LLlAMnYP

Sure. It's just a matter of picking out comparable (by mass) particles. Then the width of the distribution of their velocities (which is independent of the reference frame in a non-relativistic case) will be roughly proportional to their average (internal) kinetic energy.

Different proposition. Consider the observable universe as a gas with galaxies (or maybe clusters would be better?) as particles. What is its temperature (or average variation of velocity squared)?

http://demonstrations.wolfram.com/PlanarThreeBodyProblem/ There's no need to go to the extent of solving an n-body problem for this. For most intents and purposes, the only bodies that matter are the Sun and Jupiter. A 10-fold step-like increase in Jupiter's mass leads to an increase in the speed of the barycenter of the solar system with respect to the Earth. The orbit of Earth becomes slightly eccentric, but not significantly. For sure, not oscillating between Venus and Mars. Smaller perturbations from the other planets may accumulate with time on the scale of hundreds of years. My vote is that it's far more important to consider bodies closer to Jupiter that will get slingshotted on possible collision courses with the Earth.

Can't provide the exact link, but there was a similar discussion here (the question was "how fast do you need to go to pass through the earth intact?") with the general conclusion, that any conventional object would not penetrate the earth deeper and deeper, but instead just make a bigger and bigger *splat!* with increasing speed/mass. Otherwise, yes, high-density, exotic stuff, black holes, etc. Those would pass through the earth not too hindered.

Why, did the KSP forums implement LaTeX support?

How about traveling fast enough for relativistic contraction to make the planet on the order of a Planck's length in thickness?

Anthropomorphism? As in "How can I describe the attractive force between an electron and a proton in a hydrogen atom without resorting to drawing two happy little anthropomorphic balls colored red and blue holding hands?" Upd: Because I really don't see the problem. There wasn't much anthropomorphism back when I was studying, say, condensed matter physics The theory of evolution might have some thoughts on altruism and such, but in general, especially so in physics, I don't come across anthropomorphisms often. Maybe you could elaborate your question somewhat further?

Soter's discriminant, qualitatively is by definition a measure of how much the object has cleared its neighborhood, therefore it will be applicable to any star system. I'm not sure about the derivation of the Stern-Levison parameter, it is, essentially, a measure of the capability of an orbiting object to scatter other objects (within a certain large amount of time). It is tied to the Hubble time which, I accept, is somewhat arbitrary. There is, however, nothing arbitrary about scattering power alone, which would allow us to use that as a criterion of the capability of a planet to clear its neighborhood (yes, in any star system where Newtonian physics work). Soter's discriminant and the Stern-Levison parameter are by no means "the same for all intents and purposes". Soter's discriminant actually quantifies the extent, to which the neighborhood is cleared, while Stern-Levison's parameter is merely a measure of the capability of an object to do so. I certainly reject the notion of admitting Ceres (and possible some of the other large objects in the asteroid belt) to the planet's club. They share the same orbit with each other and a few hundred thousand other rocks. I equally reject including the Plutinos and other large KBOs. Again, they are merely several rocks (some estimates suggest a possibility of hundreds of object that have achieved hydrostatic equilibrium in the Kuiper Belt) in one big trans-neptunian asteroid field. I would reconsider my point of view, had we had no asteroid belt or Kuiper belt. In that case there would have been little reason not to include the dwarf planets in the planet's club. If we find out that other star systems do not generally have a cloud of debris around them, such as the Kuiper belt, it would also be a case to reconsider. However, in the absence of data, going with a prior that our solar system is not super-special seems more justified to me, than saying "no, our solar system is totally unique, this definition will totally not work for extrasolar planets". Hydrostatic equilibrium alone isn't a sufficient criterion to separate planets from non-planets. Take Saturn's tiny moon Methone, for example. It is a mere 3km across, yet because of its composition is most likely in hydrostatic equilibrium. It's very likely, that we may find several further objects that would, by this measure, also be dwarf planets, even if they would be just tiny balls of fluff among a swarm of asteroids. It is true, that the definition seeked by the IAU was such as to include the "classical" planets. There is little wrong with that. Indeed, before more recent developments in astronomy we could only detect the largest and most significant objects in our solar system and call them planets. With advances in measurement techniques came a need to formalize the definition. I do feel, that the inclusion of the "classical" eight is a must. Otherwise, in formalizing the definition we would have simultaneously completely redefined the concept of "a planet". You are welcome to suggest a much better criterion than "clearing the neighborhood" if you wish to, but I beg you to go over this wikipedia article first, so as to avoid the failures of some preliminary drafts of the IAU definition. I would, actually, also accept a definition that might exclude Mars or Mercury from planets if you can justify that sufficiently.

Are you even reading what I wrote (two or three times now)? Because we are not using solely mass to categorize them! It's obviously a bad criterion!

I don't see, why you compare Mercury to its nearest neighbors of lesser mass, but then compare it to its most distant cousin of higher mass. For a fair comparison I would say that the second lightest planet to Mercury is Mars, at 2 masses of Mercury, while the heaviest object after Mercury is Eris at 1/20th of its mass. Alternatively, you may compare the trio Ceres-Mercury-Jupiter (lightest (?) in hydrostatic equilibrium - lightest "proper" planet - heaviest planet). Then Ceres would be "only" 330 times lighter than Mercury, while Mercury would be a huge 5000 times lighter than Jupiter. That would be somewhat more convincing. In any case, as I said, this just goes to show that mass isn't a great parameter.

That's not an entirely accurate analogy, though. You can have quasi-Majorana-Fermions and quasi-Magnetic-Monopoles, but we have yet to discover their fundamental (i.e. real) counterparts, although we have a good hunch on the neutrinos. Magnetic monopoles (the real ones) are spooky though. I've read a long time ago, that they can annihilate everything they touch, that is to say they convert every particle they meet to energy and you're left with gamma radiation and a magnetic monopole ready to continue its rampage. I'm pretty sure, that can't be true, but if it was, a handful of monopoles plus any matter would be a perfect energy source. Who'd wan't silly cold fusion then? :-)

Let me make this somewhat clearer. I've taken the data from wikipedia about the eight planets and five dwarf planets. First I've ordered them by mass and plotted that on a log-scale: Then I've ordered them by the value of Soter's discriminant: And finally by the Stern-Levison parameter: All three parameters have physical meaning. We could use either of them. So let's say, we take mass, as some of the folks here really would like to. Then we have thirteen planets, there's really no place to draw a specific line here. But oh wait... what about the other big rocks in the asteroid belt? Vesta, Pallas, and Hygeia are in the same league as Ceres and on the plot of masses would not stand out. Shall we promote them to planethood as well? Is it okay, that we would have at least four planets sharing a common orbit (without being in some sort of resonance) with a few hundred thousand smaller rocks? The other two parameters are 1) dimensionless 2) have a clear gap around unity 3) separate the planets from the dwarf planets in an equal way (into the same two groups).

Actually, his point is convincing. It's perfectly fine to categorize things according to a dimensionless parameter. >>1 or <<1. Especially convenient, when objects with a parameter on the order of 1 do not exist. No one has quite correctly stated, that when you look at mass, Mercury seems quite an arbitrary place to draw the line. That is precisely why just mass alone is a bad parameter to separate planets and non-planets. Also, dimensionless parameters FTW.

By what standards exactly? Soter's planetary discriminant says that the difference between Mercury and Jupiter is a factor of 7. The difference between Mars and Ceres is a factor of 500000. According to the Stern-Levison parameter, the difference between Mercury and Jupiter is about the same as between Mars and Ceres. In terms of "clearing the neighbourhood" the 8 planets are clearly within one league. In terms of scattering power there's a big gap clearly separating dwarf planets and the big eight, although it is true that the big eight are quite widely spread out themselves.

Thank you, good Sir, this has just made my day.

For one thing, because the gravitational influence of all the stuff except the planets (and the Sun) is negligible. The 8 planets (and the Sun) are the objects that dominate the orbital mechanics of our solar system. Everything else is just debris.

I don't think so. That would require magnetic charge and then they can't be their own antiparticle. Or which properties did you have in mind?

I didn't say anything about charge, though. But being fermions they must have a half-integer spin. Magnetic moment too, perhaps?

Wouldn't storing them (assuming we have them) be quite trivial thanks to Pauli's principle if you get them spin-polarized?

You can take into account that the rockets mass decreases linearly with time. However, that is not entirely correct in KSP, because variable specific impulse with changing air pressure.

Of course. This has been covered in a recent article here: http://www.askamathematician.com/2014/08/q-how-many-times-do-you-need-to-roll-dice-before-you-know-theyre-loaded/ For all you know, this winning streak could have been in the middle of a series of 2^100 rounds.

I must have misunderstood you then. You meant to say that the minecraft world is experiencing a constant acceleration of 23 m/s^2 upward? Sure, that's a way to explain it. As for mountains deviating the pull or not, or gravity changing by a tiny fraction - these are, as you pointed out, tiny fractions. I've checked the video that measures the 23m/s^2 gravity and the error bars on its numbers are huge. The tiny fractions you speak of would be undetectable. (Also, what was the guy doing? Measuring game time with a real stopwatch? What about server latency? It's clearly visible on the video itself). Terminal velocity on the other hand doesn't really tell us much. Matching densities and form-factors within the accuracy of our measurements.

Actually note my two examples: One is about us flipping a coin 100 times, the other is us not getting killed by an asteroid in a century several times over the course of human existence. They are completely opposite in nature. If you know with a certainty of unity, that the coin is unbiased, then the next flip will be 50:50 in any case. That was a counterargument to the statement of the original post "statistically, it's more likely now, than 30 MYA". Basically if there's a certain fixed chance of something happening and the game has "no memory", then regardless of a winning streak beforehand, you'll still stand the same chance of winning or losing in the next round. So just because we haven't had a major impact in 30M years, doesn't mean that we've got it coming to us now (or not). EDIT: However, off the hand, we may or may not know the probability of a major impact in a hundred-year timeframe. The point is, that just because it didn't happen for a while, doesn't mean that the probability has changed. The next paragraph deals with estimating this probability. Suppose, on the other hand, that we don't know whether the coin is biased or not. In that case after 100 heads in a row, I'd bet precisely 100:1 that the next outcome will also be heads (as you said, by a huge margin of confidence, the coin is biased). Similar logic follows: we haven't had a major impact in over 300'000 centuries. I'd bet 300'000:1, that we won't have a major impact in the coming century. And, of course, to speak with any real authority on the coin problem we have to first set our prior probabilities of the coin being biased or not.

Nothing complex in the gravity field of a plane. Taking things at face value though (extended plane, only 256 blocks thick, nothing more to the world than this) one would expect irregularities in the plane to significantly alter the gravitational field. For example, standing near a mountain, the player should experience a significant pull towards this mountain. This is not observed. Therefore the source of gravity should be predominantly located at or below the bedrock. Apparently only when said matter is in Steve's inventory. On the other hand, it doesn't matter. If gravity doesn't change when you fall below the bedrock layer into the void, then this hypothetical infinite massive plane that creates the observed uniform gravitational field is located quite far down in the void. Or, as K^2 suggested, the void IS the source of gravity.

If you flip a coin for a while and come up with 100 heads in a row, is it more likely that the next throw will give you tails? /rhetorical question Or did you mean something different, such as "there are more potential impactors around now, then 30 MYA"? PS On the poll - we didn't get rekt in several centuries before, so there's two alternatives. We've been incredibly lucky and it's been a long time coming (small likelihood), or we're unlikely to get rekt in the space of a century. In the absence of new info my vote's "no".