Jenab

I have a mild case of tinitus: illusory noises of high pitch constantly humming on both sides of my head. The tone apparently in my left ear is higher than the tone apparently in my right ear. Both tones sometimes warble a slight bit in frequency, occasionally briefly causing some sort of musical chord. Clenching my jaw causes brief amplitude spikes which go away quickly whether I relax my jaw or not. Although I have a vivid musical imagination and can "play" often-heard songs in my head with great fidelity, this is distinct from the tinitus condition that I've described. I can most often ignore the tones.

Mathematics is the servant of empiricism. In itself, mathematics contains no epistemology: no reference to actual things in the physical world. Empiricism bring mathematics its input. Mathematics exists to prevent confusion, to balance accounts, to simplify, to make attempts at describing observables, to find evidence for relationships between observables, and to predict the future behavior of observables. But without empiricism, mathematics has no bearing whatever on the real world.

Departure from Vesta: 4 February 2004, 19h 12m UT JD 2453040.3 Arrival at Earth. 16 September 2004, 21h 36m UT JD 2453265.4 The transit time is therefore 225.1 days. The point of departure in heliocentric ecliptic coordinates can be calculated from a reduction of Vesta's orbital elements and the time of departure. The point of arrival in heliocentric ecliptic coordinates can be calculated from a reduction of Earth's orbital elements and the time of arrival. With these points (the endpoints of the intended trajectory) both known, it becomes much simpler to solve for the elements of the transfer orbit. Had only the departure time and position been known, it would have been necessary to construct a large table of TRIAL transfer orbits from Vesta to various points on Earth's orbit, and checking each of them to see whether Earth and the spaceship had the same transit time. In general, they would not; i.e., most of the trial transfer orbits would not be actual transfer orbits between the two planets. Only when you discovered a match between transit times would you have found a valid transfer orbit. Now that you have the arrival time, you can straightforwardly proceed to solve for the elements of the transfer orbit. If nobody ventures a serious attempt at a solution in a few days, I'll begin solving the problem myself. Jerry Abbott

Consider that the maximum separation for keeping the binary planet bound can't be more than Dmax = (1/3) R { ( Ma + Mb ) / Ms }^(1/3) In words: The components (both of them habitable planets) must have a maximum separation not greater than one third of the cube root of the ratio of the sum of the planets' masses to the mass of the star, multiplied by the distance between the star and the barycenter of the binary planet. Consider that R must be always within the liquid water temperature region around the star. Consider that, to a good approximation when 0.8 < (M/Msun) < 2.5 the luminosity of a star may be found from its mass by the relation: (L/Lsun) = (M/Msun)^4.15 Where Msun = 1.989E+30 kilograms, Lsun = 3.826E+26 Watts. So, following the Stephan-Boltzmann radiation law, R (in astronomic units) = (M/Msun)^2.075 Consider that the main sequence lifetime of a star is about Tms = 10.1 billion years (M/Msun) / (L/Lsun) Tms = 10.1 billion years (M/Msun)^(-3.15) Consider that a planet probably needs about 3 billion years from its formation to become habitable, thus (M/Msun)max = 1.47 Is there a minimum star mass? For a planet to be habitable, it must be freely rotating with a reasonable day/night cycle - i.e., not tidally locked to another body. The smaller the star is, the closer to it the binary planet must be to remain in the liquid water zone. A single planet in its sun's liquid water zone becomes tide locked to the star if the star's mass is less than about 0.8 suns. Things are tighter than that for binary planets. As that distance becomes smaller, the two components of the binary must get closer together to avoid the disruption of their pairing by the star's tides. Below some value of star mass, the maximum planet separation required by the low-mass star conflicts with the minimum planet separation required to prevent the two planets becoming tide-locked to each other. My guess is that if you require a planet to have a circular orbit with a radius that give it a constant subsolar temperature equal to Earth's average subsolar temperature (393.6 K), the minimum star mass for a binary habitable planet may be found from logbase10 Mmin = 0.117 - 0.574 logbase10 f Where Mmin is the minimum star mass and f is the greatest fraction of the orbital stability limit of the binary with respect to the star's tides, that you're willing to accept. In my test simulations, f=0.9 gives good behavior, so... Mmin = 1.39 So binary planets with both components habitable are probably OK only within a narrow window of star masses: 1.39 <= (M/Msun) <= 1.47 These stars are spectral types F1 to F3. On the other hand, if you can think of a way to have a habitable planet at a subsolar temperature equivalent to that of Mars (greenhouse effect?), you can get an f=9 dual habitable planet's star mass nearly down to one solar mass. logbase10 Mmin = 1.44 - 0.574 logbase10(R / 1 astronomical unit) Does anybody notice any spectacular goof-ups here? In case somebody wants to try arranging for a reasonable day/night cycle to occur from putting the binary components so close together that their mutual orbit provides the diurnal period, be wary of the Roche Limit. To estimate that, you'll need an estimate for the density of your component planets. Here's one I got from curvefitting Earth, the moon, and Mars: average density = 0.5286 (logbase10 M)^2 + 2.144 logbase10 M + 5.515 Where average density is in grams per cubic centimeter, and M is the planet's mass in Earth masses. One Earth mass is 5.976E+24 kilograms. (Mercury deviates from this curvefit, probably because it's close enough to the sun to have had volatile substances vaporized and escaped.) Jerry Abbott

Right. SOMEBODY is going to win the lottery, no matter what the odds were. Jerry Abbott

What we call time came into existence with the rest of the universe. It's a dimension, a measure of extent or separation, much the same as a spatial dimension. Perhaps the largest share of the confusion in this discussion comes from the assumption that the time dimension we recognize is the only possible one of its sort and that all events are related to this time dimension in a serial fashion. Let's move away from that. We will find that the difficulties disappear. Our universe came into existence as a statistical fluke permitted by the uncertainty principle. It's overall energy content is zero, but the positive and negative energy portions are separate. Zero in sum (when dE*dt > h-bar) is all the conservation of energy requires, and that does not imply a zero deviation. If we're careful, we can see that the statistical energy fluctuations that gave our universe existence is ubiquitous: it goes on everywhere and all the time. It gives us the Lamb shift, the Casimir effect, and Hawking radiation. Not all of these fluctuations are universes. Universes are complicated structures, and most uncaused quantum events must involve simpler ones. But all universes, including ours, originate as quantum fluctuations of zero energy. What I've said here isn't a scientific statement because it can't be tested. In principle, testing is impossible. A universe appears as a self-contained causal unity with a two-way bar to information ever entering from the outside or escaping from the inside. But it looks like a reasonable guess, which is better than the deity-guess because it does not require an additional entity (a god) whose existence is not subject to testing. (Event horizons, such as those of black holes, might permit matter to exit: however, they do not permit information to exit.) The time dimension of our universe has no relevance to anything that is not also a part of it. Anyway, it can be argued that time and space are perceptual only; i.e., they are the way our senses interpret the texture of potential differences created by the fields of force from non-singular sources. Jerry Abbott

Okay fellows. Here's my challenge. There existed a transfer orbit from asteroid Vesta (IAU number 4) to Earth with a departure date of 4 February 2004. (Go look up the orbital elements of Earth and Vesta; that's part of the work!) Find: The classical orbital elements of the transfer orbit, the transit time, and the change-of-velocity vectors at departure and at arrival. The classical orbital elements are: semimajor axis, eccentricity, inclination to the ecliptic, longitude of the ascending node, argument of perihelion, and Julian date of perihelion passage. The delta-vee vectors should be referred to heliocentric ecliptic coordinates. Please show your enough of your work to prove that you know what you're doing. High praise will reward the poster who provides the correct answers first! Good luck to all who try. Jerry Abbott

There's a lot of moralizing up tempests in teapots on the subject of cloning. Persons with especially favorable genetic endowments - naturally gifted physical and mental superstars - might be "saved" like a computer program and replicated if the original person dies prematurely, or duplicated to facilitate the natural re-infusion of positive traits in a weakened race. If a horse breeder could clone his best stallion, I expect that he would. The reason for the moralizing on cloning might be the very eugenic utility that cloning offers. We may take notice that in nature two similar species, or subspecies, with similar demands on the environment, are natural competitors. When there isn't enough for both groups, they usually struggle against one another for mastery, along with which comes principal access to the contested resources. One thing a competitor wants to do is deny advantages to its opponent. If cloning represents a technically feasible advantage to one group, we might expect that an opposed group would attempt to blackguard it with trumped up denunciations heavily larded with pseudo-morality. Whether this applies to our situation, I'll leave that to others to judge. Jerry Abbott