make a generalization relating the mass and lumosity of main sequence stars?
375382
The mass and luminosity of main sequence stars can be related by the Mass-Luminosity Relation.  The Mass-Luminosity Relation is when the logarithm of a stars luminosity is plotted on a graph against the logarithm of a stars mass.  Essentially the two plots fall almost exactly in a straight line on most occasions.  This indicates that the luminosity and mass of a main sequence star are directly related.  This indicates very strongly that the luminosity of a star depends very strongly on its mass.  This theory only holds up for main sequence stars, it does not include white dwarfs, red giants etc.
652025
Many stars are between 1 billion and 10 billion years old. Some stars may even be close to 13.7 billion years old, which is the observed age of the universe. (See Big Bang theory and stellar evolution.) They range in size from the tiny neutron stars (which are actually dead stars) no bigger than a city, to supergiants like the North Star (Polaris) and Betelgeuse, in the Orion constellation, which have a diameter about 1,000 times larger than the Sun—about 1.6 billion kilometers. However, these have a much lower density than the Sun.\n\nOne of the most massive stars known is Eta Carinae, with 100–150 times as much mass as the Sun. Recent work by Donald Figer, an astronomer at the Space Telescope Science Institute in Baltimore, Maryland, suggests that 150 solar masses is the upper limit of stars in the current era of the universe. He used the Hubble Space Telescope to observe about a thousand stars in the Arches cluster, a massive young star cluster near the core of the Milky Way, and found no stars over that limit despite a statistical expectation that there should be several. The reason for this limit is not precisely known, but the Eddington limit is part of the answer. The very first stars to form after the Big Bang may have been larger, up to 300 solar masses or more, due to the complete absence of elements heavier than lithium in their composition. This generation of supermassive stars is long extinct, however, and currently only theoretical.\n\nWith a mass only 93 times that of Jupiter, AB Doradus C, a companion to AB Doradus A, is the smallest known star undergoing nuclear fusion in its core. Smaller bodies are brown dwarfs, which occupy a poorly-defined grey area between stars and gas giants. The minimum mass a star can have is estimated to be in the vicinity of 75 Jupiters.
117146
It's the same way that scientists look at all massive measures: density*volume.  The density (ie the number of stars per square lightyear) is assessed by counting the frequency of galaxies and the size of galaxies.  The mass of galaxies can be inferred by the speeds of rotaion, and the mass will give you an idea as to how many stars there are in the galaxy by looking at the average mass of a star.  Then you get a sense of how many galaxies are in a given volume of space.  They use this, and extrapolate from the size of space (set by the tenets of general relativity, the Big Bang theory, the red-shift observed speed of expansion, etc), and they can thereby infer how many stars there are in the universe.\n\nIt's like the mass of the earth.  We can't figure it out with 10 kilograms, or even 100 kilograms, but we can get an idea as to the magnitude of the mass.  With magnitude, i mean the number of digits to the left of the decimal place.  We call the difference between 10 and 100 "one order of magnitude," and the difference between 100 and 100,000 "three orders of magnitude."  Such scales are commonly used in science for things where exact numbers are impossible to get, but the range of magnitude is important.  Some such commonly known scales are the measure of sound in decibles, the Richter scale for earthquake power, and the pH scale for acidity.  With a pH of seven, one can infer that a liter of water has 3,344,000,000,000,000,000 hydronium ions per liter, whereas it only has 3,344,000,000,000,000 hydronium ions per liter at a pH of 10.  In these cases, the magnitude, rather than the exact number, is the matter of interest.\n\nIt's the same in counting stars.  We can't know the exact number of stars, especially since they constantly form and die--but we can get a pretty good idea as to the magnitude of the number by looking at stellar density and extrapolating the size of the universe.
864425
One source that breaks down these classifications by temperature, or maybe it was only color photometry (I don't recall) is Kenneth Lang's Astrophysical formula:\n\nhttp://www.amazon.com/Astrophysical-Formulae-Radiation-Processes-Astrophysics/dp/3540296921/sr=1-1/qid=1163374728/ref=sr_1_1/102-7735916-8685767?ie=UTF8&s=books\n\nVolume I has some tables I think you will find helpful.  You might need to do a little interpolation...\n\nanother place to look would be the iau website http://www.iau.org . The IAU is the kind of group that would define a standard, though this might be too detail oriented for them to mess with.\n\nYou will be hard pressed to find an equation, however.  You are going to be stuck with a lookup table.
1035251
- The mass of the protostar, the gestation period is inversely proportional to the mass\n- The amount of turbulence and the rotation speed of the nebula
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Well, we look at the light and determine "this light is about a million years old." :-) Not really, but that's the general idea.\n\nFor galaxies of very large distance, we can determine how fast the galaxy is receding from us. The easiest way is the Doppler shift - we can see the galaxy (obviously) and therefore astronomers can determine how big it is, what type of stars must be in them, and therefore what color light we should see. However, the light is slightly redder than what models predict (and what nearby galaxies have). We can measure this "red shift", plug it into Doppler's equation, and determine how fast the galaxy is moving. (This is similar to how when a police siren passes you, it drops its pitch - and how much it changes is proportional to how fast the police car is going.)\n\nThen there's a nice relationship called Hubble's Law, which states that the farther a galaxy is from us, the faster it's receding. This is a consequence of the Big Bang, and indeed the constant in this equation must be the reciprocal of the age of the universe. So we can then estimate (within a few thousand years or so) how far the galaxy must be from us.\n\nFor closer galaxies, there are some other techniques. There are certain types of variable stars (stars that, every few hours or days, increase and decrease their brightness) that in order to be stable must vary between two known brightnesses. Of course the brightness isn't exact, but the average among the thousands of variables in a galaxy is very close to exact. Now when we measure brightness (actually, apparent magnitude) from Earth, we see stars dimmer if they're farther from us. But because we know the absolute magnitude of these variables, and we can measure their apparent magnitude, we can calculate the distance we must be for them to become this much dimmer.\n\nThere are actually a lot of techniques, which work better for certain distance ranges. Look up the "distance ladder" if you're interested.
201708
Several different ways depending on the distances involved.\n\nFor close stars, we look at where the star appears to be in the sky at times about half a year apart. Think of looking at your outstretched thumb through your left eye, and then your right eye. The thumb appears to be in a different position with respect to a distant building. In the same way, a star will appear to be in a slightly different position when we look at it from different ends of the earth's orbit. The amount of shift depends on the distance to the star and that allows us to figure out the distance. This method is called paralax.\n\nFor slightly more distant stars, we look at clusters of stars and measure their apparent motion across the sky over a course of *years*. Just as train tracks appear to converge at the horizon, the motions of the star will appear to converge. The rate of convergence is related to how far away the cluster is.\n\nWith these methods, we get enough stars to do statistical analyses of the brightness of the stars versus their chemical composition and other aspects of their spectrum. With this knowledge, we can estimate the distances to further stars by just comparing their spectrum to that of already measured stars. Scientific models of stars are used at this stage.\n\nFarther away than this, we look for 'standard candles', that is, stars of known brightness. By comparing the brightness they appear to be versus their actual brightness, we can estimate their distances. A particular type of 'standard candles' are the Cepheid variables. Their actual brightness depends on how fast they vibrate. Since we can see these stars in other galaxies, we can use them to determine the distances to those galaxies.\n\nFinally, after we know the ditances to some galaxies, we can measure the rate at which they move apart as a function of distance. By measure red-shift (hence speed) of more distant galaxies, we can determine their distances.
902366
Heres a web site that discusses the fate of stars of 20 solar masses and up:\n\nhttp://observe.arc.nasa.gov/nasa/space/stellardeath/stellardeath_3.html
872306
1.  Red dwarf\n2.  Red giants or red supergiants\n3.  White dwarf
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I think maybe the separation is smaller than the resolving power of my eyes rather than the angular separation of my eyes. So I can't resolve the two sources and just see one bright star. \n\nBest of luck - Mike
435493
It's mass.  And its not just in star clusters.  Mass is the only major characteristic of stars.  Almost everything else can be derived (temperature, evolutionary track, luminosity) can be determined by their mass.
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The brightest stars, the ones you can see with the naked eye, are all B8 and B9.  Some of the dimmer ones are of other classes--B,A,F, and perhaps some cooler classes, too.
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Largest Star (By Size) - VV Cephei - 1900 times diameter of sun\n\nMost Luminous Star - LBV 1806-20 - 40,000,000 times luminous than the sun\n\nHowever, the brightest objects in our universe are the quasars... Check the links below for more info\n\nI hope these were the answers u were lookin for...
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It depends on whether you are talking about a planet in our solar system or an extra solar planet. I'll describe both.\n\nFor a planet in our solar system, the apparent size can be directly measured optically. One way is to take a picture of the planet through the telescope and measure the size of the picture with a ruler. Calculations based on the focal length of the telescope will tell you how many degrees (or fractions of a degree, since it will be less than 1) wide the planet appears to be in the sky for a given measured size on the photograph. Then the distance to the planet must be measured, which is not so easy. Basically it comes from triangulation to nearby asteroids combined with kepler's laws. Knowing the distance and apparent size allows you to calculate the real size and volume. To get the density, you need to know the mass. If the planet has Moons, the orbital period of the moons gives you the planet's mass from orbital mechanics calculations. If the planet has no moon, like Mercury and Venus, then theoretically their mass can be gotten from the effect their gravity has on the orbits of other planets, asteroids and comets, but this is not so accurate since those other objects don't usually pass close enough to the planet we want to measure to show much of an effect on their orbits. Fortunately we have sent space craft to Mercury and Venus and measured their mass directly by the effect their gravity had on the space craft's path.\n\nFor a planet orbiting another star, it is not so easy, because such planets cannot even be seen. Their presence is deduced from tiny Doppler shifts of the star they orbit. A planet does not just orbit a star, the star and planet orbit each other around their common center of gravity. Since the star is much heavier than the planet, it doesn't move much, but it does move, and modern instruments can measure the tiny Doppler shift in the star's light to get the motion of the star. Stellar evolution models tell us how heavy the star is and orbital mechanics tell us how heavy the planet is. (We can calculate the mass of double stars using orbital mechanics and the Doppler shift of each star's light, but we have no direct knowledge of the mass of single stars.) If the planet also happens to orbit in a plane parallel to our line of site, it will cross directly in front of the star once each orbit, like Venus sometimes crosses the face of our sun as seen from Earth. When it does, it blocks a small percentage of the star's light and the star looks slightly dimmer. If the star dims by 1%, then the disk of the planet has 1% the area of the disk of the star. Again, from stellar evolution models, we can deduce the diameter of the star and so get the diameter of the planet. (We can measure the diameter of some large, nearby stars, directly with the largest telescopes and adaptive optics, but for most stars we have no direct knowledge of their diameter.)\n\nThere is much more detail, but enough is enough, don't you think?
232112
planets, stars, and quasars
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Size of Star depends on how it was formed originally. I don't think it could be said precisely. U can take the size of our sun as a measure. Radies=6400kms
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T Tauri stars have bipolar outflows, to the best of my knowledge.  They form Herbig-Haro Objects when the collide with slower matter from the interstellar medium.  They might not always show up with T Tauri stars because of nearby nebula, but my astronomy professor (James Kaler, UIUC) assures me that they are there.\n\nIf you're talking about mass outflows that the T Tauri stars outputs in addition to the bipolar flows, then I'm sure Doppler shifting can be used.  The speeds for the regular outflows should be pretty similar to that of the T Tauri itself, whereas the bipolar flows (depending on orientation to earth, of course) should be much higher.  I hope this helped!