Ring of Famer
Join Date: Jan 2004
I enjoyed Plait's takedown of McCanney's "comets gain mass" claim...
Imagine McCanney's scenario: an asteroid the size of the Moon is moving through the solar system. It gains mass, so much so that in roughly one year (the time Hale-Bopp spent in the inner solar system) it gains enough mass to equal the mass of Mercury. It does this by having small particles slam into it as it plows through the solar wind and other material.
OK, so let's think about this. What happens when a particle hits the surface of that object? The particle is moving pretty fast, and that motion has energy (called kinetic energy). That energy has to go somehwere, and in a collision like this the energy is released as heat. Kinetic energy depends on the mass of the object and its velocity. The mass might be small for each particle, but there are a lot of particles; enough, according to McCanney, to more than quadruple the comet mass! Also, the velocities of collision are quite high. Near the Earth, such collisions are typically 40 or 50 kilometers per second. But let's be generous to McCanney, and say the velocities are much lower, say, 10 km/sec. You'll see why this is generous in just a minute.
The amount of energy released as heat is easy to calculate in this case; it's roughly 1038 ergs. An erg is a small unit, but 1038 is an awful lot of them. The total energy released by the Sun every second is only about 4 x 1033 ergs, so the energy the comet "feels" from impact is more than 25,000 times the Sun's total energy output! Another way to think about it: a one megaton nuclear bomb (about 50 times the explosive energy of the bomb dropped on Nagasaki) releases about 4 x 1022 ergs, so the amount of energy absorbed by the comet as it gains all that mass is the same as dropping 2,500,000,000,000,000 nuclear bombs on it. Since the mass is gained in less than a year, that's the same as exploding 80 million nuclear bombs per second on the comet.
Maybe it's just me, but I'm thinking a comet wouldn't do so well under such treatment.
Obviously, that's so much energy that it would easily vaporize the comet. The amount of energy it takes to totally destroy an object can be calculated in a number of ways. One way is to use what's called its gravitational binding energy. I won't go into details, but I'll point out a terrific page that describes it (using the Death Star from Star Wars as an example!). It turns out that to vaporize a comet of the Moon's mass, it would take about 1036 ergs, or one-hundredth the heat released by the impacts. So, ironically, the heat caused by McCanney's mass gain is actually enough to destroy the comet itself!
I'll note that a comet is not held together by just gravity, but also by molecular bonds and other forces. This means it would take more energy to vaporize one. It could conceivably be a much closer contest between the amount of energy holding the comet together, and the amount trying to tear it apart. However, this amount of heat generated is still enormous (enough to make the comet shine as brightly as 80 million nuclear bombs per second, remember), and I already showed comets are not hot, but cold. And of course, the solar wind is neutral, and comets lose mass. Don't forget those! So McCanney is wrong on all these counts.
Remember too I was generous with the collision velocity. The higher the velocity, the higher the kinetic energy, and the more heat generated per impact. In reality, the velocities are much higher, resulting in a heat energy more than ten times what I calculated! So that's what I meant by being generous. The numbers are even worse for McCanney's theory than I calculated, making him even more wrong. If that's possible.
Conclusion: if Hale-Bopp had gained mass the way McCanney claimed, the heat of this would have torn it apart. And if they were as big as he claims, we'd know it. McCanney is wrong.
Last edited by W*GS; 02-05-2013 at 08:32 AM..