, and it does this more on satellites that are near to it. In other words, if the Sun weren't present, the Moon would orbit nearer the Earth. This is one of the reasons why the moons of Mars are much nearer to it, with Phobos orbiting at only 9,000 km. If it weren't for the Sun, Phobos would be even closer, but the Sun doesn't effect Phobos as much as our Moon, both because Phobos is smaller and because it is farther away. The simple reason for this is that the Sun “pulls” our Moon more when the Moon is nearer the Sun, than when the Moon is farther away. If we divide the Moon's orbit into a near half and a far half (near being near the Sun), then the Sun tends to increase the orbit in the near half and decrease the orbit in the far half. But it must increase it more than it decreases it, because it is closer in the near half than in the far half. The E/M fields adjust for this effect if it gets out of hand, but within certain margins the Moon is free to “float”, and it does so by increasing its orbit to suit the Sun.
But let us move on to look at the second sort of Roche limit, the one that mirrors more closely the current one. We want to find a distance at which the E/M field would break up an orbiter. As should already be clear from our analysis of Pan above, this limit is a phantom. If Pan is still experiencing accretion when it is so near the surface of a huge planet, then we may assume that the tidal Roche limit is a complete myth. The E/M Roche limit would also be a myth, in that case, because we can see from Pan that neither field is strong enough to disintegrate a moonlet, even when it is low density and hammered by collisions.
Now let us look at a near approach of Jupiter and Saturn, using these new equations. How close did the two great planets come millions of years ago, in order to create a resonance? We can now find out.
^{5}http://en.wikipedia.org/wiki/Pan_(moon)
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