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Widdekind

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Posts posted by Widdekind

  1. Planetary Mass Growth Rates, in Proto-Planetary Disks, are calculated to be (C.A.Scharf. Extra-Solar Planets & Astrobiology, pg. 89):

    [math]\frac{dM}{dt} = \pi \; R^{2} \left(1 + \left( \frac{v_{esc}}{v_{rel}} \right)^{2} \right) \; \rho_{disk} \; v[/math]

    And (ibid., pg. 102):

    [math]\rho_{disk} \; v \approx \sigma_{disk} \; \omega[/math]

    where:

    [math]\sigma_{disk} \approx 1700 \; \left( \frac{D}{1 AU} \right)^{3/2} \; g \; cm^{-2}[/math]

    We assume that the average Relative Impact Velocity (vrel) is equal to the Keplerian Disk Velocity (v)*.

    *
    This can be verified, by assuming that all potential
    Impactors
    possess, at the beginning of their planet-ward trajectories, the
    Keplerian Disk Velocity
    at that
    Orbital Distance
    ; and, that said potential Impactors impinge upon the
    Proto-Planet
    from all directions equally. Then, by integrating over
    Velocity Space
    , the
    Average Relative Velocity
    turns out to be just the
    Keplerian Disk Velocity
    .

     

    We may now estimate the Planetary Formation Time-Scales:

    [math]\tau \equiv \frac{M}{\frac{dM}{dt}}[/math]

    for the Planets & Dwarf Planets* in our Solar System.

    *

     

     

    RESULTS:

     

    Planet Formation Time-Scales are plotted against Planet Orbital Distances in the attached figure. We find that:

    • Terrestrial Planets -- formed over hundreds of thousands of years
    • Gas Giants -- formed over tens of millions of years
    • Ice Giants -- formed over hundreds of millions of years
    • Kuiper Belt Objects -- formed over billions of years

    In particular, please ponder the pronounced "dips" corresponding to both the Asteroid- & Kuiper- Belts. This may imply, that the Giant Planets "stole" material from adjacent disk regions, thereby "strangling" Planetary Growths there.

     

    Note, too, that the Outer Kuiper Belt Dwarf Planet Eris, with an estimated Planetary Formation Time-Scale exceeding the age of the Solar System, may still be (albeit slowly) accumulating material through collissions.

     

     

    ANALYSIS:

     

    The Ice Giants, being depleted in Hydrogen & Helium compared to the Gas Giants, are thought to have formed after the Sun's Solar Wind blasted out the Lighter Elements from the Planetary Disk (citation needed). That "sweeping out" happened when the Solar System was tens of millions of years old*. This is completely consistent with the above results, which indicate that the Ice Giants took hundreds of millions of years to form.

    *

    The roughly-linear main trend indicated has a slope of roughly 5/2, indicating that [math]\tau \propto D^{5/2}[/math].

    Planet_Formation_Times.jpg

  2. In your opening post you say this:

    "If all Methane comes from Biological processes, and if Methane is common across the Cosmos, then perhaps Biology is common across the Cosmos."

     

    In your last post you say this:

    "Present Observations infinitesimally favor Life being everywhere (or at least quite common)."

     

    There's an important "common" word, shared by both those statements. Please explain to me, how you conclude that they are "importantly" different.

     

    You appear to be a native English speaker with a good command of the language. You will recognise that these two statements are different in an important way. I have no objection to you changing your position, but it would be helpful if you made it clear - as you did in your thread on Martian plate tectonics - when you have done so.

     

    I don't think I suggested you were assigning a specific probability, but you were assigning a significant probability. You have now modified this to there being an infinitesimal balance of probability in favour of life. Now I don't see that an infinitesimal balance of probability in favour of life merits any discussion, or argument, or debate - well perhaps an infinitesimally small one.

     

    I would say, that there is a significant "possibility", not "probability". The very word "probable" / "probably" connotes a likelihood in excess of 50%. Such a claim exceeds the limits of present primitive observations, which can only "hint" & "suggest".

     

    But, present observations are completely consistent w/ abundant Life, making the possibility worthy of serious consideration.

     

    That's all I said -- "Life is likely to be likely".

     

    All the "hints" of which we're aware "suggest" that Life is likely to be likely. That's not an opinion, but a promising possibility suggested by present observations, to anybody w/ an open mind. Adhering stringently to a "Rare Earth" hypothesis, in the face of present observations which (weakly) favor the converse, is a (mildly) pre-judged position.

     

    ANALOGY: After one inning (or even 1/2 inning), Life is leading Rare Earth 1-0. So, if you had to bet, you'd (barely) prefer Life. That's all I said.

     

    To quote Br. Guy Consolmagno, SJ (Intelligent Life in the Universe -- Catholic belief & the search for extra-terrestrial Intelligent Life), "we don't know, we don't know, we don't know, we don't know" (which words apply both to Alien Life & Alien Intelligent Life). But, it's completely possible, so there's no reason to a priori prefer Rare Earth.

     

    That seems be a source of some concern, for other people posting about this important topic. It seems that there is some sort of preference for the position, "bah humbug, we Humans are all there is, in all the Cosmos" (my words). Hypothetically, that position could be the case. It could be correct. But, it could also be incorrect, and present primitive observations, which are witnessing repeated "hints" & "suggestions" for frequent Life, tend to imply the opposite position.

     

     

     

     

    ADDENDUM:

     

    Just to be blunt, it is my opinion, that if I could get people drunk on a cocktail of Vodka & Truth-serum, I could quickly get them to say, "bah humbug, we Humans have the whole entire complete Cosmos to ourselves, there's nothing doing anywhere else, never has been, never will be, we Humans are the pinnacle of all Creation, somebody has to be Tops and it just so happens to be my species".

     

    It is also my opinion -- as I am suspicious of such self-spoken beliefs -- that, as according to Folk Wisdom, "there's always a bigger fish".

     

    These are my opinions regarding Intelligent Life, which are only opinions, b/c I cannot conclusively answer Fermi's Paradox (if they [Alien Intelligences & Civilizations] are everywhere, where are they?). But, for basic primitive microbial-caliber Life-forms, I can graduate from "opinions" to "possibilities" based upon "hints & suggestions" of actual observations.

     

    Everybody posting so far, seems to mutually agree, that Intelligent Life "should" be less frequent than more primitive types of Life. That, then, seems to be a common ground which everybody here can accept.

  3. I only pursued the "semi-Relativistic" scenario some more, "for fun", "to see what happened".

     

     

    Would you (DH) please explain how GR can account for Martin's observation, that the "GPE" gained by particles sinking into Gravity Wells can be radiated away ?? For, if "GPE" is fictitious, akin to Coriolis Energy, then, how could GR account for a particle being able to produce Light Energy as it nears other massive bodies ?? Where could that Radiated energy come from, if not from the fictitious GPE ??

     

    (Thanks again in advance.)

  4. ..

    Yes, we see life on Earth.

     

    There is the possibility of life on Mars, yes. However, you have implicitly engaged a cyclical argument that we should view the methane as good evidence of life on Mars because life is probably abundant in the universe.

     

    I never said that.

     

    I said, "all the evidence available, at present, is completely consistent w/ Life being abundant".

     

    That's all I said, nothing more.

     

    The abundance of organic chemicals is irrelevant. Sure, they demonstrate that the raw materials for life are abundant, but until we understand the mechanism of abiogenesis in detail we cannot know whether its origin is inevitable, or unique.

     

    So, Life could be inevitable & frequent...

     

    and, if it were inevitable & frequent...

     

    then things would look exactly like they do look ("the raw materials for Life are abundant").

     

    Again, the available evidence is completely consistent w/ Life being abundant. Again again, that's all I said.

     

    Who's assigning specific probabilities ? All I said was, "if Life was frequent across the Cosmos, then the first few primitive observations to appear would be Life on Earth, possible Life on Mars, & copious quantities of Organics across the Cosmos". This is precisely what we do see, completely consistent w/ Life being common across the Cosmos.

     

    Er go, in the absence of any understanding of Abiogenesis as you said, we have no A Priori reason to prefer "Life-Phobic" positions.

     

    For example, our primitive & puny present comprehension of our position is completely consistent with their being Microbial Life, in at least trace amounts, on every single planet in the whole Universe. Even the Hot Jupiter Exoplanets could support some sort of Extremophiles in their Atmospheres -- we don't know.

     

    I mention this example, b/c it's equally consistent with their being no Microbial Life, on any planet in the Universe, beyond Earth. So, see what I'm saying ?

     

    Even so, in loose language limited by keyboard & ASCII, our presently-known Data Set looks like this:

     

    Life, Life?, Life
    ???, ??????????????????????????????????????????????????????????????????????????????????

     

    All I'm saying, is that is completely consistent with an "Objective Truth" of:

     

    Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life...

     

    And, it is slightly, but importantly (you agree, yes?) more consistent with all that Life, than the diametrically opposite "Objective Truth" of:

     

    barren world, barren world, barren world, barren world, barren world, barren world, barren world, barren world, barren world, barren world...

     

     

    SUMMARY:

     

    Completely Barren Cosmos Hypothesis:

    barren world, barren world, barren world, barren world, barren world, barren world, barren world, barren world, barren world, barren world...

    Life-is-Everywhere Hypothesis:

    Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life, Life...

    Primitive Present Observations:

    Life, Life?, Life
    ???, ??????????????????????????????????????????????????????????????????????????????????

     

     

    CONCLUSION:

     

    • We can already exclude the Completely Barren Cosmos Hypothesis.
    • We cannot yet exclude the Life-is-Everywhere Hypothesis.
    • Present Observations infinitesimally favor Life being everywhere (or at least quite common).

  5. For a power-law IMF, the you must increase the exponent [math]\alpha[math] above about 4.5, before you start getting M-L Ratios of order 100-1.

     

    Note, in particular, that you must increase the IMF exponent above four (4), from the Luminosity-Mass estimate (L* ~ M*4). Without doing so, although the bigger brighter stars are less frequent (M*-2.3), they still produce much more radiation (M*2.3 x M*+4 = M*+1.7). Thus, in sum, you get such huge quantities of radiation, even from a few such stars, that it depresses the M-L Ratio.

     

    Only if bigger & brighter stars were incredibly infrequent ([math]\alpha[/math] ~ 4.5+), would even their incredible brilliances be offset by so many smaller dimmer stars as to darken the whole population.

  6. Also I can only presume that widdekind is deliberatlely missing the point again. I was pointing out that extrapolating from one local observation to the whole universe is so bizarely unscientific as to be funny.

     

    I deny the accuracy of that assertion.

    We can do better than merely "one local observation"... albeit, barely better.

     

    For, we can see Life on Earth...

    possible Life on Mars...

    and copious quantities of Organic Chemicals across the Galaxy.

     

    CONCLUSION: I would agree, that a "completely primitive" Cave Man, looking out across Ice Age Europe, and saying, "Man, I'm convinced there's Life across the Cosmos", actually would be "extrapolating from one local observation to the whole Universe". But I deny that that is what Mankind is doing today, having, as we do, partial information, from across the Cosmos, all of which could be construed as completely consistent, with Life being abundant across the Cosmos.

     

    Present data is doesn't settle the issue, but it hints & suggests more strongly for frequent Life, as for its miraculous rarity (which would, incidentally, violate the Copernican Principal).


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    Consecutive posts merged
    Wieddekind, how do you address the several abiogenic mechanisms for generating the observed methane on Mars? The simplest explanation is the non-biological one. Unless you can find substantive fault in each alternative mechanism the biological source for the methane must be rejected.

     

    Martin, I have serious reservations about the process by which the Viking data was interpreted as failing to reveal life. This incident is certainly not conclusive, but the approach was sloppy science at best and leaves serious question marks. While I should not be at all surprised if we established conclusively there was no life on Mars, I should nod knowingly (and somewhat smugly) if we ever confirm its presence.

     

    According to NASA,

    Living systems produce more than 90 per cent of Earth's atmospheric methane; the balance is of geochemical origin.

    Thus, brashly applying these statistics to Mars, all its Methane could quite conceivably come from Life.

     

    Why is the "simplest" explanation a non-Biological one? What is so "complicated" about "hey, man, Martian microbes make Methane" ? Is not there some sort of preconceived "Life-phobia" in such assertions ?

     

    W/o being flippant, I see it, as an assumption, that admittedly more complex Bio-Chemical Processes must be more rare. For, as afore-cited, on Earth, the exact converse is true -- the more complex Bio-Chemical Processes produce most of the Methane.

     

    Therefore, from my current understanding, I deny the assumed equivalence of "Complexity <=> Rarity".

  7. (Thanks DH for the fuller, Relativistic, explanation.)

     

     

    Brashly combining Newton & Einstein again, would deny the existence of Black Holes. For, from our Escape Velocity Equation, Relativistically revised, we have that:

    [math]KE = -U[/math]

    [math]\left( \gamma - 1\right) \; m \; c^{2} = \frac{G \; M}{R}[/math]

    And, the LHS of that equation is unbounded. Thus, for any positive & finite Mass & Radius, you can find some finite Relative Velocity ([math]0 \leq \beta \leq 1[/math]), such that your KE exceeds your GPE.

     

    CONCLUSION (?!?): Sufficiently relativistically-fast particles can always plow up out of any Gravity Well. Only the sufficiently slower particles would be bound back to the Gravitating Body.

     

    Likewise, Light could be claimed to Gravitate, by Mass-Energy Equivalence:

    [math]F_{g} = - \frac{G \; M \; \left(\frac{h \; \nu}{c^{2}}\right) }{R^{2}}[/math]

     

    However, for Light, there would still be some sort of Black Hole criterion, requiring:

    [math]h \; \nu > \frac{G \; M \; \left(\frac{h \; \nu}{c^{2}}\right)}{R}[/math]

    [math] 1 > \frac{G \; M}{c^{2} \; R}[/math]

    which would seem to make the "Schwarzschild Radius" half of its Relativistic value (being the same radius, at which a massive body's GPE exceeds its RME-eq., as per previous posts).

  8. ...

    During the aero-braking maneuver to place it in orbit, Mars Global Surveyor detected linear magnetic anomalies in the southern hemisphere of Mars. Researchers, using the data from two full Mars years of polar orbital data and with an improved technique to eliminate the effects of external fields, constructed a global map of remnant crustal magnetization (I note in passing that the strength of this magnetism is more than an order of magnitude greater than comparable magnetism on the Earth.)

     

    ...

     

    According to the Science News article I cited:

    Surveyor detected several magnetized patches of terrain, some with fields as strong as 400 nanoteslas, or 1.3 percent of Earth's field (SN: 10/18/97, p. 246).

    According to a diagram from the NASA article I cited, the maximum Magnetic Field Strength the MGS detected was 1200 nT (roughly 4% [math]B_{\oplus}[/math]).

     

    CONCLUSION (?): While Mars' Remnant Magnetism is much weaker than Earth's Dynamo-driven Planetary Magnetic Field, it's still much greater than Earth's own Remnant Magnetism.

     

    Does this imply, that Earth's Planetary Magnetic Field inhibits Crustal Magnetism upon this planet ?

  9. Mars' Planetary Magnetic Dynamo, generated by Core Convection, apparently dissipated by about 3.8 billion years ago:

    Astronomers believe that these craters formed when chunks of debris pelted the inner solar system some 3.8 billion years ago. As old as these craters are, the global magnetic field that once existed on Mars must have vanished before they formed, Acuna asserts.

    And, the collapse of Core Convection is likely linked to the collapse of Plate Tectonics (from Mantle Convection), at about the same time:

    The younger, northern lowlands of Mars show no evidence of striping, and much less of the crust appears to be magnetized, Connerney says. These observations suggest that both the Martian magnetic field and plate tectonics had died away before volcanic activity melted and resurfaced this vast region of the planet.

     

    It's possible that the fading of the global magnetic field and plate tectonics are intimately linked, Connerney speculates. When the interior lost so much heat that it could no longer power the dynamo, it may also have had too little energy to drive plate tectonics.

    Thus, on Mars, all Convection Currents completely stopped by about 3.8 billion years ago, when Mars was merely ~3/4ths of a billion years old.

     

     

    REVISION of THEORY:

     

    Mars being some ~60 times less Convective than Earth (Ra ~ 0.016), Convection-driven processes, and in particular Plate Tectonics, stopped on Mars much sooner than upon this planet. To wit, the Martian Mantle did once Convect, but only in the deep past.

     

     

    REFERENCES:

  10. http://en.wikipedia.org/wiki/Ice

    So, any normally liquid or gaseous covalent compounds. Rocks and minerals are generally ionic compounds and thus are out of the equation.

     

    That's true, and those Chemical Properties determine specific details, like Melting Points & Heats of Fusion. However, I'm only speaking in generalities -- water is "molten ice", much as magma is "molten rock". And, icy worlds will have "molten ice", much as rocky worlds will have "molten rock".

     

    NOTE: From the above figure, you can estimate the size of Uranus & Neptune's Rock-Ice Cores, by simply projecting them, straight down, onto the Rock-Ice Curve. That amounts to keeping the mass constant, but reducing the radius. This is a "zeroth order" approximation, implicitly assuming that the atmosphere doesn't mass much.

     

    Visually, it looks like both Uranus & Neptune's cores are roughly 1/2 [math]R_{\oplus}[/math] smaller in radius that the whole planets. Since both of these "hidden planets" are quite big (~ 10 [math]M_{\oplus}[/math], ~ 3 [math]R_{\oplus}[/math]), perhaps they are still Geologically Active, deep beneath their thick protective Green House Atmospheres. Perhaps they still undergo "Rock-Ice Volcanism", and the like. Perhaps they could be used to study, and model, Geological Activity on Terrestrial-type planets too.

  11. You are mixing and matching Newtonian and relativistic mechanics here. This is not a good idea in general and is a very bad idea in this case. Gravitational force is a fictional force in general relativity. There is no such thing as gravitational potential energy in general relativity.

     

    The mass-energy an infalling object adds to a black hole is the object's energy-at-infinity. That the object follows a geodesic into the black hole doesn't change that.

     

    Wow. How does GR explain the infalling particle's increased energy, [math]\gamma m c^{2}[/math] ? Where does the KE come from ?


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    Consecutive posts merged
    ...

    Is that right? Or did I make a mistake? Notice that the Schw radius is 2GM/c^2, not GM/c^2. You forgot a factor of two in your calculation (something physics teachers habitually do.) If I made an error let me know please. In any case this would make a nice 15 minute class discussion and might lead some of the students to learn a whole lot more about gravity and black holes on their own. "Black holes as an energy source" etc etc.

     

    That's true. I was only making an Order-of-Magnitude estimate, since I suspected that something was amiss, w.r.t. GR vs. Newtonian.

  12. By analogy with Widdekind's post;

    On the basis of one extensively studied case*, everyone is a 43 year old bloke with a beard.

     

    *That's me, by the way, and I have checked.

     

    Some of the ideas put forward here are really so funny there should be a comedy section.

     

    That's not fair -- we can actually observe 6 billion humans, in enough detail, to disprove that claim.

     

    The fact is this -- everywhere we've looked, to the maximum of the detail our primitive detectors, we have observed Life (Earth), possible Life (Mars), and the necessary pre-cursors to Life (ISM, GMCs).

     

    A better revision of your "beard analogy" would be this:

    You're near-sighted, 20/400...

    You know you've got a beard...

    And everywhere you look around your room, your blurry vision sees dark splotchy shadows on peoples' faces precisely where beards
    would
    be if they wore them.

    Does that guarantee that everybody in that room has a beard? No. But it's perfectly consistent w/ that possibility -- that possibility, that everybody there has beards, is not flagrantly false.

     

    And, here's a counter-example -- "The Moon is made of Cheese". The obvious rebuttle is, "The Moon's density is completely incompatible w/ that". That is a fair & balanced example, of something, that is completely & blatantly & flagrantly false.

     

    But, that is absolutely dis-similar from a "Blurry Vision & Beards" situation, which is what Mankind currently faces, w/ his primitive detection equipment, & limited lack of data.

     

    We've excavated 1% of the archaeological site... and, so far, all the data is consistent w/ a really big building.

     

    "
    The jury's still out, but it looks promising
    " --
    fair & balanced summary of situation

  13. OBSERVATION: The Biomass of various living species decreases w/ increasing species Complexity & Intelligence. For example, on Earth, there is one Civilized species (H. sapiens), several reasonably intelligent species (Chimpanzees, Dolphins, Octopuses, Squid), many cunning species (Wolves, Crows, Ravens, Elephants, Lions, etc.), and so on, until ultimately there is more Biomass in microbes than all other Earth Life-forms combined. And, surely (?), there is more mass in non-living Organic Chemicals, than Organic Chemicals in living creatures.

     

    CONCLUSION: If we lived in a very fertile Universe, supporting Life across the Cosmos, the most basic observable "footprint" of that fact, apparent even to our present primitive detection capacities, would be copious quantities of Organic Chemicals distributed liberally & ubiquitously across the Cosmos.

     

    This is exactly what we observe.

     

    Thus, although, at present, our data is very limited -- Complex Life is known on 1 of 1 intensely studied planets*, and basic Organic Chemicals are blatantly apparent across the Cosmos -- everything we know is consistent with our Universe being very fertile, supporting an abundance of Life.

    *
    Venus may still support microbes up in its
    Sulphuric Acid
    clouds, as survivors from its long-evaporated oceans
    (T. Haines & C. Riley. (
    BBC
    )
    Space Odyssey: Voyage to the Planets
    ; National Geographic Channel
    Naked Science -- Deadliest Planets
    (TV))
    . And, on Earth, there is more
    Biomass
    of microbes in the deep subsurface, than
    Biomass
    of all
    Life
    on the surface
    (Discovery Channel
    Inside the Earth
    (TV))
    , implying that Mars, too, may indeed still support primitive microbial-type
    Life
    -forms in its deeper, and warmer, subsurface, as survivors from its warmer & wetter past.

  14. The Mass Distribution of stellar (star) populations is described by the Initial Mass Function (IMF), denoted N(M) dM, which describes the number of stars between masses M & M+dM, in some specified volume of space. The IMF is typically modeled as a Power Law, with exponent [math]\alpha[/math] around -7/3:

    [math]N(m) dm \propto M^{-\alpha}[/math]

    Now, Stellar Luminosities scale as L* ~ M*4(Bowers & Deeming. Astrophysics I: Stars, pg. 28). So, from the IMF, we can calculate the expected overall Mass-to-Light Ratio of that population of stars:

    [math]\Upsilon \equiv \frac{M_{tot}}{L_{tot}} = \frac{\int M \times N(M) dM}{\int L(M) \times N(M) dM} \approx \frac{\int M \times M^{-\alpha} dM}{\int L_{\odot} \times \left(\frac{M}{M_{\odot}}\right)^{4} \times M^{-\alpha} dM} = \left(\frac{M_{\odot}^{4}}{L_{\odot}}\right) \frac{\int M^{1 - \alpha} dM}{\int M^{4 - \alpha} dM}[/math]

    [math] = \Upsilon_{\odot} \; M_{\odot}^{3} \left( \frac{5 - \alpha}{2 - \alpha} \right) \frac{ M^{2 - \alpha} |_{M_{min}}^{M_{max}} }{M^{5 - \alpha} |_{M_{min}}^{M_{max}} }[/math]

    [math] = \Upsilon_{\odot} \left( \frac{5 - \alpha}{2 - \alpha} \right) \frac{ \mu^{2 - \alpha} |_{\mu_{min}}^{\mu_{max}} }{\mu^{5 - \alpha} |_{\mu_{min}}^{\mu_{max}} }[/math]

    where [math]\mu \equiv M / M_{\odot}[/math]. Plugging in approximate values for the IMF exponent ([math]\alpha \approx 7/3[/math]), as well as the minimum & maximum star masses ([math]\mu_{min} \approx 0.1, \mu_{max} \approx 100[/math]), we obtain:

    [math] \frac{\Upsilon}{\Upsilon_{\odot}} \approx 7.2 \times 10^{-5}[/math]

    However, the normalized Mass-to-Light Ratios ([math]\frac{\Upsilon}{\Upsilon_{\odot}}[/math]) of most Galaxies range from 2 - 10, some 5 Orders-of-Magnitude greater.

     

    CONCLUSION: Standard stellar populations cannot account for the observed Galactic Mass-to-Light Ratios. This could be consistent with the inference of copious quantities of Dark Matter in the same.

  15. Please ponder the Gravitational Potential Well of a massive central body:

    [math]U = - \frac{G \; M}{R}[/math]

    Crucially, Gravitational Potential Energy is negative. Thus, other bodies placed into this Gravity Well will lose Energy -- and, hence, by Einstein's Mass-Energy Equivalence (E = m c2), they should lose Mass, equal to:

    [math]\Delta M = \frac{U}{c^{2}} = - \frac{G \; M}{c^{2} \; R}[/math]

    Plugging in appropriate numbers, this yields Fractional Mass Loss effects of order:

    • At Earth's surface -- 10-9
    • At Earth's orbit -- 10-8
    • At Sun's surface -- 10-5
    • At Neutron Star's surface -- 10-2
    • At Black Hole Event Horizon -- 1

    Thus, by these admittedly primitive classical arguments, objects passing through a Black Hole's Event Horizon have lost more Energy than their Rest Mass Energy Equivalent (!!), ignoring of course any gains of Kinetic Energy*.

    *
    It seems strange, to this author, that, from the perspective of a distant observer,
    Time
    slows for objects accelerated to large
    positive
    Kinetic Energies
    , and for objects dropped down into large
    negative
    Potential Energies
    .

  16. Smaller, dimmer stars typically produce far fewer Terrestrial-type planets, but make more Jupiters & Kuiper Belt Objects:


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    ...So the energy you have to blow off is proportional to M/M^2 which is 1/M.

     

    So the energy cost to the colonizer of getting down into the habitable, where he can do a flyby of the planet, is reciprocal to the mass of the star.

     

    Habitable planets of low-mass stars are more costly to visit. Because a low M means a high 1/M..

     

    That is an excellent extension of the reasoning !


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    That's probably more to do with astronomers only looking at K,G & F stars because they are looking for the holy grail of planet hunting, an Earth-like world. After all the possible K, G & F stars are examined, astronomers will look at M stars and probably find more planets around them than K, G, & F stars.

     

    The cited Wikipedia article accounts for that:

    Most known Exoplanets orbit stars roughly similar to our own Sun, that is, main-sequence stars of spectral categories F, G, or K. One reason is simply that planet search programs have tended to concentrate on such stars. But even after taking this into account, statistical analysis suggests that lower-mass stars (red dwarfs, of spectral category M) are either less likely to have planets, or have planets that are themselves of lower mass and hence harder to detect.


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    Oh please don't misunderstand, I really enjoyed the thought exercise. I've thought it through and for the reasons outlined above, I disagree with the assertion that space travel is more difficult for certain stars than for others; based simply on the fact that I think the variables I pointed out will dominate the variables Widdekind suggested.

     

    But I freely admit I could be totally wrong (and would welcome being proved wrong BTW) and in no way intended to throw cold water on these ideas. Its very clever, IMO, to try to deduce the consequences of stellar type with regards to space travel; I would never have thought of it! And his logic is indeed compelling.

     

    You raise a valid concern. However, how does the Escape Velocity of Earth compare with that of the Sun, from Earth's Orbit ??

     

    Isn't the latter basically Earth's Orbital Velocity ? And, isn't Earth's Orbital Velocity ~30 km/sec, or around 3x that of its Escape Velocity ?

     

    Moreover, don't Gravitational Potential Wells "add" or "super-impose" ? Thus, if you put the same planet, down deeper into a low-mass stars' Habitable Zone, havn't you actually twice-increased the Energy costs ?

  17. I think this is the link:

    Note that the Brown Dwarf Desert applies only to "companions to normal stars":

    This means the so-called "Brown Dwarf Desert" (the absence of brown dwarfs around solar-type stars) extends to the smallest stars in the universe...

     

    "We still did not find brown dwarfs around small red stars whose mass is only slightly above the hydrogen burning limit. Especially when we consider the fact that brown dwarfs binaries do exist, the fact that there are very few binaries whose components lie on different sides of the Hydrogen Burning Limit is significant," says Dieterich

    Indeed, according to the article Unlikely Suns, Improbable Planets in the June 2009 AD issue of Scientific American, Brown Dwarf sub-stars are as common as true stars, in the Sun's vicinity. Thus, although the nearest Star System is the Alpha Centauri Trinary at 4.3 light-years, Brown Dwarf sub-Star Systems could be closer still. And, Brown Dwarfs could also likely have planets.

     

    So, it seems that Brown Dwarfs are quite common "on their own", but not as Stellar Companions.

  18. Work-Night Rough Draft

     

     

    Stars are born from Giant Molecular Clouds (GMCs), in big "batches" that become -- upon the condensation & dispersal of the parent GMC -- Open Clusters. Now, "stars inside an Open Cluster are at first tighly packed, moving at the same speed around the center of the Galaxy"*. Such Open Clusters typically persist for several hundred million years, before becoming disrupted**.

    *

    **
    ;
    cf
    .

    Now, the Ursa Major Cluster is an aged (~500 million years old*), and partially disrupted Open Cluster.

    After
    half a billion years or so
    , a classic
    Open Cluster
    such as the
    Pleiades
    or the
    Hyades
    (both in
    Taurus
    )
    tends to be disturbed by external factors
    (such as
    Molecular Clouds
    passing by)
    , setting its stars moving at slightly different speeds, and so causing them to drift apart,
    exactly like the one in
    Ursa Major
    has done
    .

     

    When this happens,
    the
    [Open] Cluster
    becomes a stream of stars
    , not close enough to be a cluster but all related and moving in very similar directions at similar speeds...

     

    Sirius is a former member of this
    [Open] Cluster
    and our sun is in the outskirts of what is called
    The Ursa Major Stream
    , a group of stars that are all ex-members of the
    Ursa Major Cluster
    spanning over
    a thousand light years
    in space
    **
    .

    These partially disrupted post-Open Clusters are called Moving Groups, and can be up to 2 billion years old***. But, typically,

    After a billion or so years
    , the
    Cluster
    is totally lost. Some stars will be on the far side of the galaxy, some on the near
    . The sun's original cluster is like this, there is no way to tell which are former members and which just happened to have formed at the same time but somewhere else.

    Indeed, "extremely dense Open Clusters can stay together for longer, but no Open Cluster could stay together for the age of the Sun, five billion years**". However, the HR 1614 Moving Group could be about 5 to 6 billion years old#.

    *

    **

    ***

    #

  19. Inspired by the National Geographic documentary Journey to the Edge of the Universe (DVD), it occurred to me, that our visual observations of the Cosmos could, quite conceivably, be sufficient for "retro-dicting" the Known Universe (Causally Connected regions of Spacetime beneath our Lightcone), and "pre-dicting" the Unknown Universe (Causally Disconnected regions of Spacetime above our Lightcone) -- including, in particular, the Modern Universe (what's happening, right now, across the Universe, even though the Light from those regions & events won't reach us for millions & billions of years more).

     

    "A picture's worth a thousand words", so please see the attached figure.

     

    Conceptually, such a simulation would amount to "total situational awareness", at the ultimate Cosmic scale.

    Predicting_the_Universe.jpg

  20. I would like to point out, that iron is not a product of blast furnaces. Smelting only extracts previously existing Iron from rocks.

     

    An apt, and accurate, analogy would be:

     

    Iron is produced by
    Big Stars
    , and distributed by
    Supernovae
    . The presence of Iron implies the past presence of
    Big Stars
    , and
    Supernovae
    .

     

    I'm sure, however, that there are Industrial Byproducts specific to Smelting & Blast Furnaces. And, the presence of those specific "Smelting signature compounds" (as it were) would, in fact, imply the presence of Heavy Industry on our hypothetical planet, yes?

     

    I am glad everybody found this discussion stimulating. Logically, the link between Methane & Biology, coupled with the ubiquity of the former, suggests the possible ubiquity of the latter.


    Merged post follows:

    Consecutive posts merged
    ...

    Unless somebody does the general theory here (electron-donors dominate versus where electron grabbers dominate) I will give it a try. In a reducing environment, methane and ammonia are the default, the natural way for C and H and N to exist. Earth has an oxidizing environment, Mars too, and methane is not the default---so on Mars and Earth, methane and ammonia are not the default. C likes to be CO2, H likes to be H2O, and all that. Somebody want to discuss?

     

    Are Molecular Clouds, where most Methane is apparently observed, Reducing Environments ?

  21. On Earth, Methane is primarily produced by Biological processes*. So strong is that link, that Methane in Mars' atmosphere strongly suggests the presence of sub-surface Methanogen micro-organisms:

    • Methane is a product of Biology. For Methane to be in Mars' atmosphere, there has to be a replenishable source... The most obvious source of Methane is organisms. So if you find Methane in an atmosphere, you can suspect there is Life**.

    And, Methane is commonly observed across the Cosmos.

    • * Martin Ince. [Rough Guides] Earth, pp. 256-257.
      **
    http://www.telegraph.co.uk/scienceandtechnology/science/sciencenews/4243321/Mars-methane-discovery-hints-at-presence-of-life.html; cf. http://news.nationalgeographic.com/news/2004/10/1007_041007_mars_methane.html, http://dsc.discovery.com/news/2009/01/15/mars-methane-life.html; Volcanoes ruled out for Martian Methane, see: http://www.newscientist.com/article/dn8256-volcanoes-ruled-out-for-martian-methane.html

     

    CONCLUSION (?):

     

    If all Methane comes from Biological processes, and if Methane is common across the Cosmos, then perhaps Biology is common across the Cosmos.

  22. Perhaps the Big Bang was the Explosive Evaporation of a "Hyper-Massive Black Hole":

    Perhaps your SMBHs are "chunks" of BH material blown outwards by that explosion, akin to knots of gas blown out by Supernovae. Those "BH fragments" then formed the seeds of Galaxies w/in our Universe -- to wit, inside the expanding "Explosion Remnant" (akin to Supernova Remnants).

  23. http://www.sciencemag.org/cgi/content/abstract/1172740v1?sa_campaign=Email/pap/21-May-2009/10.1126/science.1172740

     

    Radio pulsars with millisecond spin periods are thought to have been spun up by transfer of matter and angular momentum from a low-mass companion star during an x-ray-emitting phase. The spin periods of the neutron stars in several such low-mass x-ray binary (LMXB) systems have been shown to be in the millisecond regime, but no radio pulsations have been detected. Here, we report on detection and follow-up observations of a nearby radio millisecond pulsar (MSP) in a circular binary orbit with an optically identified companion star. Optical observations indicate that an accretion disk was present in this system within the last decade. Our optical data show no evidence that one exists today, suggesting that the radio MSP has turned on after a recent LMXB phase.
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