Piltdown man Posted May 29, 2009 Share Posted May 29, 2009 (edited) The discovery that galaxies, or island universes, were exhibiting red-shift in degrees that increased with distance, showed that the universe was/is not static. But it could show that the universe is either expanding, or collapsing, or, more likely, a mixture of both. Why then, and by whom, was it decided to go with the expanding option. Could it have been more acceptable to have "Gods" work grow larger, and perhaps more magnificent, than for it to be seen as possibly collapsing? Edited May 29, 2009 by Piltdown man typo Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted May 29, 2009 Share Posted May 29, 2009 The discovery that galaxies, or island universes, that were exhibiting red-shift in degrees that increased with distance, showed that the universe was/is not static. But it could show that the universe is either expanding, or collapsing, or, more likely, a mixture of both. Why then, and by whom, was it decided to go with the expanding option. Could it have been more acceptable to have "Gods" work grow larger, and perhaps more magnificent, than for it to be seen as possibly collapsing? If it was shrinking it would be blue-shifted. Link to comment Share on other sites More sharing options...
purintjp Posted May 30, 2009 Share Posted May 30, 2009 Maybe it's already started to contract and we don't know it yet. The light we see is pretty old. Our closest galaxy neighbor Andromeda is coming towards us now. Could be just gravitational attraction, though. Link to comment Share on other sites More sharing options...
Martin Posted May 30, 2009 Share Posted May 30, 2009 The discovery that galaxies, or island universes, were exhibiting red-shift in degrees that increased with distance, showed that the universe was/is not static. You have the story backwards, Piltdown. General Relativity was proposed in 1915, before the discovery of redshift-increase-with-distance (before the discovery of Hubble's Law) General Relativity implies that the universe's geometry is not static. This conclusion could be drawn without anyone observing redshift. In fact Alex Friedman derived the mathematical model of expanding universe in 1921---this was still some years before Hubble observed anything. There are many ways to check GR and many tests have been devised, starting with studying the orbit of Mercury. Including lightbending, binary pulsars, the GPS satellites, and so forth. GR is a coherent whole. If you can check GR by testing it against other kinds of observations, you get the expanding universe model as a byproduct. So far it has passed all the tests with admirable precision. This lends a lot of credibility to the universe model derived from it. The model itself can then be evaluated by fitting observation data to it. It is a simple model with few adjustable parameters and gives a remarkably good fit. Based on the standard model the masses of data which it fits, we then have pretty good idea of what to expect. Maybe it's already started to contract and we don't know it yet... Well that's an entertaining idea, but it isn't consistent with our theory of gravity which has been tested rather thoroughly (since proposed in 1915) and it is not consistent with our dynamic model of the unverse which dates back to 1921 and has also been well tested (especially since the 1990s with a bunch of new space instruments.) Right now cosmology is in a mode of refining the parameters. (And finding out more about the physics underlying them.) Any damn fool thing is possible, but don't hold your breath. Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted May 30, 2009 Share Posted May 30, 2009 You have the story backwards, Piltdown. General Relativity was proposed in 1915, before the discovery of redshift-increase-with-distance (before the discovery of Hubble's Law) General Relativity implies that the universe's geometry is not static. This conclusion could be drawn without anyone observing redshift. In fact Alex Friedman derived the mathematical model of expanding universe in 1921---this was still some years before Hubble observed anything. There are many ways to check GR and many tests have been devised, starting with studying the orbit of Mercury. Including lightbending, binary pulsars, the GPS satellites, and so forth. GR is a coherent whole. If you can check GR by testing it against other kinds of observations, you get the expanding universe model as a byproduct. So far it has passed all the tests with admirable precision. This lends a lot of credibility to the universe model derived from it. The model itself can then be evaluated by fitting observation data to it. It is a simple model with few adjustable parameters and gives a remarkably good fit. Based on the standard model the masses of data which it fits, we then have pretty good idea of what to expect. Well that's an entertaining idea, but it isn't consistent with our theory of gravity which has been tested rather thoroughly (since proposed in 1915) and it is not consistent with our dynamic model of the unverse which dates back to 1921 and has also been well tested (especially since the 1990s with a bunch of new space instruments.) Right now cosmology is in a mode of refining the parameters. (And finding out more about the physics underlying them.) Any damn fool thing is possible, but don't hold your breath. In the current model the expansion is accelerating, correct? Is that consistent with GR? Or did they have to add (and start searching for) a factor to make it work? Link to comment Share on other sites More sharing options...
Piltdown man Posted May 30, 2009 Author Share Posted May 30, 2009 It matters not that GR predicted a dynamic universe, even though Einstein didn't realise the full implication of his equations. The point is that there was no possible way that it could have been known which galaxies we were moving away from, and which were moving away from us. Consider the "raisin bread" analogy. All raisins are moving apart, but there is an overall movement in one direction, away from the baking tray. The analogy is in fact, only half a universe, the other half is beneath the baking tray. There are two points away from which all could be moving. The first is the centre, in the event of an all expanding universe. The second is the point of maximum expansion from which all could be retreating. A moments thought and it will be seen that red-shift will be exhibited in both scenarios. Link to comment Share on other sites More sharing options...
Martin Posted May 30, 2009 Share Posted May 30, 2009 In the current model the expansion is accelerating, correct? Is that consistent with GR? Or did they have to add (and start searching for) a factor to make it work? Acceleration is not consistent with that one particular early version of GR with zero cosmo constant, and it is consistent with several other versions of GR. This is one of the things that makes the discovery of acceleration exciting. It enables and motivates choice. I guess everybody knows that acceleration is consistent with the original GR, that Einstein put a positive cosmo constant into. But fewer people are aware of another GR which he proposed in 1919, called "unimodular" GR. It is very interesting. The cosmo constant occurs in it in a way that I think is more natural. Unimodular is now attracting some attention. Acceleration was discovered in 1998, that's when the two key papers were published. If you would like to study what the situation was about the cosmo constant before that, there is a paper by Nobel laureate Steven Weinberg, from 1989, called "The Cosmological Constant Problem". It seems that there were always mainstream figures who did not take for granted that it was zero. Raphael Sorkin predicted a small positive value back in the 1980s, based on quantum gravity theoretical grounds. It's interesting. If you look carefully at what the smart mainstream people were doing, that parameter was always there. It didn't have to be added in 1998 as a "fix". But you are welcome to think of it as a fix, if that pleases you. After all, what is one adjustable parameter in an otherwise very elegant theory? Here's the latest paper on unimodular GR (the 1919 invention, a dark horse contender) http://arxiv.org/abs/0904.4841 Merged post follows: Consecutive posts merged Could it have been more acceptable to have "Gods" work grow larger, and perhaps more magnificent, than for it to be seen as possibly collapsing? Piltdown, I don't understand your question. What are you implying or suggesting? Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted May 31, 2009 Share Posted May 31, 2009 Acceleration is not consistent with that one particular early version of GR with zero cosmo constant, and it is consistent with several other versions of GR. This is one of the things that makes the discovery of acceleration exciting. It enables and motivates choice. I guess everybody knows that acceleration is consistent with the original GR, that Einstein put a positive cosmo constant into. But fewer people are aware of another GR which he proposed in 1919, called "unimodular" GR. It is very interesting. The cosmo constant occurs in it in a way that I think is more natural. Unimodular is now attracting some attention. Acceleration was discovered in 1998, that's when the two key papers were published. If you would like to study what the situation was about the cosmo constant before that, there is a paper by Nobel laureate Steven Weinberg, from 1989, called "The Cosmological Constant Problem". It seems that there were always mainstream figures who did not take for granted that it was zero. Raphael Sorkin predicted a small positive value back in the 1980s, based on quantum gravity theoretical grounds. It's interesting. If you look carefully at what the smart mainstream people were doing, that parameter was always there. It didn't have to be added in 1998 as a "fix". But you are welcome to think of it as a fix, if that pleases you. After all, what is one adjustable parameter in an otherwise very elegant theory? I guess my point was that if the parameter could be adjusted for an acceleration, could it not be adjusted for a deceleration, and since enough deceleration leads to contraction... then how can it be inconsistent with the theory? Having said that, bringing things back to another thread with respect to time frames, if the contraction started everywhere at "once", we would notice a blueshift locally far before waiting for the blueshift from the far reaches of the universe, correct? Link to comment Share on other sites More sharing options...
Piltdown man Posted May 31, 2009 Author Share Posted May 31, 2009 The question is as stated. Why was the fact that galaxies could be seen to be exhibiting red-shift in degrees that increased with distance, reported as evidence that the univere is expanding, when it could not possibly have been known which were moving away from us, and from which were we moving away? Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted May 31, 2009 Share Posted May 31, 2009 The question is as stated. Why was the fact that galaxies could be seen to be exhibiting red-shift in degrees that increased with distance, reported as evidence that the univere is expanding, when it could not possibly have been known which were moving away from us, and from which were we moving away? All but the most local are red-shifted. That is evidence they are moving apart from us. From our rest frame it is them moving, from their rest frame it is us moving. Link to comment Share on other sites More sharing options...
NowThatWeKnow Posted May 31, 2009 Share Posted May 31, 2009 ...when it could not possibly have been known which were moving away from us, and from which were we moving away? And that is why it is called relativity, It is all relative. Link to comment Share on other sites More sharing options...
purintjp Posted June 1, 2009 Share Posted June 1, 2009 You have the story backwards, Piltdown. General Relativity was proposed in 1915, before the discovery of redshift-increase-with-distance (before the discovery of Hubble's Law) General Relativity implies that the universe's geometry is not static. This conclusion could be drawn without anyone observing redshift. In fact Alex Friedman derived the mathematical model of expanding universe in 1921---this was still some years before Hubble observed anything. There are many ways to check GR and many tests have been devised, starting with studying the orbit of Mercury. Including lightbending, binary pulsars, the GPS satellites, and so forth. GR is a coherent whole. If you can check GR by testing it against other kinds of observations, you get the expanding universe model as a byproduct. So far it has passed all the tests with admirable precision. This lends a lot of credibility to the universe model derived from it. The model itself can then be evaluated by fitting observation data to it. It is a simple model with few adjustable parameters and gives a remarkably good fit. Based on the standard model the masses of data which it fits, we then have pretty good idea of what to expect. Well that's an entertaining idea, but it isn't consistent with our theory of gravity which has been tested rather thoroughly (since proposed in 1915) and it is not consistent with our dynamic model of the unverse which dates back to 1921 and has also been well tested (especially since the 1990s with a bunch of new space instruments.) Right now cosmology is in a mode of refining the parameters. (And finding out more about the physics underlying them.) Any damn fool thing is possible, but don't hold your breath. Originally Posted by purintjp Maybe it's already started to contract and we don't know it yet... Well that's an entertaining idea, but it isn't consistent with our theory of gravity which has been tested rather thoroughly (since proposed in 1915) and it is not consistent with our dynamic model of the unverse which dates back to 1921 and has also been well tested (especially since the 1990s with a bunch of new space instruments.) Right now cosmology is in a mode of refining the parameters. (And finding out more about the physics underlying them.) Any damn fool thing is possible, but don't hold your breath. Does this mean that we now know exactly when the universe will start it's contraction ? How can we possibly know what the current state of the universe is when most of what we see is not current time ? It would seem that the biggest changes would start with the farthest objects. Would they collapse towards us faster than the speed of light in reverse of what is happening now ? Link to comment Share on other sites More sharing options...
Piltdown man Posted June 1, 2009 Author Share Posted June 1, 2009 Re posts 10 and 11. Quite so. So why the assertion that the universe is expanding when the red-shift displayed could equally well state collapse. "Acceleration" is another example of less than accurate reporting. If the universe is collapsing, then in some directions it would indeed be acceleration. If not, then it is an increase in the rate at which galaxies are moving apart, and this is how it should have been reported. Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted June 1, 2009 Share Posted June 1, 2009 Re posts 10 and 11. Quite so. So why the assertion that the universe is expanding when the red-shift displayed could equally well state collapse. "Acceleration" is another example of less than accurate reporting. If the universe is collapsing, then in some directions it would indeed be acceleration. If not, then it is an increase in the rate at which galaxies are moving apart, and this is how it should have been reported. How can a redshift indicate collapse? Link to comment Share on other sites More sharing options...
Martin Posted June 1, 2009 Share Posted June 1, 2009 ...Does this mean that we now know exactly when the universe will start it's contraction ? Where did you get the idea that the universe is destined to contract? Was it a professional source from the last ten years? I am curious to know. Please find an online source and give us the URL web-address so that we can evaluate the source. How can we possibly know what the current state of the universe is when most of what we see is not current time ? It would seem that the biggest changes would start with the farthest objects... Before 1998 (when the acceleration was discovered) it was believed that expansion was slowing. Professional cosmologists took seriously the possibility that it would eventually stop---all at the same time throughout according to their models---and reverse. Those models with collapse do not fit the data that has become available in the past 10 years, so they have been discarded. But if we did live in that kind of universe, we would see the end of expansion FIRST IN NEARBY objects---by nearby I mean within 10 to 100 million lightyears. There is no reason to expect such a slowing down/reversal to happen on a significantly inhomogeneous schedule. The universe appears to be approximately uniform. If contraction was destined to occur---if we lived in that kind of universe---then we would see SLOWING DOWN in nearby objects' recession speeds long before contraction actually began. And I mean billions of years before---in a universe resembling ours but lacking the acceleration factor, so that eventual collapse might be predicted, we would see ADVANCE WARNING in the behavior of nearby stuff long long long before actual contraction began. ...changes would start with the farthest objects... No. There is no rational reason to suppose that. But like I say, anything is possible! Pink unicorns could magically appear and begin to eat the stars! And for some unknown reason the unicorns could appear first only in distant locations far from the Milky Way, so that we would not see them at first! I don't know why they would take special care to avoid our neighborhood, at first, but they might! And then we wouldn't know! Anything is possible. What dististinguishes reasonable possibilities from unreasonable is that they conform to mathematical models based on tested physics laws, fitted to observation data. Merged post follows: Consecutive posts mergedAcceleration is not consistent with that one particular early version of GR with zero cosmo constant, and it is consistent with several other versions of GR. I guess my point was that if the parameter could be adjusted for an acceleration, could it not be adjusted for a deceleration, Well sure! The parameter was always there. If a really radical slowing had been observed they could have tried fitting the data by giving Lambda a negative value. But as I'm sure you realize, you get natural slowing even with zero Lambda, just from the matter density. and since enough deceleration leads to contraction... then how can it be inconsistent with the theory? I don't know. You tell me! I certainly didn't say that contraction was inconsistent with theory. Some models (which don't fit the data) actually predict contraction! So how could contraction be inconsistent? Maybe there is a verbal confusion here. Consistency is broader than implication. A theory can have several different outcomes consistent with it. Something is consistent as long as it is not ruled out, as long as it is possible with some adjustment of the the parameters. Link to comment Share on other sites More sharing options...
lucaspa Posted June 1, 2009 Share Posted June 1, 2009 Consider the "raisin bread" analogy. All raisins are moving apart, but there is an overall movement in one direction, away from the baking tray. The analogy is in fact, only half a universe, the other half is beneath the baking tray. If you were a raisin in the bread, some of the raisins would be moving toward you even tho the bread were expanding. That isn't the case with the universe. No matter which direction we look, galaxies beyond our local group are all moving away from us. There are two points away from which all could be moving. The first is the centre, in the event of an all expanding universe. The second is the point of maximum expansion from which all could be retreating. A moments thought and it will be seen that red-shift will be exhibited in both scenarios. The universe doesn't have a "centre" as you are using the term. And, if all were collapsing from a maximum expansion, those at the "edge" of the maximum expansion would look like they are moving towards us. They would be blue-shifted, not red-shifted. I suggest you read the Scientific American article "Misconceptions about the Big Bang". Merged post follows: Consecutive posts mergedThe question is as stated. Why was the fact that galaxies could be seen to be exhibiting red-shift in degrees that increased with distance, reported as evidence that the univere is expanding, when it could not possibly have been known which were moving away from us, and from which were we moving away? For expansion, it doesn't matter whether they are moving away from us or we moving away from them, or both. In any of these scenarios, the universe must be expanding. As it happens, every galaxy (beyond the local group) is moving away from every other galaxy. They would all see a red shift from every galaxy beyond their own local group. (Within our own local group of galaxies, there are a few that are moving towards our galaxy and show a blue shift.) Merged post follows: Consecutive posts mergedWhy then, and by whom, was it decided to go with the expanding option. Because only that option was consistent with the data. Could it have been more acceptable to have "Gods" work grow larger, and perhaps more magnificent, than for it to be seen as possibly collapsing? Since many of the physicists who accepted the expansion were either agnostics or atheists, they would not have been swayed by any appeal to deity. Remember that the preceding accepted theory was Steady State, where supposedly "God's work" just remained static. Theists were content with that. As several people pointed out, if the universe were collapsing we would be seeing blue shifts, not red shifts. Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted June 1, 2009 Share Posted June 1, 2009 I don't know. You tell me! I certainly didn't say that contraction was inconsistent with theory. Some models (which don't fit the data) actually predict contraction! So how could contraction be inconsistent? Maybe there is a verbal confusion here. Consistency is broader than implication. A theory can have several different outcomes consistent with it. Something is consistent as long as it is not ruled out, as long as it is possible with some adjustment of the the parameters. No confusion. That is what I meant to ask - So collapsing (as well as expanding) is consistent with GR, but not with observation. Link to comment Share on other sites More sharing options...
Martin Posted June 1, 2009 Share Posted June 1, 2009 No confusion. That is what I meant to ask - So collapsing (as well as expanding) is consistent with GR, but not with observation. Definitely! In fact (although the current model predicts continued expansion) it could turn out that somehow sometime in the remote future the dark energy factor may change so that (then with different parameters in the model) we get a collapse. There is currently no indication of that, no reason to suspect it. But cosmologists are naturally interested in that as a possibility and on the lookout for anything that might enable it to happen. would be interesting. We are talking tens of billions of years, not anything abrupt. For practical purposes one can ignore it. but still nice to think about. BTW i just ran across an excellent video talk about early universe and CMB: Nobelist George Smoot talking about the CMB and what things it tells us. Very skillful presentation with animated graphs, shows what bumps in the power spectrum mean, and why. Part of the "Honeywell Nobel" lecture series. http://www.revver.com/video/827006/the-history-and-fate-of-the-universe-part-1-of-9/ http://www.revver.com/video/827106/the-history-and-fate-of-the-universe-part-2-of-9/ http://www.revver.com/video/827171/the-history-and-fate-of-the-universe-part-3-of-9/ http://www.revver.com/video/832550/the-history-and-fate-of-the-universe-part-4-of-9/ http://www.revver.com/video/832599/the-history-and-fate-of-the-universe-part-5-of-9/ http://www.revver.com/video/832643/the-history-and-fate-of-the-universe-part-6-of-9/ http://www.revver.com/video/832679/the-history-and-fate-of-the-universe-part-7-of-9/ http://www.revver.com/video/832724/the-history-and-fate-of-the-universe-part-8-of-9/ http://www.revver.com/video/832788/the-history-and-fate-of-the-universe-part-9-of-9/ See what you think. It is a public lecture, so not mathematical. But Smoot is very skillful with verbal analogies and animated graphics. Great communicator. Delivers a whole lot of insight and information, on a general audience level. Link to comment Share on other sites More sharing options...
purintjp Posted June 3, 2009 Share Posted June 3, 2009 Is the average density of the universe one of the defining parameters ? If so, I was wondering how that number was derived. Could it be off more than we posit ? Was it adjusted to reflect recent discoveries like super-massive black holes in galaxy centers or is that to small to matter ? Does it reflect estimates from current time observations or does it compensate by calculating the actual positions of far distant objects in current time ? What about dark matter or energy affecting the density ? Link to comment Share on other sites More sharing options...
Martin Posted June 3, 2009 Share Posted June 3, 2009 Is the average density of the universe one of the defining parameters ?If so, I was wondering how that number was derived. ... That is a beautiful question. You must learn how to calculate the critical density. I suspect you were educated in some place where young people are taught to calculate stuff and not to fear numbers. I long for the company of people who like to calculate stuff. Indulge me. You take the Hubble rate, say H = 74.2 km/s per megaparsec, and simply do this with it 3 c^2 H^2/(8 pi G) That is called the critical density, expressed as an energy density. The beautiful Friedman equation which describes an homogeneous isotropic universe says that if space has this density then it will be FLAT, in the sense that Euclidean 3D geometry is flat, angles of triangles adding up to 180. Volumes of spheres being (4 pi/3)R^3. and all that. If the density is significantly greater than crit, then the geometry will have some positive curvature and you will notice non-flatness. Like volumes of spheres not going with R the way you expect. Like galaxy counts by distance not being right etc etc. If the actual density is less than crit then you will notice other deviations from flat geometry. The size of the bumps in the CMB map is one way they tell. There are various ways to measure how close to flatness. So the key thing for you Purin to do is to calculate crit. Calculate the sucker! If you went to highschool in India, say, then you will experience no trouble with this. Tell me what you get. It should come out in terms of nanojoules per cubic meter. Which is the same as nanonewtons per square meter (do you see why?) which is the same as nanopascals. OK? If you have any trouble at all, like not knowing what a megaparsec is, tell me. Link to comment Share on other sites More sharing options...
purintjp Posted June 3, 2009 Share Posted June 3, 2009 Actually, I went to Downey High in Downey, CA in 1962. My math is a bit rusty but I can do it. What does 'G' stand for in '8 pi G'. I noticed you said "If density is SIGNIFICANTLY greater than crit". Would we notice a not so significant greater crit ? It is pretty amazing that the key value seems to be the Hubble constant. Link to comment Share on other sites More sharing options...
Martin Posted June 3, 2009 Share Posted June 3, 2009 (edited) Actually, I went to Downey High in Downey, CA in 1962. My math is a bit rusty but I can do it. What does 'G' stand for in '8 pi G'. I noticed you said "If density is SIGNIFICANTLY greater than crit". Would we notice a not so significant greater crit ? It is pretty amazing that the key value seems to be the Hubble constant. Yes, it is amazing. It's beautiful. Wikipedia has an article on the Friedman equations (actually there are two equations). It is too technical for me to recommend but just so you know. G is Newton's constant. There are several different ways to measure or estimate the overall average spatial curvature. One is from microwave background temperature maps, the bumpiness. One is from galaxy counts, how they depend on radial distance or redshift. Measurements of curvature keep getting refined. One thing the Planck spacecraft that was launched last month will do is improve the measurement of curvature beyond what was achieved by the WMAP spacecraft. The Friedman equation has a spatial curvature parameter k which if you set it to zero and solve for the presentday density you get the critical density (what is needed for exact spatial flatness) and it comes out in that formula I mentioned, in terms of the presentday Hubble rate H. In 1962 California had about the best highschools of any state in the Union and US highschool education was some of the best in the world and Americans were not afraid of numbers and we didn't have to import so many overseas-trained engineers. Google has a calculator built into the search window. If you type in "1 parsec in meters" and press search it will tell you what is one parsec in meters. If you type in "(74 km/s per megaparsec)^2/G" it will probably calculate what that is in some units and tell you. I never tried that exact thing. But anyway the Google calculator knows units, so that can save trouble looking up what G is in a handbook, or what a parsec equals in kilometers. On the other hand it could be argued that it makes you strong to do it on your own without crutches etc. I used to use a physics handbook and an HP calculator but I got seduced by how easy Google is. What "we would notice" depends on how refined the measurement of curvature is. The error-bar on curvature gets translated directly into an errorbar estimate of the current density and that is how you see it published. There is a 95 percent confidence interval published last year that says we are within one or two percent of crit. I'll get the figure later. Edited June 3, 2009 by Martin Link to comment Share on other sites More sharing options...
purintjp Posted June 3, 2009 Share Posted June 3, 2009 What is the 'G' in '8 pi G' ? Link to comment Share on other sites More sharing options...
Martin Posted June 3, 2009 Share Posted June 3, 2009 (edited) What is the 'G' in '8 pi G' ? Oh, sorry. You asked that earlier and I said "G is Newton's constant". You want a numerical value, and some explanation. Put this into the Google window: "G = " without the quote marks. Or just do a search for "gravitational constant." Now I'm worried, Purintjp. If you are not already familiar with Newton's grav. constant G then this little exercise of finding the critical density needed for flatness is not likely to mean much to you! that means I misjudged and over-reached. G is a universal constant that tells you the force between two things if you specify both their masses and the distance between them. But almost by miracle, even though it was discovered around 1680 by Newton it reappeared in 1915 in the Einstein equation showing how masses influence the geometry around them. In the Einstein Equation of general relativity it appears not as G but as 8 pi G. I want to let you off the hook, because I misjudged. But here is a simpler more classic vintage-1680 problem: A 100 kilogram man is standing on an asteroid whose radius is 1000 meters. The mass of the asteroid is 10 trillion kilograms, let's say, (that's 10^13 kg). What is the force pulling between them? If you type this in Google it will tell you the force in terms of the metric unit of force G (10^13 kilograms)(100 kilograms)/(1000 meters)^2 If you type this instead, it will tell you the force in a more familiar unit, "pounds of force" G (10^13 kilograms)(100 kilograms)/(1000 meters)^2 in pounds You multiply G by the two masses and then divide by the square of the distance between centers (which in this case is about 1000 meters). Edited June 3, 2009 by Martin Link to comment Share on other sites More sharing options...
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