[1] Not to be confused with Harvard’s Fred L. Whipple, leading authority on comets and coiner (in 1950) of the “Dirty Snowball” theory of cometary composition. [Return to text.]

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Question: Is Jack’s Air-Braking Mechanism Broken?

(Submitted in response to Soapbox Seminar #13: The Vurdalak Conjecture)

Anything hitting the Earth from interplanetary space will hit at at least escape velocity, 11 km/sec. In order to be slowed down by the atmosphere sufficiently that it doesn’t punch out the other side fo the Earth, it would have to be slowed to 0 miles per hour by the time it got to the ground. This is, of course, impossible, but let’s assume that for the sake of argument. That would mean that, starting at about 50 miles/80 km altitude, it would have to decelerate at about 77 gravities. Since “Vurdalak” is said to mass ten billion tons, that means a drag force of 770 billion tons.

To reduce this to something simple enough to be worth doing in my free time, use some basic rocket equations:

Mdot (mass flow rate) = thrust/(Exhaust Velocity*9.81).

In this case, thrust is that 770BTons [converted to appropriate units, 7,554 trillion Newtons], EV is 11,000 m/sec. Basically what we’re doing is accelerating air to 11 km/sec to match the black hole.

Thus, mass flow rate (the mass of air per second that must be accelerated to the same speed as the black hole) works out to 7E10 kilograms of air per second that the black hole must accelerate from 0 meters per second to 11,000 meters per second.

Oversimplifying to an air density of 1.25 kg/cubic meter, that’s 5.6E10 cubic meters of atmosphere per second. That’s a box 3800 meters on a side.

This would not have produced the Tunguska Event; this would have wiped Siberia off the map and likely destroyed the entire planetary biosphere.

In any event, the cometary fragment theory for the Tunguska Event more than adequately explains the event. A twenty megaton explosion some kilometers in the air, and descending at the right angle and velocity, has been shown to produce the same butterfly-shaped pattern of destruction on the ground, with of course no crater.

Doctor Jack's Answer

First off, let me say thanks for bringing this up. The whole mechanics of magnetic air-braking gets a little too deep into the math for the introductory soapbox seminars, but it’s just right for a Q&A. So, to take up your points, more or less in order...

You start off by assuming that Vurdalak “would have to be slowed to 0 miles per hour by the time it got to the ground.” In actual fact, not only does it not have to be slowed to zero mph — it can’t be. Because if it did come to a dead stop like that, it couldn’t go into orbit inside the earth.

What you probably meant to say is that the vertical component of its velocity — and only the vertical — has to be killed. The horizontal component can still be substantial, provided that it’s less than circular velocity at 0.001 meters above sea level. That’s about 8 km/sec. For sake of argument, I’ll assume the velocity at apogee (for the eventual inside-the-earth orbit) is an even 5 km/sec.

What we do have to assume is that Vurdalak didn’t just plunge in vertically, pointed straight down, but entered instead at a fairly shallow angle. But the evidence for an oblique entry like that is about as well documented as any other aspect of the Tunguska phenomenon: The villagers in Siberian settlements 400 km from the epicenter, reported seeing a “fiery body” rush “headlong from the south to the northwest.” If we assume the object was still some 50 km up at that point, that gives us an 8-to-1 “glide” ratio. So it’s moving 8 units of horizontal distance for every one of descent. The effect is to stretch out the deceleration track, which in turn spreads the momentum and energy through a larger volume of atmosphere.

I don’t think we need the rocket science here, since all that really matters is the total delta-momentum (which all winds up in the air) and the total delta-energy (which is mixed between air kinetic energy, heat, light, and ionization). We don’t care about the exact velocity-profile. A momentum and energy balance tells us all we need to know.

So on that basis, start with an object of Vurdalak's mass, which Singularity pegs at 5.5 billion tonnes (p. 265), or 5.5e12 kilograms. Plug that mass, together with the initial and final velocities, into MV^2 / 2 and we get:

5.5e12 x (11,000^2 - 5,000^2) / 2 = 2.64e20 joules

...Or 2.64e27 ergs. That’s about equivalent to the energy released by the tides over the course of ten days. Or, put it another way, about two and a half all-out nuclear wars.

Definitely a good-sized bang, but not anywhere near what it’d take to erase all of Siberia, much less trash the planetary biosphere. It’s only about twice the size, in fact, of the volcanic eruption on the isle of Thira in 1470 BCE. That one was enough to kill off the Minoans, but other civilizations around the globe at the time didn’t even take notice. And that’s assuming the whole energy release is concentrated in one place.

It isn’t. Planets are BIG and the magnetic broom spreads the momentum widely. You’re actually underestimating the amount of air involved, since almost none of it reaches anything like the speeds you’ve suggested. Instead, it gets dragged along for a short while and then left behind. We got socked with a pillow, not a bullet. Tens or hundreds of cubic kilometers of air were definitely involved, but they were spread out along the entire descent path, and only a tiny fraction of that dragged-along air actually hit the ground.

In addition, a lot of the energy would’ve been released way high up, where the hole was moving at its fastest. Meteorites, of course, have to get pretty low before the air’s dense enough to begin to affect them, but that’s not the case here: A monopolar field has a long reach, and it can make do with thin air as well as thick.

The energy and momentum would have been spread even wider by shocks and turbulent mixing on the way down. ’Course, all of that momentum would make it to the ground — eventually — but it’d be pretty dilute by then. When a 747 flies overhead, you’re not aware that a fraction of its weight is falling on your shoulders, are you? That’s because the effect is diffusing through miles of atmosphere. Earthquakes, tsunamis, and ground-level A-blasts, OTOH, are disproportionately destructive because they have lots of solid matter, close at hand, to work with. Again, that’s not the case here.

But, by the same token, the closer to the ground Vurdalak came, the less dissipation there was. The final seconds of plunge through the lower atmosphere were followed by a real hammerblow of air trying to catch up. And you’ve seen the results of that! A steeper entry angle might not have let us off so “lightly.”

* * *

You closed by bringing up the “cometary fragment theory” as an alternative, “more than adequate” explanation for Tunguska.

Actually, that one’s looking pretty inadequate these days. But don’t take my word for it — ask NASA. Here’s James Oberg, NBC News space analyst quoting NASA Ames Research Center’s David Morrison in an article this past summer:

The Tunguska impactor “couldn’t have been a ‘dirty snowball’ — that is, a light, fluffy comet,” [Morrison] continued. “... cometary objects with this mass, of low density and/or icy composition, would explode tens of kilometers above the surface and cause no harm.” We know this now because Pentagon satellites have actually been observing such explosions for several decades.

Unfortunately, Morrison adds, “the old comet theory persists out of inertia.”

And, as if the evidence from down-looking spy satellites weren’t enough, that same “butterfly-shaped pattern of destruction on the ground” you mention also cuts against the comet-fragment theory. That’s because there’s indications, preserved in the pattern of the forest fall, that something survived the initial multi-megaton blast — as a 1992 article by N. V. Vasil'ev pointed out:

...Detailed analysis of the [forest fall] vector structure led, however, to the conclusion that the axisymmetrical deviations occur not only before the epicenter, but also beyond it, along the continuation of the trajectory. Inasmuch as the only explanation proposed for these deviations from the radiality is the action of the ballistic wave, there follows from this the conclusion that the Tunguska meteorite (or, at least, part of it) did not end its existence at the moment of the explosion, but continued its motion along the trajectory at supersonic speed. [my italics]

If one takes into account that the nucleus of a comet of the sort which, it is proposed, the Tunguska meteorite was consists of chunks of freezing gases with a density of 1 gram per cubic centimeter (?), it is unclear, how this sort of object, having these kinds of characteristics, could be preserved even partially after undergoing the super-powerful thermal and mechanical loads characterized above.

So, whatever it was caused the Tunguska Event, it’s looking less and less likely that it could have been a piece of a comet. And more and more likely that maybe it was something we haven’t seen before.

Yours truly,
Jack Adler

copyright (c) 2005 by amber productions, inc.

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copyright (c) 2005 by amber productions, inc.