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No, its not. There is a good reason the old quantum theory, with the Bohr model playing a central role, was abruptly dropped in 1925, including by Bohr himself. It had very limited applicability. It is not a good model.

That's not a fair comparison for at least three of reasons. First off, stars radiate more or less uniformly over all space (i.e., over 4*pi steradians). Quasars are highly directional. Second, stars burn for millions of years, billions of years, or more. Active galactic nuclei burn fiercely, and quickly. Third, quasars are from a long, long time ago. The universe was denser and much less metallic.

Not really. There are other effects such as frame dragging and gravomagnetism. Ignore those and you do indeed get that "mass is attracted to where another gravitational body appears to be at that moment", and you also get a system that is far worse than Newtonian mechanics. Take all of general relativity into account and you get something that is much closer to Newtonian mechanics than that simplest "lag only" gravitational model.

I didn't think you were arguing against relativity, John. I did tell you in words that the combined effects of frame dragging, gravitomagnetism, and finite transmission speed nearly cancel in our solar system. If you want the math behind those words, it gets real hairy real fast. If you want to read more, here are some relevant keywords to help you along the way: - Parameterized post-Newtonian formalism - Post-Newtonian expansion - Linearized gravity.

First, forget what I said about using the fixed point iterator. It is agonizingly slow for large eccentricities. Let's step back just a bit. We are trying to find a zero of [math]f(E;e,M)=E-e\sin E - M[/math]. Without any loss of generality, we can restrict the mean anomaly to a range of 2*pi, [0,2*pi] for example, or [-pi,pi]. We can do even better by noting that [math]f(-E;e,-M) = -f(E;e,M)[/math]. This means reduce M to [-pi,pi] and then further reduce this to [0,pi] by negating negative values of M. Simple negate the result when the mean anomaly reduced to [-pi,pi] is negative. Next note that for M in (0,pi) that [math]f(0)=-M<0[/math] and [math]f(\pi)=\pi-M>0[/math]. From this it can be seen that 0 and pi "bracket" the solution. The bisection method is a very safe but rather slow approach to finding the root of some equation. The basic idea of the bisection method is to always maintain a pair of values that bracket the solution. The method is called bisection because each step shrinks the size of the search window by half. Here's how the method works: To find a root of some function f(x), you first need to find a pair of values x0 and x1 such that f(x0) is negative and f(x1) is positive. You have just bracketed the solution. In general, if the function f(x) is continuous, at least one root is guaranteed to exist somewhere between x0 and x1. Next evaluate the function at the midpoint between x0 and x1, x2=(x0+x1)/2. One of three cases will apply: f(x2) is equal to zero, within some tolerance. You have just solved the problem. f(x2) is negative. In this case you now know that a root exists somewhere between x2 and x1. You have just halved the size of the search window. f(x2) is positive. In this case you now know that a root exists somewhere between x0 and x2. You have once again halved the size of the search window. The bisection method can be used in conjunction with a potentially faster but also potentially non-convergent technique such as Newton Raphson. The basic idea: Always maintain a bracketed solution. Use the faster iterator to generate a tentative next guess. If that tentative next guess lies within the bracketed region, use it. Otherwise reject it and use the safe but slow midpoint of the bracketed region as the next guess. You can use this approach to take advantage of even more than two techniques. For example, Brent's method uses Newton Raphson first, then the secant method, and finally bisection as the safe backup plan. With regard to Kepler's equation, there is a method that is faster than Newton Raphson, but is also even more fragile than Newton Raphson. This is Halley's method (the discoverer of Halley's Comet): [math]x_{n+1} = x_n - \frac{f(x)f'(x)}{f'(x)^2 - f(x)f''(x)/2}[/math] While Newton-Raphson yields quadratic convergence for points sufficiently close to the root, Halley's method yields cubic convergence. It can be very, very fast.

I did give an answer, many times. I gave an inkling of the underlying math in this post, http://www.scienceforums.net/topic/52968-tides/page__p__574204#entry574204. I gave you names and keywords in post #8. I expected you to do some of your own research. I cannot give a full explanation of the tides in an internet forum. That would require me to write a book. Your entire problem with understanding of tides is that you have a misunderstanding of Newton's law of gravitation. That misunderstanding is centered on this quote that you made from Encyclopedia Britannica. Quoting you from post #7, bold emphasis is mine, So what are those "certain" calculations in which the mass of a body can be envisioned as being concentrated at the center of mass? The answer is that this simplification is only valid for rigid bodies with a radial mass distribution. The Earth's oceans make the Earth a non-rigid body. You cannot use that simple computation. What you can do is make a series of refinements. You can start with a spherical, rigid Earth and put a single drop of water on the surface of that spherical, rigid Earth. Now you can apply that simple form of Newton's law of gravitation to determine the gravitational forces on that drop of water from the perspective of an Earth-fixed frame. The result is exactly what I showed in that earlier post. The picture gets a lot more complicated when you add lots of water and make the Earth itself non-spherical. However, it all starts with that simple calculation. This is the tidal forcing.

Newton's law of gravitation does indeed require instantaneous action at a distance. So, what happens if we modify Newtonian gravity to take into account the finite transmission time? Chaos is what happens. For example, orbits are no longer stable, and a solar system simulation based on this correction would yield much less accurate results than would a solar system simulation based on Newton's law. Numerous crackpots, including some PhD physicists, have used this as an argument against general relativity. These arguments against general relativity are straw man arguments. While general relativity does say that gravity propagates at the speed of light, it says a lot more than that. There are other affects such as frame dragging in addition to this propagation delay. The net result is that these effects nearly cancel for objects with lowish densities (much less than the Schwarzschild density), lowish relative velocities (much less than light speed), and separated by largish distances (much greater than the Schwarzschild radii). The limiting result is Newtonian gravity. What about those cases where distances are small, velocities are large? That describes Mercury. At the end of the 19th century Mercury's orbit was known to deviate from calculations based on Newtonian mechanics. General relativity perfectly explains those deviations. This was one of the reasons for the relativity quick acceptance of general relativity by physicists.

Don't just make up numbers! That is not how engineering or science works.

Nonsense. Absolute zero is absolutely as low as a system can get in terms of energy.

Here is what what Sisyphus and I are talking about, in numbers: Earth's orbital velocity about the Sun is 29.79 km/s. Solar system escape velocity at 1 AU from the Sun is 42.12 km/s. An orbit with an apohelion of 1 AU and a perihelion of 0.005 AU will just intersect Earth's orbit and the Sun's surface. The orbital velocity for this orbit is 2.97 km/s at apohelion. That means that only 12.34 km/s needs to be added to a vehicle launched from Earth to place it on a solar system escape trajectory while 26.81 km/s needs to be removed from a vehicle launched from Earth to place it on a Sun-intersecting trajectory. Given the nastiness of the rocket equation, it is a whole lot harder to place a vehicle on a Sun-intersecting trajectory than it is to make it escape the solar system.

Try a naive implementation of a Newton Raphson iterator with an eccentricity of 0.999, M=1.999*pi, E0=0. This diverges. That said, there are some easy ways to make a Newton Raphson iterator extremely robust. Restrict the mean anomaly to [-pi,pi], use the mean anomaly as the initial guess. Finally, if some step either changes the sign of E or makes abs(E)>pi, use the fixed point iterator E=M+e*sin(E) in lieu of that found by Newton-Raphson iteration. (The fixed point iterator is guaranteed to converge, but slowly.) The number of papers written on different techniques for solving Kepler's equation is immense. It is quite amazing that good old Newton's method remains right at the top of the heap.

Earth's orbital velocity around the Sun is about 66,600 miles per hour. Your 10 mile/hour figure won't even begin to make a dent in that number. It is very, very hard to make a dent in that number. In fact, it is easier to make a vehicle launched from Earth escape the solar system than it would be to make that object hit the Sun. Even getting to Mercury is hard. That is why we have had so few missions to Mercury.

Yes. What you typed makes no sense. It isn't even nonsense. Try again, without the dots, and more words. What are you trying to say?

Beautifully done website, isn't it? It's very professional looking and is nicely organized. There's a lesson to be learned here: Don't believe something you see on the 'net, at least not until you have done a sanity check. Does this pass a sanity check? No. There is no "lunar time scale problem" except in the eyes of various crackpots, mostly young earth creationist crackpots. There is immense amount of evidence that the Moon was only slightly closer to the Earth way back to the pre-Cambrian. 900 million years ago, for example, the Earth-Moon distance was about 90% of the current value. Evidence of tides goes back to 3.2 billion years. The Moon has been dated to just after the Earth finished forming. This is a crackpot notion, done very nicely.

You can add "boned" to that list: "We're having boned turkey and dressing for supper" (bones removed) "She has a delicately boned facial structure" (bones present) "We boned up on physics this weekend" (bones (of knowledge) added) "..." (Crude meaning elided)

Negative temperatures are not "colder" than 0K, alpha2cen. Your below 0K, meaning colder than absolute zero, is a nonsense proposition.

There you go. Problems everywhere you look. Incredibly low thrust, incredibly high power consumption. Non-existant generators, at least to the extent needed to generate meaningful thrust. Plans to use VASIMR to get people to Mars predicate one kilogram per kilowatt generators. The Soviet Union's TOPAZ generator: 100 kilograms per kilowatt. The United State's NERVA generator: 65 kilograms per kilowatt. Predicating nearly two orders of magnitude in improvement is in general a no-go. About the only place that works is in the world of computing, Moore's law. There is no equivalent to Moore's law in space technology.

Even if it was true, how would it help? Superconductors are not power sources. All superconductors would do is eliminate resistive power loss between the generator and thruster. Given the short distances involved on a spacecraft, that loss is not going to be the big problem. Generating thrust and generating power will be the big problems.

Except that this is apparently bogus. No papers published in peer reviewed journals (they would be all over this if it was legit); even wikipedia steers clear (check the discussion page on wikipedia's high-temperature superconductivity page).

Assuming that "colder than" means that heat flows from a warmer object to a colder one, that is exactly correct.

Two comments. 1. "My episodes usually occur when I've been resting, napping, or sleeping for a long time, and I suddenly get up ..." Don't do that then. Get up slowly. 2. I am not a doctor. You should go see someone who is a doctor.

For all elements. Consider U-238. It has 146 neutrons, 92 protons, and an atom mass of 238.0507826. 146 neutrons and 92 protons have an atomic mass of 239.934513. That 239.934513 amu is 1.88373002 amu or 1,754.68338 MeV more than the atomic mass of U-238. Another way to look at this 1754 MeV is in terms of energy per nucleon. Dividing that energy by 238 yields a binding energy of 7.4 MeV per nucleon. Compare that to the 8.8 MeV per nucleon for iron-56. What happens is that the binding energy per nucleon for stable nuclei increases with increasing mass for lighter elements and then starts decreasing with heavier elements. The binding energy remains positive, however. A nuclide with a negative binding energy cannot exist (for any length of time, that is).

That's possible, particular so since their parser does appear to have precedence correct. That said, their example should have been something more reasonable and helpful such as Make sure you enclose powers in brackets. For example, the cube root of x should be written as x^(1/3) rather than x^1/3 and 3x^2+3x should be written as 3^(x^2+3x). Hmm. I just assumed that it wouldn't understand log2(x) and used log(x)*5/log(2) in lieu of 5*log2(x).

Your article should mention that there are many such isotopes that decay via β+ emission and that Carbon-11 is but one example. β+ decay is one way, but not the only way, to produce positrons. Pair production can be a much more prolific source of positrons that β+ decay. I suggest that you read http://www.aps.org/meetings/unit/dpp/vpr2008/upload/LLNL_Chen.pdf. I gave two excellent references in post #25. I suggest you read them. I also referred to Type Ia supernova in post #27. I suggest you read up on Type 1a supernova as well. While the evidence for pair instability supernovae is currently rather scanty, there is plenty of evidence for Type 1a supernovae, so much so that scientists use them as "standard candles". Stop putting words in our mouths, steevey. Use of fallacies is strongly discouraged at this site. Nobody here has said that pair instability supernova or Type 1a supernova do not produce iron. In fact, they produce quite a bit of iron. The iron is produced by the supernova event in the case of a pair instability supernova or a Type 1a supernova. That the prior production of iron is the cause of the supernova event is true for core collapse supernovae but it is not true in general. You appear to be making hasty generalizations here. I suspect that you read an article on β+ emission and assumed that this is the mechanism (the one and only mechanism) by which positrons can be created. I suspect you read an article on core collapse supernova and assumed that this is the one and only mechanism that fuel a supernova.

Exactly. It is, however, close to -0K. There is a funny thing about a system with a negative temperature. Plop it down next to a system with a positive temperature. Heat will flow from the system with negative temperature to the system with positive temperature. The system with a negative temperature is "hotter" than the one with a positive temperature. A couple of lay references: A recent Science News article: http://www.sciencenews.org/view/generic/id/66435/title/Negative_temperature,_infinitely_hot Physics FAQ article: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html