“Irrelevant. What’s relevant is that the period of a comet is cut short as it gets beyond the orbits of ever more objects, hence more mass.”

When these objects are lined up such that they don’t pull the comet outward, but instead pull it inward, you mean? That’s true, as far as it goes. The orbiting objects each pull the comet toward themselves at all times; sometimes that pull is more-or-less in line with the pull of the Sun, sometimes it’s orthogonal to the Sun’s pull, and sometimes it is opposite to the pull of the Sun. The Sun pulls a lot harder than anybody else, mind you.

“Except that when the other object is ahead of the object one day, a little to the side another, further to the side the day after that, and one of these years it’s behind the object, everything cancels out over the entire period. That is, until the object in question passes beyond the second object’s orbit. Then the second object is always behind, and the pull is always in the same direction: back.”

No. Let’s use the Sun-Earth-Jupiter system as our model. Every time Jupiter and the Sun are in opposition from Earth’s POV (so the alignment is S-E-J), Earth feels a force outward (or a lessening of the net force inward toward the Sun if you prefer). Every time the Sun and Jupiter are in conjunction from Earth’s POV (so the alignment is J-S-E) the Earth feels an increased inward force, _but the magnitude of the inward force increase is smaller than the magnitude of the outward force increase from the earlier opposition._ This is because gravity is an inverse square force, so the pull from Jupiter when it is on the far side of the Sun is much weaker than the pull of Jupiter when it is on the same side of the Sun and therefore closer. The result over a single Earth orbit is a net force in the outward direction.

Now, it is true that over many, many, Earth orbits there will be many points at which Jupiter and the Sun are at opposition, and the orientation of that alignment against the background stars will slowly change from one alignment to the next. Also, the distance between Earth and Jupiter at opposition varies because of the orbital eccentricities of each planet. Therefore the magnitude of the force on Earth from Jupiter is variable from pass to pass, and direction of the outward force that Earth feels every time it passes inside Jupiter will, over many orbits, walk around in a complete circle. But this is not true over a single orbit, or a handful of orbits. If we were in resonance with Jupiter, then we would get a nudge outward in the same direction repeatedly, which over time would work to change our orbit (see Kirkwood gaps in the asteroid belt).

_If_ this is the effect that you are relying on (gradual precession of the alignment of the opposition) to make the claim that ‘everything cancels out over the period’ – I don’t think that it is, but I’ll be generous in my interpretation – then you have to account for the fact that the same effect applies to the outer body being tugged inward by the intermediate body. So if Earth feels no net outward force from Jupiter over many orbits, then Jupiter feels no net inward force from Earth over many orbits. But that doesn’t jibe with your claim that the pull on the outer object ” is always in the same direction: back”. How can one always pull the other back without in return always being pulled out? Equal and opposite, and all that?

Over a single orbit, of course, there is a net force that is felt in a particular direction – roughly in the direction of the outer planet at the point of opposition (opposition being sun-inner object – outer object). If the approach at opposition is close enough, that force can be quite large and can alter the orbits of one or both objects significantly, depending on their relative masses.

Apply that to a comet now. The comet is attracted to the barycenter of the solar system, because that’s where the sum of all the force vectors from the Sun and all the various planets, moons, etc. points to. Those individual force vectors are always changing, though, in both direction and magnitude. The force vector pointed toward the Sun dwarfs all the others in magnitude, but those other force vectors don’t disappear suddenly when the comet passes inside the orbits of the various planets: those force vectors persist even when the comet is between the planet and the Sun – they now oppose the Sun’s pull to some extent. If the comet passes close enough, that planetary pull can be significant.

From your other statements though it seems as though that you think that one planet (or comet) orbiting closer to the Sun than the other feels no force from that outer planet, either momentarily or averaged over a complete orbit. It has been pointed out to you before that this is not true. The only mass distribution that this would apply to is a hollow spherical shell of uniform density, with the ‘comet/planet/test mass’ inside. A ring, disk, torus, or isolated point masses like planets do not act that way. A toroidal distribution or ring will pull objects _away_ from the axis of the torus/ring towards its inner curvature. Dr. Brown seems to understand this, so I have to assume that the misunderstanding is yours. See

link to mathpages.com

Objects above or below a ring, disk, or torus are drawn down toward the plane of the ring. See

link to youtube.com or

link to galileo.phys.virginia.edu

Returning to Dr. Brown, his efforts to show that a comet with a (conventionally calculated) aphelion of 50,000 AU and period of ~4,000,000 years _could_ have a ‘true’ aphelion of just 585 AU and a period of 5000 years under his model make so many unfounded leaps as to be worthless. Remember that he’s proposing a ring or shell of mass beyond Neptune that is sufficient to slingshot long-period comets back to the inner solar system without affecting the orbits of the outer planets.

To begin with, he uses the formula for the energy per unit mass of an elliptical orbit. However, the shape of the orbit that would be produced by a comet passing through a spherical shell of matter around the Solar System (or some other distribution) would not be elliptical. The mass ‘seen’ by the comet would be a function of time/position on the orbit rather than a constant, M (strictly speaking, M1+M2 but here M1>>>>M2). As a result, to keep the total energy of the orbit the same, the instantaneous calculated semimajor axis, a, would be a function of time/position on the orbit. So the orbit would be noneliptical – more of an egg shape with one sharp end and one blunt end – but the exact shape would depend on the exact mass distribution around the outer solar system. A disk or torus there would behave differently than a hollow spherical shell, warping the orbit in different ways. One could not predict the ‘real’ shape of such an orbit, including the aphelion distance, without knowing the details of this mass distribution. Suffice it to say that the energy of such an orbit could not be described as -GM/2a. It would be tricky to show that such orbits could even be stable.

Second, Dr. Brown states that a comet with a period of 5,000 years (number chosen to make it fit the Flood date) has an aphelion of 585 AU. This is derived, I wager, from Kepler’s third law that the period squared in years is equal to the semimajor axis cubed in AU. For earth, 1 year^2 = 1 AU^3. Thus 5000yr^2 = 292.4AU^3, so aphelion =2(292.4) = 585 AU. This would be true for an elliptical orbit in which M and a are constants, but as we have seen the comet’s orbit in Dr. Brown’s model is very much nonelliptical. There is no simple equation that will tell you what the aphelion of a noneliptical orbit with a given period is. To know that you would need to know the mass distribution, which isn’t specified. But it won’t be true that P^2=a^3.

Dr. Brown then shows that an elliptical orbit with an aphelion of 50,000 AU would have the same energy as an elliptical orbit with an aphelion of 584 AU if the Solar System was 1.0017 times heavier than believed. That doesn’t seem so bad; it’s about a Jupiter-worth of unknown mass, but it does have to be present at the barycenter for the math to work – it has to act over the entire orbit, not just over the outermost parts. The whole calculation would make sense if he were merely arguing that the mass of the central solar system has been underestimated by about eight times the current uncertainty, and that 4 million year period comets are actually 5 thousand year period comets traveling along standard elliptical orbits. That’s a tough sell, since it doesn’t fit with all the other experimental data and observations we have about the visible solar system, and it seems even Dr. Brown doesn’t believe that that is the case. So why bother to derive that 1.0017 number at all? Dr. Brown uses an equation that does not hold in his model, and plugs in some numbers calculated from other equations that do not hold in his model, and reports a mass number that is not applicable to his model. Let’s be clear: if his model is true, then the orbital energy equation for very long period comets is wrong, but he uses it. Also, if his model is true, the aphelion calculation for long period comets is invalid, but he uses that as well. The result demands ~1 Jupiter mass more in the central solar system. Ignoring that result, he then argues that trans-Neptunian mass is responsible: mass that has no effect on the solar system out to beyond Pluto (except for when it does, like his claim that it explains the Pioneer anomaly which was first noticed at the orbit of Saturn, but is too weak anyway), but which does affect things that go out farther (except for when it doesn’t, like the lack of an effect on the Voyagers out at ~120 AU, where the effect should have been building for some time). But the only hint about math to back up _this_ claim as opposed to the excess-mass-in-the-sun claim is this footnote: “In November 2005, Jon Schoenfield showed that if the mass is spherically distributed 40 AU or more from the Sun, the required extra mass would exceed 70 Jupiters. It is much more likely that the mass is distributed as a hoop or torus. If so, the extra mass is much smaller than 70 Jupiters.” Caculations not shown. In his model, there are somewhere between 2 and 70 Jupiter-masses of material between 40 and 600 AU from the Sun, distributed something like a hoop, torus, or sphere (not specified). What is also not shown, tellingly, is exactly how this theorized mass produces the effects that he claims – the 5000 year period instead of a 4,000,000 year period, for example. I’ll wait to find his theory credible until he can show how this math works out for multiple objects, like Eris out at 96 AU or Sedna out at ~90 AU, or the Voyagers or Pluto or the long-period comets.

Hey, this has been fun. I’ve gotten to brush up on my astronomy again.