<p>seems my posts are oddly cut off when I look a them...anybody else notice this (there should be along calculus derivation of gravitational contraction in the first post.</p><p>For the time being, a repost in full:</p><p>As it currently exists (and imo will continue to exist) the Standard Model of stellar evolution claims that the stars is powered by nuclear fusion of various elements (mostly hydrogen). <br /> <br />Many people have problems with this statement, and produce alternative models, like the "electric sun" theory (

http://www.electric-cosmos.org/sun.htm). Ignoring some of the problems with the underlying premisis (that sunspots are holes to the interior for instance) there is a fundamental question which must be answered by any stellar model. <br /> <br /><strong>Where does the energy come from?</strong> <br /> <br />stars radiate energy and very high rates, for a very, very, long time. Even if you believe that the sun was much dimmer in the past, say even half as bright, you are dealing with a large amount of energy. This reduction, at most, can add only 2 orders of magnitude to any life-time estimate of a stellar model. This is because you can only reduce the luminosity by 100%, or 10^2. An order of magnitude is a power of ten. As such if a energy scheme is off by a factor greater than 100x the required value, it is not a viable energy source by itself. <br /> <br />As an example for such an analysis, (which I was required to write up for an advanced lab course) I give you the following (if the math gets you, skip on a bit) treatise on using gravitational contraction as an energy source. This is the same energy source that makes a brick hurt if you drop it on your foot. <br /> <br />The short version: The total time an object can radiate at a given luminosity, is determined by dividing the total energy provided by the method (in this case gravitational potential energy U) by the luminosity. I.e. T = U/L. For the sun, this gives a lifetime of only 30 million years (before it's <em>gone</em> competely) and thus any model that relies on gravitational contraction a significant source of energy, will not work. <br /> <br />The Long Version: <br /> <br />A note on Notation: As the format from word doesn't translate well, any terms that are 10 followed by a number (e.g. 1041) should be read 10^41, as the superscript may not have translated well. I tried to catch all the instances, but I may have missed one or two. <br /> <br /> Can gravitational contraction be a viable energy source to power the sun? Ignoring the effects hydromagnetic dynamics, virial theorem, and other complicating details, (which are shown to be unnecessary in this analysis) this can be easily determined by considering the amount of energy available to the sun via contraction, and considering the rate of contraction required. <br /> <br /> All contracting, or falling, objects are converting gravitational potential energy into kinetic. The amount of potential energy available to a spherical object is: <br /> <br />U ~ GM^2 / R <br /> <br />G is the gravitational constant (6.67 x10-11), M is the mass of the object, and R is the radius. The sun has a radius of 695,000 km (~700 million meters), and a mass of 2x1030 kg. . This is derived from the fact the sun radiates a spectrum that approximates a blackbody curve (with an excess in the infrared, and deficiency in the ultraviolet) with a shape that puts the sun’s temperature is approximately 6000o K. If luminosity equals: <br /> <br />L = 4 * π * σ * R^2 * T^4 <br /> <br />Then the sun then radiates energy at ~4 x 1026 joules per second at the surface. <br /> <br /> If energy radiated by the sun is due entirely to the gravitational potential energy, then the luminosity of the sun (the energy radiated per unit time) is given by: <br /> <br />L = dE/dt = dU/dt <br /> <br />By the chain rule we can put this in terms of the radius, allowing us to consider the change of radius due to the energy loss. <br /> <br />L = dU/dt = dU/dR * dR/dt <br /> <br />Substituting the spherical potential energy in for U, we obtain: <br /> <br />L = - d/dt[ -GM2/R ] = - GM2/R2 dR/dt <br /> <br />This equates the change per second of the potential energy to the change per second of the radius. <br /> <br />dR/dt = L / GM^2/R^2 = L*R / U <br /> <br />The value of U, obtained from the figures above, is 3.82 x 10^41 J. Thus dR/dt is: <br /> <br />4 x 1026 W * 7 x 108 meters / 3.82 x 1041 J = 7.3 x 10-7 meters per second <br /> <br />This equates to 23 meters a year. At that rate, the sun shrinks from 7 x 10^8 meters to zero in ~30 million years. While this is easily long enough to sustain the sun for recorded history, it does not match the radioactive dating of the earth to ~4.5 billion years. It is an easy premise to accept that the earth must have formed during, or after the sun’s formation. Especially if one considers the earth’s nearly circular orbit about the sun, good evidence it formed in place as opposed to being a captured object (which should result in much more elliptical orbits) to talkorigins.org, thirty million years ago primitive monkeys didn’t exist, let alone the older (and often extinct) species. The K-T extinction event (thought to be the demise of the dinosaurs) is dated to 65 million years ago (sdnhm.org). Under gravitational contraction the sun wouldn’t exist that long. In order for the sun to radiate at it’s current luminosity for the age of the earth, it would have to have a radius of ~10^11 meters. As the earth is only 150 x10^9 meters from the sun, the earth would have been enveloped by the sun in the beginning, most likely rendering earth’s formation impossible. <br /> <br />An even shorter analysis is merely comparing the observed sun’s luminosity, to the potential. U/L gives ~10^14 seconds, or 30 million years (as expected). A similar analysis for Sirius (U/L) produces an even shorter time period of ~10^13 seconds, or 3 million years. Sirius is larger (R= 2*Rsun) and more massive (M = 2*Msun), giving it a higher store of potential energy, but it has a much higher luminosity as well, at 23 Lsun. This higher mass, larger radius trend, but exponentially higher luminosity, is typical of ninety percent of the stars in existence. The other ten percent are stars that are bloated, having a much higher radius, and luminosity for a given mass. The higher luminosity is due to a greater surface area, as the temperature is lower. A typical example of such bloated red giants is Betelguese. With a mass roughly equal to 15 solar masses, radius of about 650 solar radii, and a luminosity ofapproximately 70,000 times that of the sun (uiuc.edu). Under those conditions, Betelguese lasts for a mere 5 x 10^9 seconds, or about 150 years. <br />These time scales do not suffice for the full life time of the star, though they do apply to the dynamics of star formation as it coalesces out of interstellar gas and dust (which is a gravitational contraction phase). The time scales here approximately match those sited at southalabama.edu (except for betelguese, which is off by 10^3 for some reason). <br /> <br />Any mechanism for the power of the sun must explain the initial origin of the released energy. The Electric sun model must supply an energy source to separate the charges and induce the “lightning” that is the sun. The first response is usually to claim that currents of plasma are carrying charge, however something needs to drive these currents. Convection requires a temperature differential, which requires and energy source. Gravitational contraction cannot supply the energy needs of the sun for the duration required (4.5 billion years) at the current luminosity. <br /> <br />According to nasa.gov the sun’s luminosity, after protostar formation, was about 50% of the current output. Even reducing the luminosity of the sun for the entire duration to this new, lower, output will not suffice, as our timescale for gravitational contraction is orders of magnitude to short. <br /> <br /> <br /> <br /> <br />Electronic References <br /> <br />

http://image.gsfc.nasa.gov/poetry/ask/a11496.html <br /> <br />

http://www.southalabama.edu/physics/lectures/clark/LectPH101/starform.htm <br /> <br />

http://www.astro.uiuc.edu/~kaler/sow/betelgeuse.html <br /> <br />

http://sdnhm.org/fieldguide/fossils/timeline.html </p> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>