Brown’s backstepping of cometary orbits doesn’t strike a nerve so much as it elicits Wolfgang Pauli’s famous “it is not only not right, it is not even wrong” response. The premise is interesting – if you could accurately track these comets back, there will inevitably be a single point in time that is their closest clustering of perihelia. That date might or might not be of interest depending on when it is and how tight the clustering is.

The problem is that Brown’s method of stepping back, clocklike, from a given date in the past using a single selected period is fundamentally flawed. Projecting backward like that totally ignores the effects of gravitational perturbations of the orbits caused by proximity to other solar system bodies. Does it not give you pause to see that the group that modeled the orbits of comet Halley back to 1403 B.C. stopped their modeling there because a flyby of Jupiter at that point rendered any further backward projection fundamentally unreliable? And that’s with stepwise gravitational modeling software, too. That even they have to introduce ’empirical correction factors’ into their model to make the simulation conform with historical observation over more recent time scales? That they at least considered the effects of mass loss over time and jet effects, which Brown doesn’t?

Adding additional comets using this flawed technique does not statismagically make the resulting answer meaningful. Garbage in, garbage out. As I already pointed out, if Brown’s technique is sound the same result should occur if you start with, say, Halley’s earliest _observed_ perihelion rather than its earliest _calculated_ perihelion. But making small changes like that in the starting conditions shifts the resulting least-squares minimum point by thousands of years back and forth, sometimes producing much tighter clusters than Brown’s 3356 B.C. date. I’m not conceding the validity of the method, mind you – I’m only pointing out that Brown’s technique is not only unphysical, it’s also highly sensitive to the initial conditions chosen, which it really shouldn’t be if choosing five comets was supposed to be able to law-of-large-numbers-central-limit-theorem-handwave away the errors introduced by the clocklike backstepping in the first place.

Try this, Dr. Hurlbut – add in three, or two, or even one of those comets that we expect to see again in the next twenty or so years. You can try ones we’ve seen twice, like 122P or 153P, and therefore have ‘earliest observed perihelion’ and ‘earliest period’ data for, and see if you get the same 3346 B.C. number. There’s no need to worry about the sigma, unless you can show where Brown actually used it somewhere other than to add a column to a figure. Let us know what comets you add to the ‘five most clocklike’ and what results you get.

Directly from Brown:
“The most authoritative source of information for all known comets is the Catalogue of Cometary Orbits 2008 (17th Edition). It lists on page 157 the comets that have been seen on __at least three consecutive orbits__ and have the longest periods.” Underlining mine; I don’t know how to do italics here.

So, yes, three consecutive observed orbits. Not that that matters really – for comets with periods greater than 50 years, there are only 6 that have three total observed perihelia, much less consecutive – and Brown rejected one because modeling suggested that it had been greatly perturbed in the last 2000 years (comet 95P/Chiron, for those playing the home game). I don’t know why this is a sticking point, unless you think that there were lots of candidate comets and Brown selected only a few of the very best, least variable of them.

Dr. Brown puts that sigma(sqrt(N)) column in there to impress us that there is relatively little error in his backstepping, but that interpretation is simply incorrect. The assumptions involved just don’t match physical reality. Brown backsteps from the earliest known perihelion using the earliest known period. If that technique were sound, we should be able to step back from a recent perihelion, using the period associated with it, and reproduce known, more historically remote perihelia within the same sigma(sqrt(N)) error that Brown is proposing. Would you agree to that in principle?

Let’s set up a worksheet where we use the Halley data to check this assumption. Pick a known perihelion and its associated period, step back 26 orbits, and compare to the real observed perihelion 26 orbits back. Why 26? Because that’s roughly the same span of time that Dr. Brown steps back from the 1403 BC date to get the 3344 BC date.

Starting from the 1910 perihelion we can repeat this for 19 earlier perihelia back to 530, matching each with a historical perihelion 26 periods earlier, e.g. 1910 -> 86 BC, 530 -> 1403 BC. According to Brown, with a sigma of 0.95 and an N of 26, sigma(sqrt(N)) should be 4.84 years, so naively we would expect 65% of the true perihelia to fall within 4.84 years of the predicted stepback date, and ~95% to fall within 9.68 years of the stepback date. If Dr. Brown’s method is accurate. If.

So, how do you think it turns out in real life? How many real perihelia fall within 4.84 years or 9.68 years of the predicted stepback date, using Brown’s method?