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The Constitution gives an outline, and a somewhat vague one at that, of what the job entails. Some silly nations, and some silly states (*cough* California *cough*), have very explicit and very inflexible constitutions. Our Constitution has a lot of wiggle room. IMHO, that those who argue that judges must always defer to the founding fathers' original intent are way off-base, because it is rather obvious to me that the founding fathers' original intent was to be rather non-specific. The Constitution makes no mention of the Air Force, or NASA, or the NIH, for example. Speaking of lack of direction: The Constitution is intentionally vague in the makeup of the Electoral College. "Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress ...". The selection method is explicitly deferred to the states and there is absolutely nothing about the mechanics of the Electoral College. The only explicit direction in the Constitution is "... but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector." Unintended Consequences result because of this lack of direction. (That the popular vote may be in conflict with the Electoral vote is an intended consequence.) One unintended consequence results from the winner-take-all scheme adopted by all but two states. Residents of Florida, Ohio, Pennsylvania, and a handful of other states get to choose our President. The other states essentially don't count. Getting rid of the winner-take-all selection scheme would help fix this problem. "Each State shall appoint, in such Manner as the Legislature thereof may direct, an Elector to represent each Congressional District and two Electors to represent the State as a whole. Each Elector shall, on the first ballot of the Electoral College, vote for President and Vice President in concordance with the plurality vote for President/Vice President of the United State of the District or State they represent." The Unintended Consequence of this proposal is that it gives small states even more power. Win Wyoming and you get three electoral votes. Win the Umpteenth District of some largish state and you get one electoral vote, even though that district might well have three times the population of Wyoming.

Pangloss opened the door to this off-topic rant. I have three things to say about FAFSA: #$&^, @#$!, and %#@? One more thing: I am so glad that last two of my kids to put through college are now in their senior year.

Fortunately, Obama did a complete 180 on human spaceflight back in August. At the time, the polling in Florida indicated that Obama's anti-human spaceflight stance was a major impediment to his winning Florida -- and a major impediment to the victory of Florida Democratic House and Senate races. You can read about his change in stance here. He later came out with a rather detailed space policy (danged if I can find it though). That he did so at all is rather amazing since NASA represents just 0.6% of the federal budget.

Both speeches were incredibly well done. Text of McCain's concession speech Text of Obama's victory speech

You can keep your land line -- for a couple more years, anyhow. I suspect it will be eerily silent tomorrow.

This is a straw man, Jeff. You are intentionally omitting the Hubble Flow. The motion toward the Great Attractor is small compared to the motion induced by the expansion of space. We would only see blue shifted galaxies if the Great Attractor dominated the expansion of space.

No robocalls President in Texas, but I am getting slammed for every stinking local election, state election, constitutional amendment, and even congresscritters for whom I cannot vote because I don't live in a contested district. Many of the robocalls courteously report "Political Call" on caller ID. Press the answer button once, phone stops ringing. Press it again, voice stops talking. I've gotten pretty quick on the draw.

It follows from the definition of multiplication of the natural numbers as repeated addition. The only way to extend multiplication to the integers and retain distributivity of multiplication over addition is to have [math](-m)\times(-n) = mn[/math] In other words, it is the only way to define multiplication that makes sense.

That is just because everything you learned before is only approximately correct. Take the case of two cars colliding head on: The relativistic velocity addition rules are not a new set of governing rules. They are true even for a pair of cars traveling at speeds of 30 mph (relative to the road) but heading toward each other. The result is a head-on collision at 59.9999999999999 mph, not 60 mph. That 1.2×10-13 mph difference is of course unnoticeable. At the typical velocities we encounter in everyday life, the relativistic velocity addition rules simplify to the straighforward vector addition/subtraction rules you have been taught for some time.

We sell guns to and train the militaries of Zimbabwe? North Korea? Somalia? Myanmar? That's news to me! Exactly which of the world's failed states do our companies (and they aren't "our" companies; the biggest companies are multinationals) profit from? It is not in the best interest of our country or "our" companies for any nation to have a completely failed political/social/economic system. Rather than hating America first, maybe you should open your rolled eyes. The world's emerging markets are Argentina, Brazil, China, Egypt, India, Indonesia, Mexico, Philippines, Poland, Russia, South Africa, South Korea, and Turkey. Many of these countries have albatrosses around their necks of their own making that have retarded their advancement. Argentina, Brazil, and Mexico have abundant natural resources and a fairly well-educated populace, but like the state of Louisiana, are saddled with a Spanish/Portuguese legal system. China, Russia, and Poland are/were restrained by communism. India, Indonesia, and the Philippines have overly huge populations, and India has a caste system to boot.

There are several countries natural resources that rival those of the first world nations nations but remain developing nations at best because they are either too socialistic or too plutocratic. The first world nations have attained their status because they have achieved some kind of balance between socialism and plutocracy.

Asking "what is the big bang theory" is shorthand for "do my homework for me". This is homework, and our policy here is not to do students' homework for them. We offer assistance. So, what have you found in your studies so far?

Do you think all men are created equal in modern Western society?That's right. The intent of the statement is that all people are born with the same rights and allowances.[/quote']And do you think this is true in the West? That is the intent (maybe not the "allowances"; I don't know what iNow meant by that) and it is not the intent in a caste society.

The gas cloud should comprise a bunch of little chunks of matter all orbiting the star more-or-less circularly and in more-or-less the same plane. Any protoplanets that form should thus have nearly circular orbits. The protoplanet will orbit slightly faster than the gas around it, so the gas cloud will provide a drag force on the protoplanet. This will make protoplanet's orbit circularize even further and will make the protoplanet migrate starward. This inward migration explains why we see so many star systems with hot Jupiters. It does not explain why we see so many star systems with planets in highly eccentric orbits.

Assuming a constant temperature and a constant bulk modulus leads to [math]\rho® = \rho_0 \exp(P®/\kappa) [/math] where [math]\rho_0[/math] is the density at the surface (where P=0). [math]\frac{dP}{dr} = -\rho® g®[/math] where g® is the acceleration due to gravity at radius r: [math]g®=\frac {GM®}{r^2}[/math] [math]M® = \int_0^r 4\pi \rho(r') r'^2 dr'[/math] Putting it all together, [math]\frac{dP}{dr} = -\,4 \pi G \rho_0^2 \frac{\exp(P®/\kappa)}{r^2} \int_0^r \exp(P(r')/\kappa) r'^2 dr'[/math] The goal is to find some R such that g® is 9.80665 m/s2. I can't find a closed form solution; that doesn't mean that one doesn't exist.

So I take that to mean you consider anything but an equal distribution of wealth to be unfair? See how nasty that word is, and why you won't find it in the Constitution or in law?

Some reading on this subject: Lin, D.N.C. (2008), "The Chaotic Genesis of Planets", Scientific American, May 2008 http://www.sciam.com/article.cfm?id=the-genesis-of-planets The study of planet formation lies at the intersection of astrophysics, planetary science, statistical mechanics and nonlinear dynamics. Broadly speaking, planetary scientists have developed two leading theories. ... Although researchers have not settled this controversy, most consider the sequential-accretion scenario the most plausible of the two. I will focus on it here. Ford, E.B., Lystad, V., Rasio (2005), "Planet–planet scattering in the upsilon Andromedae system", Nature 434, 873-876 A major puzzle is why many of their orbits are highly eccentric; all planets in our Solar System are on nearly circular orbits, as is expected if they formed by accretion processes in a protostellar disk. Several mechanisms have been proposed to generate large eccentricities after planet formation, but so far there has been little observational evidence to support any particular model. Free summary: "Mystery of extrasolar planets' eccentric orbits", Spaceflight Now, April 19, 2005 http://www.spaceflightnow.com/news/n0504/19orbits Instead of the nice circular orbits our nine planets enjoy, most of the more than 160 extrasolar planets detected in the last decade have eccentric orbits: so elongated that many come in very close to the central star and then go out much further away. Thommes, E.W., Duncan, M.J., Levison, H.F. (2002), "The formation of Uranus and Neptune among Jupiter and Saturn", The Astronomical Journal 123 2862-2883 arXiv preprint: http://arxiv.org/abs/astro-ph/0111290 The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the solar system where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies very difficult. Previously, we proposed a model that addressed this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and proto-Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogs to our solar system for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.

That's a rather strong statement to make in a scientific forum without any backing. I would argue the other way around: A caste system is anathema to societal survival in the modern world. It most certainly is anathema to the underlying principles of the US, and I do have a reference to back up this claim: That, too, is a rather strong statement. I don't see the word "fair" or "fairness" anywhere in the Declaration of Independence or in the Constitution. The word "fairness" is loaded with a lot of hidden meaning, and that hidden meaning depends on context and on who is beholding something to be fair or unfair. Closer to the topic of this thread, what constitutes "fairness" or lack thereof in taxation varies incredibly from one end of the political spectrum to the other. Nice.

Space (spacetime, to be precise) does have a shape, described mathematically by the metric tensor. General relativity has been tested and retested, every which way to Sunday. Your hypothesis that spacetime does not have a shape fails these tests. In short, it is wrong.

The only way you can overcome this problem is by practice. I gave an equation for the gravitational acceleration due to a uniform sphere and an equation for the mass of a uniform sphere: [math]g=\frac {G M}{R^2}[/math] [math]M = \frac 4 3 \pi \rho R^3[/math] All you have to do to solve this simple version of the problem is to substitute the mass in the first equation with the expression on the right hand side of the second equation. Simplify and solve for R. Give it a shot before you give up.

The Earth's mass distribution is obviously different when expressed in different frames. The obvious frame of choice is an Earth-centered, Earth-fixed frame, but no matter what reference frame you choose the mass distribution will vary with time because the Earth is not a rigid body. People who use the gravity models to look for oil, for example, don't want to be bothered with these temporal variations. They want a static view of the planet. One of the things the model developers have to do then is to come up with this static view. Regarding your question on tides: while gravity is an inverse square relationship, tidal forces are more-or-less an inverse cube relationship. This means the Moon plays a greater role than the Sun, and the planets are extreme bit players at best. Jupiter has 1/1000 of the Sun's mass and orbits at ~5 AU, so the magnitude of the tides induced by Jupiter are about 1/100,000 of those induced by the Sun. The theoretical models of the tides was developed in the late 19th century / early 20th century by George Airy, George Darwin (Charles' son), and A.E.H Love. Love's formalism involves a lot of different factors called Love numbers (a search for which can return some incredibly unrelated and embarrassing results). If you want to avoid the annoying "what is your love number" hits, I suggest you google something more specific such as "Love number formalism". A good reference on earth tides: http://www.agu.org/reference/5.5_wahr.pdf The different terms in the Love number formalism represent different frequency responses of the Earth to the Moon (and the Sun) induced primarily by the Earth's rotation. The responses are grouped according to period: roughly half a day (semi-diurnal), roughly one day (diurnal), and smaller long term variations driven by the month, the year, and the 18.6 year lunisolar cycle. The developers of a model of the Earth's mass distribution must account for these tidal variations. To do that, they need good models of the Earth's rotation and of the motions of the bodies in the solar system. To do that, they need good models of time and a good inertial reference system. The people who develop models of the Earth's mass distribution, the Earth's rotation, the solar system, time, and reference systems work together to improve their models because the errors in these models are interconnected.

That's the end result. The zeroth moment is simply the total mass. Since there is no such thing as negative mass, the dipole moment of any mass distribution about the distribution's center of mass is necessarily zero. So the first non-trivial components of a multipole expansion of a mass distribution are the quadrupole moments (2nd degree). This model of the Earth's gravity field goes up to degree and order 2159 (plus a partial expansion to degree 2190). Using these models is relatively easy. All it takes is a good spherical harmonics algorithm. The hairy mathematics is coming up with the models in the first place. The Earth is not a rigid body. There are short and long term variations in the Earth's mass distribution. Over shorter periods of time, earth tides (the entire earth, not just the oceans, heaves and buckles do to the moon and sun, by about 0.35-0.5 meters) and ocean tides really make a mess of things. Over longish periods of time, mass northward during northern hemisphere winter and back toward the equator in northern hemisphere summer. One of the goals of GRACE is to uncover climate changes based on subtle variations in how a couple of satellites orbit the Earth.

That's the end result. The zeroth moment is simply the total mass. Since there is no such thing as negative mass, the dipole moment of any mass distribution about the distribution's center of mass is necessarily zero. So the first non-trivial components of a multipole expansion of a mass distribution are the quadrupole moments (2nd degree). This model of the Earth's gravity field goes up to degree and order 2159 (plus a partial expansion to degree 2190). Using these models is relatively easy. All it takes is a good spherical harmonics algorithm. The hairy mathematics is coming up with the models in the first place. The Earth is not a rigid body. There are short and long term variations in the Earth's mass distribution. Over shorter periods of time, earth tides (the entire earth, not just the oceans, heaves and buckles do to the moon and sun, by about 0.35-0.5 meters) and ocean tides really make a mess of things. Over longish periods of time, mass northward during northern hemisphere winter and back toward the equator in northern hemisphere summer. One of the goals of GRACE is to uncover climate changes based on subtle variations in how a couple of satellites orbit the Earth.

For those of you who don't know how to read scathing remarks in scientific papers, the line I highlighted in the first post, "the flyby anomaly is merely due to an incomplete analysis using conventional physics", is shorthand for "You blithering idiots! You were chasing dark matter, the Unruh effect, and flaws in general relativity as possible causes when all you had to do was check for sloppy and errant mathematics. You might as well as have blamed the effect on witches, homosexuals, and rampant godlessness."

We do things like that as a simplification to teach students who don't have a grasp of higher mathematics needed to model things more accurately. We do that professionally as a simplification when all using a more detailed model does is add complexity. For example, modeling the sun as anything but a point mass is downright silly when planning a spacecraft trajectory from the Earth to Mars. Or, in short When I first read this I was going to add some scream icons, but then I read the next paragraph: Whew. The math for doing this is far beyond most undergraduate students. The University of Texas has an ongoing modern pyramid building project involving a large number of slaves graduate students. In this project, called the Gravity Recovery and Climate Experiment, the slaves graduate students struggle valiantly to build very detailed, non-point mass models of the Earth using some rather hairy mathematics. You can read more about GRACE here.