Hydrogen coalescence in formation of solar system?
March 31, 2009 9:04 AM Subscribe
I've been rewatching Carl Sagan's Cosmos since I found out it's available on Hulu. Last night, I was watching the episode in which Carl describes how the solar system was formed via the coalescence of particulate matter. But, something struck me as rather odd: if hydrogen and helium are lighter than the heavy elements (duh!) why is it that THEY coalesced into the center of the solar system to become the Sun? It seems to me the heavier elements would migrate towards the center of the maelstrom a bit faster than the lighter ones.
Haven't been able to find out the reason for this, hoping the hive can help.
My wild guess: Lower mass means less inertia and higher susceptibility to the gravitational forces of the surrounding particles.
posted by carsonb at 9:20 AM on March 31, 2009
posted by carsonb at 9:20 AM on March 31, 2009
Best answer: This isn't as complete of an answer to your question as I would like to write, but for the moment: What falls faster, heavy or light objects? If we're talking about the gravitational collapse of the gas that formed the solar system, then the same principle applies. There are lots of other processes involved, but to first order one wouldn't expect the heavy elements to fall-in any faster.
Hopefully that's enough of an intuitive answer; a complete answer would require a book on solar system formation. Determining why the rocky planets exist is a challenging question.
Re: TheyCallItPeace, most of the metals (everything other than hydrogen and helium) in the solar system were present in the gas cloud that formed the sun and planets. Metals are primarily formed in supernovae, so many other stars had to have exploded and contributed their metals to the pre-solar nebula before the solar system formed.
posted by kiltedtaco at 9:22 AM on March 31, 2009 [2 favorites]
Hopefully that's enough of an intuitive answer; a complete answer would require a book on solar system formation. Determining why the rocky planets exist is a challenging question.
Re: TheyCallItPeace, most of the metals (everything other than hydrogen and helium) in the solar system were present in the gas cloud that formed the sun and planets. Metals are primarily formed in supernovae, so many other stars had to have exploded and contributed their metals to the pre-solar nebula before the solar system formed.
posted by kiltedtaco at 9:22 AM on March 31, 2009 [2 favorites]
TheyCallItPeace: I thought at the formation of OUR solar system -- not a first generation star -- the heavy elements were already part of the primordial dust cloud? Yes, it takes nuclear fusion to create heavy elements, but our heavy elements were from different stars.
posted by phrygius at 9:26 AM on March 31, 2009
posted by phrygius at 9:26 AM on March 31, 2009
It's a matter of what was there in the nebula the solar system formed out of. Quoting Britannica: "[Nebulas'] chemical composition, however, is fairly uniform; it corresponds to the composition of the universe in general in that approximately 90 percent of the constituent atoms are hydrogen and nearly all of the rest are helium, with oxygen, carbon, neon, nitrogen, and the other elements together making up about two atoms per thousand." Since the sun is something like 99.9% of the mass of the solar system, it has most of the matter that was there, which was mostly H and He. Also, centrifugal force depends on mass(F_c = mv^2/r), so the heavier elements will tend to be sorted to the outside as the mass went to the inside and spun up the average rotational speed of the system (conservation of angular momentum).
posted by apathy0o0 at 9:34 AM on March 31, 2009
posted by apathy0o0 at 9:34 AM on March 31, 2009
But, something struck me as rather odd: if hydrogen and helium are lighter than the heavy elements (duh!) why is it that THEY coalesced into the center of the solar system to become the Sun?
Metals and heavy elements exist in most of the planets and in the Sun as well. So, are you asking why Hydrogen and Helium are mostly in the Sun?
Answer: Because only the Sun (and Jupiter) have enough of a gravity well to retain Hydrogen and Helium. The Earth and most other planets can't retain them.
posted by vacapinta at 9:35 AM on March 31, 2009
Metals and heavy elements exist in most of the planets and in the Sun as well. So, are you asking why Hydrogen and Helium are mostly in the Sun?
Answer: Because only the Sun (and Jupiter) have enough of a gravity well to retain Hydrogen and Helium. The Earth and most other planets can't retain them.
posted by vacapinta at 9:35 AM on March 31, 2009
Following vacapinta and doing some googling, the sun's photosphere is 0.16% iron (with the interior maybe richer).
0.16% of the mass of the sun is about 500 times the mass of Earth. That's a big twinkie.
posted by ROU_Xenophobe at 9:38 AM on March 31, 2009
0.16% of the mass of the sun is about 500 times the mass of Earth. That's a big twinkie.
posted by ROU_Xenophobe at 9:38 AM on March 31, 2009
What falls faster, heavy or light objects?
To make the point above clearer, heavy things fall at exactly the same speed as light things.
If you don't believe me, let astronaut Dave Scott explain.
Heavier elements would therefore coalesce due to gravity at the same speed as the hydrogen and helium.
posted by Ironmouth at 9:43 AM on March 31, 2009
To make the point above clearer, heavy things fall at exactly the same speed as light things.
If you don't believe me, let astronaut Dave Scott explain.
Heavier elements would therefore coalesce due to gravity at the same speed as the hydrogen and helium.
posted by Ironmouth at 9:43 AM on March 31, 2009
vacapinta is right, and I would also point out that the mass of the solar nebula was more than 99% hydrogen and helium, so of course there was a tremendous amount of those elements in the central mass which became the sun.
All matter, even light matter, feels the same gravitational force.
What were you expecting, a little lump of iron, calcium and carbon where the sun should be?
-
posted by General Tonic at 9:56 AM on March 31, 2009
All matter, even light matter, feels the same gravitational force.
What were you expecting, a little lump of iron, calcium and carbon where the sun should be?
-
posted by General Tonic at 9:56 AM on March 31, 2009
Answer: Because only the Sun (and Jupiter) have enough of a gravity well to retain Hydrogen and Helium. The Earth and most other planets can't retain them.
I'm going to have to disagree with Vacapinta. You see, there's a lot of hydrogen on Earth. A lot. It is often bound up in a substance we call water, which is 2/3s hydrogen. By molarity, nearly 2/3s of the ocean is made up of water. By mass, 10% of the oceans are made of water.
The problem, as explained above, is that gravity effects differing masses the same. Therefore, gravity should not account for the reason that some elements are more common in the Sun than in the inner planets.
I suspect the main reason we see no gas giants like Jupiter and Saturn in the inner solar system is because of solar radiation and the solar wind. Smaller elements are more likely to be moved by being physically interacted with by plasma coming off of the Sun. Charged particles from the sun likely pushed those elements out further into the proto-planetary nebula.
posted by Ironmouth at 11:26 AM on March 31, 2009
I'm going to have to disagree with Vacapinta. You see, there's a lot of hydrogen on Earth. A lot. It is often bound up in a substance we call water, which is 2/3s hydrogen. By molarity, nearly 2/3s of the ocean is made up of water. By mass, 10% of the oceans are made of water.
The problem, as explained above, is that gravity effects differing masses the same. Therefore, gravity should not account for the reason that some elements are more common in the Sun than in the inner planets.
I suspect the main reason we see no gas giants like Jupiter and Saturn in the inner solar system is because of solar radiation and the solar wind. Smaller elements are more likely to be moved by being physically interacted with by plasma coming off of the Sun. Charged particles from the sun likely pushed those elements out further into the proto-planetary nebula.
posted by Ironmouth at 11:26 AM on March 31, 2009
By the way, kiltedtaco's profile id's him as an astronomer.
posted by Ironmouth at 11:27 AM on March 31, 2009
posted by Ironmouth at 11:27 AM on March 31, 2009
Ironmouth: "Answer: Because only the Sun (and Jupiter) have enough of a gravity well to retain Hydrogen and Helium. The Earth and most other planets can't retain them.
I'm going to have to disagree with Vacapinta. You see, there's a lot of hydrogen on Earth. A lot. It is often bound up in a substance we call water, which is 2/3s hydrogen. By molarity, nearly 2/3s of the ocean is made up of water. By mass, 10% of the oceans are made of water."
Yeah, but the amount of water on Earth that came from Earth itself is still debated, there is good evidence for a significant amount of the water we see came from other sources in the deep solar system.
posted by Science! at 12:11 PM on March 31, 2009
I'm going to have to disagree with Vacapinta. You see, there's a lot of hydrogen on Earth. A lot. It is often bound up in a substance we call water, which is 2/3s hydrogen. By molarity, nearly 2/3s of the ocean is made up of water. By mass, 10% of the oceans are made of water."
Yeah, but the amount of water on Earth that came from Earth itself is still debated, there is good evidence for a significant amount of the water we see came from other sources in the deep solar system.
posted by Science! at 12:11 PM on March 31, 2009
"Answer: Because only the Sun (and Jupiter) have enough of a gravity well to retain elemental Hydrogen (H2) and Helium. The Earth and most other planets can't retain them."
FTFIronmouth.
posted by IAmBroom at 1:21 PM on March 31, 2009
FTFIronmouth.
posted by IAmBroom at 1:21 PM on March 31, 2009
As I understand it, the Solar System started out as a giant spinning disk of gas and dust, with a pretty uniform composition. Since most of the matter in the Universe is hydrogen and helium, most of the matter in the early Solar System was as well, with a sprinkling of heavy elements which had formed in stars and supernovas some time earlier. Over time most of the material in the disk fell inwards, gases and solids alike--which is why the Sun is mostly hydrogen and helium.
A small percentage of the material had too much angular momentum to fall in, so it stayed in the spinning disk orbiting around the protostar in the center. Bits of solids eventually started sticking together and became planets, still orbiting around within the gas-and-debris disk. At some point after the planets formed, solar winds (I think) swept away the remaining gas from the disk, which is why Earth and the other inner planets don't have much gaseous hydrogen and helium. Only the largest planets had strong enough gravity to collect gas from the disk and retain it.
So, partly the answer is that the heavy and light elements fell inwards at more or less the same rate, and partly the answer is that there's plenty of heavy elements in the Sun, too; the planets are just what's left over.
posted by fermion at 1:32 PM on March 31, 2009
A small percentage of the material had too much angular momentum to fall in, so it stayed in the spinning disk orbiting around the protostar in the center. Bits of solids eventually started sticking together and became planets, still orbiting around within the gas-and-debris disk. At some point after the planets formed, solar winds (I think) swept away the remaining gas from the disk, which is why Earth and the other inner planets don't have much gaseous hydrogen and helium. Only the largest planets had strong enough gravity to collect gas from the disk and retain it.
So, partly the answer is that the heavy and light elements fell inwards at more or less the same rate, and partly the answer is that there's plenty of heavy elements in the Sun, too; the planets are just what's left over.
posted by fermion at 1:32 PM on March 31, 2009
If heavier objects gravitate the same as light ones, why does the Earth fall faster towards me than the Moon, from equivalent distances?
Trying to equate the physics of particles of similar mass to the gravitation we know in daily life is a mistake.
posted by pwnguin at 1:36 PM on March 31, 2009
Trying to equate the physics of particles of similar mass to the gravitation we know in daily life is a mistake.
posted by pwnguin at 1:36 PM on March 31, 2009
Best answer: The basic answer to your question is buried in the above responses, some of which are incorrect. To clarify:
- By mass, most of the primordial solar nebula consisted of hydrogen and helium (created in the early universe), but a small fraction was in "heavy" elements due to previous generations of stars, as stated above. These ingredients are usually assumed to be initially uniformly mixed.
- One thing that might be confusing people is that the force of gravity *does* depend on the mass of an object. However, the acceleration due to gravity does not. Consider a blob in the solar nebular. Combining Newton's law (F = m_blob a) with the law of gravity (F = G m m_blob / r^2), the gravitational acceleration of a given blob in the solar nebula is just a = Gm/r^2. Here G is the gravitational constant, m_blob is the mass of the blob, m is the effective mass of the overall distribution pulling on the blob, and r is the distance of the blob from the center of the distribution. Note that the acceleration of the blob doesn't depend on its mass! Gravity doesn't segregate the ingredients if they are initially mixed.
- If only gravity were at play, then all the mass of the nebula would end up in the center, forming a star (made up of mostly H and He) without a planetary disk. However, the material has some initial angular momentum, which must be conserved. The radius of a given blob is a balance between the force of the gravity pulling it towards the center and the conservation of angular momentum, keeping it from going all the way.
- The inner planets *do* have a different ratio of heavy-to-light elements than the outer planets. This is *not* primarily due to the greater influence of the solar wind in the inner solar system, as was suggested above. Instead, the folks who said that the outer planets are massive enough to have accreted massive H/He atmospheres are correct. But nobody has addressed why the outer planets are more massive. It's mainly a matter of temperature. The inner planets formed in a hotter environment, in which only the heavier elements are in a solid state. So the cores of the inner planets had to form from the less-abundant heavy elements. In contrast, Jupiter formed at such a large distance from the sun that ices could also be used as a building block. With this additional relatively abundant building material, the cores of the outer planets were able to grow much larger. At some point, they grew so large that they could start accreting an appreciable amount of gaseous material.
- The origin of water on the Earth is controversial, but some say that it was delivered after its primary formation phase by comets, which were formed mainly out of ice in the outer solar system.
posted by pizzazz at 9:52 PM on March 31, 2009
- By mass, most of the primordial solar nebula consisted of hydrogen and helium (created in the early universe), but a small fraction was in "heavy" elements due to previous generations of stars, as stated above. These ingredients are usually assumed to be initially uniformly mixed.
- One thing that might be confusing people is that the force of gravity *does* depend on the mass of an object. However, the acceleration due to gravity does not. Consider a blob in the solar nebular. Combining Newton's law (F = m_blob a) with the law of gravity (F = G m m_blob / r^2), the gravitational acceleration of a given blob in the solar nebula is just a = Gm/r^2. Here G is the gravitational constant, m_blob is the mass of the blob, m is the effective mass of the overall distribution pulling on the blob, and r is the distance of the blob from the center of the distribution. Note that the acceleration of the blob doesn't depend on its mass! Gravity doesn't segregate the ingredients if they are initially mixed.
- If only gravity were at play, then all the mass of the nebula would end up in the center, forming a star (made up of mostly H and He) without a planetary disk. However, the material has some initial angular momentum, which must be conserved. The radius of a given blob is a balance between the force of the gravity pulling it towards the center and the conservation of angular momentum, keeping it from going all the way.
- The inner planets *do* have a different ratio of heavy-to-light elements than the outer planets. This is *not* primarily due to the greater influence of the solar wind in the inner solar system, as was suggested above. Instead, the folks who said that the outer planets are massive enough to have accreted massive H/He atmospheres are correct. But nobody has addressed why the outer planets are more massive. It's mainly a matter of temperature. The inner planets formed in a hotter environment, in which only the heavier elements are in a solid state. So the cores of the inner planets had to form from the less-abundant heavy elements. In contrast, Jupiter formed at such a large distance from the sun that ices could also be used as a building block. With this additional relatively abundant building material, the cores of the outer planets were able to grow much larger. At some point, they grew so large that they could start accreting an appreciable amount of gaseous material.
- The origin of water on the Earth is controversial, but some say that it was delivered after its primary formation phase by comets, which were formed mainly out of ice in the outer solar system.
posted by pizzazz at 9:52 PM on March 31, 2009
By the way, I think apaty0o0 means centripetal force rather than centrifugal force. In this case, the centripetal force is generated by gravity, which, as stated above, doesn't result in a segregation by composition.
posted by pizzazz at 10:02 PM on March 31, 2009
posted by pizzazz at 10:02 PM on March 31, 2009
Best answer: Another thought: Maybe people are intuitively reasoning that heavy elements are denser, so they should sink and the ligher elements should rise because of buoyancy? I believe that the density of the solar nebula is so low that the buoyant effect is very small and completely dominated by the gravitational effects discussed above. However, when the earth formed and was in a molten phase, buoyancy was important in the process of planetary differentiation, and resulted in the Earth's iron core.
posted by pizzazz at 10:14 PM on March 31, 2009
posted by pizzazz at 10:14 PM on March 31, 2009
Response by poster: thanks for all of the fantastic answers. I kinda phrased my question wrong, but pizzazz hit on my thinking with "Maybe people are intuitively reasoning that heavy elements are denser, so they should sink and the ligher elements should rise because of buoyancy?" That was exactly where my thinking was taking me.
posted by Spoonman at 6:57 AM on April 1, 2009
posted by Spoonman at 6:57 AM on April 1, 2009
Note that the acceleration of the blob doesn't depend on its mass! Gravity doesn't segregate the ingredients if they are initially mixed.
Consider a very thin cloud of gas, initially of uniform temperature and uniform density, composed of two gases of different masses, say xenon and helium for the sake of concreteness, in which the two gases are not necessarily equal in concentration but are each evenly distributed throughout the cloud. Suppose the cloud is far enough away from other masses that any gravitational field arising from them is essentially uniform throughout the cloud.
The cloud will generate its own gravitational field, however, and that, unlike the uniform external field, will cause the atoms in the cloud to move with respect to each other.
Now, in the initial condition, consider a xenon and a helium atom near the outer boundaries of the cloud, and another such pair near the cloud's center of gravitation. All four atoms will have the same (same normal distribution) kinetic energy by virtue of the uniformity of temperature, and the two at the center will have zero potential energy because they are at the gravitational center.
But the two outer atoms will have lots of potential energy because of their position in the gravitational field of the cloud, and they will accelerate (equally as people above have said) toward the gravitational center of the cloud, gaining velocity and kinetic energy (heat) as they go. On the scale of the cloud as a whole this means the cloud will contract and heat up.
However, the Xe atom has ~33 times more potential energy than the He atom and will gain ~33 times more kinetic energy than the He atom because it's that many times more massive, and so the population of Xe atoms will soon be quite a bit hotter than the He atoms and the cloud as a whole as it begins to contract.
The heat of the Xenon will even out as it collides with cooler atoms and transfers some of its energy to them (merely a particular example of heat flowing from hot to colder objects).
Now let this system reach equilibrium over time, neglecting (for the moment) radiative energy loss and the possibility of the gases condensing into a liquid, as well as the possibility some of the gas will get hot enough to achieve escape velocity.
At equilibrium, will we see a uniform distribution of Xe atoms throughout the cloud, as we we did initially? I don't see how. If that were the case, the cloud could heat up more, and minimize its potential energy more (obeying the minimum total potential energy principle*) if the Xe atoms tended to be found more near the center. The segregation would not be total because thermal motions of the two types of atoms would tend to produce some mixing.
So I would argue that you were right all along that the heavier elements would gravitate toward the center, spoonman, not despite the fact that more and less massive objects experience the same acceleration in a given gravitational field, but because of it.
* The tendency to minimum total potential energy is due to the second law of thermodynamics, which states that the entropy of a system will maximize at equilibrium. Given two possibilities - a low heat content and a high potential energy, or a high heat content and low potential energy, the latter will be the state with the highest entropy, and will therefore be the state towards which the system moves.
posted by jamjam at 5:11 PM on April 2, 2009
Consider a very thin cloud of gas, initially of uniform temperature and uniform density, composed of two gases of different masses, say xenon and helium for the sake of concreteness, in which the two gases are not necessarily equal in concentration but are each evenly distributed throughout the cloud. Suppose the cloud is far enough away from other masses that any gravitational field arising from them is essentially uniform throughout the cloud.
The cloud will generate its own gravitational field, however, and that, unlike the uniform external field, will cause the atoms in the cloud to move with respect to each other.
Now, in the initial condition, consider a xenon and a helium atom near the outer boundaries of the cloud, and another such pair near the cloud's center of gravitation. All four atoms will have the same (same normal distribution) kinetic energy by virtue of the uniformity of temperature, and the two at the center will have zero potential energy because they are at the gravitational center.
But the two outer atoms will have lots of potential energy because of their position in the gravitational field of the cloud, and they will accelerate (equally as people above have said) toward the gravitational center of the cloud, gaining velocity and kinetic energy (heat) as they go. On the scale of the cloud as a whole this means the cloud will contract and heat up.
However, the Xe atom has ~33 times more potential energy than the He atom and will gain ~33 times more kinetic energy than the He atom because it's that many times more massive, and so the population of Xe atoms will soon be quite a bit hotter than the He atoms and the cloud as a whole as it begins to contract.
The heat of the Xenon will even out as it collides with cooler atoms and transfers some of its energy to them (merely a particular example of heat flowing from hot to colder objects).
Now let this system reach equilibrium over time, neglecting (for the moment) radiative energy loss and the possibility of the gases condensing into a liquid, as well as the possibility some of the gas will get hot enough to achieve escape velocity.
At equilibrium, will we see a uniform distribution of Xe atoms throughout the cloud, as we we did initially? I don't see how. If that were the case, the cloud could heat up more, and minimize its potential energy more (obeying the minimum total potential energy principle*) if the Xe atoms tended to be found more near the center. The segregation would not be total because thermal motions of the two types of atoms would tend to produce some mixing.
So I would argue that you were right all along that the heavier elements would gravitate toward the center, spoonman, not despite the fact that more and less massive objects experience the same acceleration in a given gravitational field, but because of it.
* The tendency to minimum total potential energy is due to the second law of thermodynamics, which states that the entropy of a system will maximize at equilibrium. Given two possibilities - a low heat content and a high potential energy, or a high heat content and low potential energy, the latter will be the state with the highest entropy, and will therefore be the state towards which the system moves.
posted by jamjam at 5:11 PM on April 2, 2009
jamjam:
An important piece that's missing from your analysis is angular momentum.
A more realistic initial condition than the one you propose is a slowly rotating spherical cloud. This cloud evolves into a more rapidly rotating disk under the influence of both the law of gravity (which you take into account) and conservation of angular momentum (which you don't seem to).
Particles in the outer part of the disk that eventually forms have more angular momentum than particles near the center of the distribution. They can't lose their gravitational potential energy and gain kinetic energy without losing angular momentum.
posted by pizzazz at 7:16 PM on April 2, 2009
An important piece that's missing from your analysis is angular momentum.
A more realistic initial condition than the one you propose is a slowly rotating spherical cloud. This cloud evolves into a more rapidly rotating disk under the influence of both the law of gravity (which you take into account) and conservation of angular momentum (which you don't seem to).
Particles in the outer part of the disk that eventually forms have more angular momentum than particles near the center of the distribution. They can't lose their gravitational potential energy and gain kinetic energy without losing angular momentum.
posted by pizzazz at 7:16 PM on April 2, 2009
They can't lose their gravitational potential energy and gain kinetic energy without losing angular momentum.
I disagree; consider a small spherical asteroid with a uniform surface albedo in a very eccentric orbit around the sun. Because the sun's gravity exerts negligible tidal effects on small objects, the sun can exert no torque on the asteroid, therefore its orbital angular momentum remains the same at every point of its orbit, even though its kinetic energy is low and its potential energy is high at its farthest point from the sun, and vice versa at the nearest point to the sun. In other words, it transforms potential energy into kinetic energy and back during every orbit without altering its angular momentum at all.
Almost all the xenon and helium atoms I posit would probably not be in orbit around anything yet in a slowly spinning cloud. Conservation of angular momentum merely requires the cloud to spin faster as it contracts and heats up. The cloud's angular momentum doesn't fundamentally change the analysis.
posted by jamjam at 8:10 PM on April 2, 2009
I disagree; consider a small spherical asteroid with a uniform surface albedo in a very eccentric orbit around the sun. Because the sun's gravity exerts negligible tidal effects on small objects, the sun can exert no torque on the asteroid, therefore its orbital angular momentum remains the same at every point of its orbit, even though its kinetic energy is low and its potential energy is high at its farthest point from the sun, and vice versa at the nearest point to the sun. In other words, it transforms potential energy into kinetic energy and back during every orbit without altering its angular momentum at all.
Almost all the xenon and helium atoms I posit would probably not be in orbit around anything yet in a slowly spinning cloud. Conservation of angular momentum merely requires the cloud to spin faster as it contracts and heats up. The cloud's angular momentum doesn't fundamentally change the analysis.
posted by jamjam at 8:10 PM on April 2, 2009
For circular orbits, which I was implicitly assuming, the statement you called out is correct. (For eccentric orbits, you are correct.) Why assume circular orbits? They are realistic in the regime where the solar nebula is still mostly gaseous. Indeed, for the solar nebula that formed our solar system, most of the orbits did turn out very close to circular. The type of plunging radial orbits you are talking about (as seen in some asteroids) are from scattering events that occur once larger (dissipationless) bodies have formed.
I'm not sure what you mean when you say that the xenon and helium atoms you posit would probably not be in orbit around anything yet in a slowly spinning cloud. They are in orbit about the center of mass of the (spherical) distribution.
As I understand it, you are saying that the more massive atoms have a larger radial extent only because they are hotter. The thermal velocities should be isotropically distributed, so this would imply a compact sphere of helium gas embedded in a hotter, fluffier sphere of xenon gas. Yet, this is nothing like what we see in either our solar system or in the star formation regions elsewhere in the galaxy. We see flattened disks, a direct consequence of the conservation of angular momentum. Plus, we see lots of light elements in the outer solar system (Jupiter) and plenty of heavy elements in the inner solar system (Mercury).
posted by pizzazz at 11:29 PM on April 2, 2009
I'm not sure what you mean when you say that the xenon and helium atoms you posit would probably not be in orbit around anything yet in a slowly spinning cloud. They are in orbit about the center of mass of the (spherical) distribution.
As I understand it, you are saying that the more massive atoms have a larger radial extent only because they are hotter. The thermal velocities should be isotropically distributed, so this would imply a compact sphere of helium gas embedded in a hotter, fluffier sphere of xenon gas. Yet, this is nothing like what we see in either our solar system or in the star formation regions elsewhere in the galaxy. We see flattened disks, a direct consequence of the conservation of angular momentum. Plus, we see lots of light elements in the outer solar system (Jupiter) and plenty of heavy elements in the inner solar system (Mercury).
posted by pizzazz at 11:29 PM on April 2, 2009
However, the Xe atom has ~33 times more potential energy than the He atom and will gain ~33 times more kinetic energy than the He atom because it's that many times more massive, and so the population of Xe atoms will soon be quite a bit hotter than the He atoms and the cloud as a whole as it begins to contract.
You can't think of temperature this way. Temperature is only properly defined for an ensemble of particles where the average kinetic energy of the particles is measured with respect to the center of mass of the ensemble in a rest frame.
The way you're thinking about it, the air in my car would be hotter at 55 miles per hour than at 10 miles per hour. It isn't.
posted by mr_roboto at 11:58 PM on April 2, 2009
You can't think of temperature this way. Temperature is only properly defined for an ensemble of particles where the average kinetic energy of the particles is measured with respect to the center of mass of the ensemble in a rest frame.
The way you're thinking about it, the air in my car would be hotter at 55 miles per hour than at 10 miles per hour. It isn't.
posted by mr_roboto at 11:58 PM on April 2, 2009
I'm not sure what you mean when you say that the xenon and helium atoms you posit would probably not be in orbit around anything yet in a slowly spinning cloud. They are in orbit about the center of mass of the (spherical) distribution.
If the atoms in a nebula were all in stable circular orbits, the nebula could never contract under the influence of its own gravitational field, any more than the planets of our solar system, also in stable orbits, are now contracting toward the sun.
The cloud of gas I imagined for my little thought experiment was meant to be an idealization retaining some essential features of the sort of cloud I've seen hypothesized to be the starting point of the solar system, perhaps arising partly from material expelled from a supernova, and generally chaotic with atoms going in all different directions, and with all kinds of angular momentums with respect to the gravitational center, with all those chaotic vectors adding up to a small net angular momentum for the cloud as a whole. My ultimate purpose for this thought experiment was to investigate your categorical assertion that "Gravity doesn't segregate the ingredients if they are initially mixed." I think this is not true, and that the arguments I made are sufficient to tend to show that. The spherical cloud that you appear to imagine, on the other hand, with most of the material in circular orbits around the gravitational center, seems almost miraculously organized and completely unphysical to me.
As I understand it, you are saying that the more massive atoms have a larger radial extent only because they are hotter. The thermal velocities should be isotropically distributed, so this would imply a compact sphere of helium gas embedded in a hotter, fluffier sphere of xenon gas.
This indicates a misunderstanding of what I wrote of such depth that I am not sure anything else I might say will be more than an exercise in futility for each of us.
As I explicitly stated, I begin with a cloud in which xenon and helium are both evenly distributed and are at the same temperature throughout the cloud. Then I use a combination of dynamic and thermodynamic arguments to attempt to show that, as the structure of the cloud evolves under the influence of its own gravitational field, that initial state will change in such a way that the more massive xenon atoms will tend to be found more toward the center of the cloud as time progresses. As I also explicitly said, the xenon in the process of contraction of the cloud initially heats up because it has so much more potential energy wherever it is other than at the exact center, but that this will be equalized by collisions.
posted by jamjam at 1:55 PM on April 3, 2009
If the atoms in a nebula were all in stable circular orbits, the nebula could never contract under the influence of its own gravitational field, any more than the planets of our solar system, also in stable orbits, are now contracting toward the sun.
The cloud of gas I imagined for my little thought experiment was meant to be an idealization retaining some essential features of the sort of cloud I've seen hypothesized to be the starting point of the solar system, perhaps arising partly from material expelled from a supernova, and generally chaotic with atoms going in all different directions, and with all kinds of angular momentums with respect to the gravitational center, with all those chaotic vectors adding up to a small net angular momentum for the cloud as a whole. My ultimate purpose for this thought experiment was to investigate your categorical assertion that "Gravity doesn't segregate the ingredients if they are initially mixed." I think this is not true, and that the arguments I made are sufficient to tend to show that. The spherical cloud that you appear to imagine, on the other hand, with most of the material in circular orbits around the gravitational center, seems almost miraculously organized and completely unphysical to me.
As I understand it, you are saying that the more massive atoms have a larger radial extent only because they are hotter. The thermal velocities should be isotropically distributed, so this would imply a compact sphere of helium gas embedded in a hotter, fluffier sphere of xenon gas.
This indicates a misunderstanding of what I wrote of such depth that I am not sure anything else I might say will be more than an exercise in futility for each of us.
As I explicitly stated, I begin with a cloud in which xenon and helium are both evenly distributed and are at the same temperature throughout the cloud. Then I use a combination of dynamic and thermodynamic arguments to attempt to show that, as the structure of the cloud evolves under the influence of its own gravitational field, that initial state will change in such a way that the more massive xenon atoms will tend to be found more toward the center of the cloud as time progresses. As I also explicitly said, the xenon in the process of contraction of the cloud initially heats up because it has so much more potential energy wherever it is other than at the exact center, but that this will be equalized by collisions.
posted by jamjam at 1:55 PM on April 3, 2009
This indicates a misunderstanding of what I wrote of such depth that I am not sure anything else I might say will be more than an exercise in futility for each of us.
Sorry I misunderstood you, but I'm glad it *was* a misunderstanding, because it didn't make much sense!
My ultimate purpose for this thought experiment was to investigate your categorical assertion that "Gravity doesn't segregate the ingredients if they are initially mixed." I think this is not true, and that the arguments I made are sufficient to tend to show that.
I'm sorry to say that your arguments (as written and interpreted) are not sufficient. I'm a professional astronomer and I had a hard time figuring out what you were talking about. Just to be sure, I had two of my colleagues down the hall read what you wrote, and they didn't buy it either.
BTW, it wasn't categorical. I allowed for the effects of buoyancy at high densities, and gave the example of planetary differentiation and the Earth's iron core as an example.
The spherical cloud that you appear to imagine, on the other hand, with most of the material in circular orbits around the gravitational center, seems almost miraculously organized and completely unphysical to me.
When talking about circular orbits, I was referring to the nature of the orbits in the subsequent disk, which is denser and rapidly rotating. The planets formed form this disk material, and they have remarkably circular orbits. Check out this simulation! (You have to scroll down a bit).
At equilibrium, will we see a uniform distribution of Xe atoms throughout the cloud, as we we did initially? I don't see how. If that were the case, the cloud could heat up more, and minimize its potential energy more (obeying the minimum total potential energy principle*) if the Xe atoms tended to be found more near the center. The segregation would not be total because thermal motions of the two types of atoms would tend to produce some mixing.
It seems like this is the crucial paragraph where you try to explain why the Xe and He spatial distributions should evolve differently from one another. No one I showed this to understood the logic here. A star eventually forms in the middle. By equilibrium, are you talking about stellar hydrostatic equilibrium, where the gravitational force is balanced by thermal pressure? By this point, the densities are high enough that buoyancy is important, as I noted above. But of course, looking at the system at this stage doesn't address the original poster's question of why the Sun is made mostly of Hydrogen. If you don't think it's futile to try to clarify, you can assume we know about the Second Law.
posted by pizzazz at 8:17 PM on April 3, 2009
Sorry I misunderstood you, but I'm glad it *was* a misunderstanding, because it didn't make much sense!
My ultimate purpose for this thought experiment was to investigate your categorical assertion that "Gravity doesn't segregate the ingredients if they are initially mixed." I think this is not true, and that the arguments I made are sufficient to tend to show that.
I'm sorry to say that your arguments (as written and interpreted) are not sufficient. I'm a professional astronomer and I had a hard time figuring out what you were talking about. Just to be sure, I had two of my colleagues down the hall read what you wrote, and they didn't buy it either.
BTW, it wasn't categorical. I allowed for the effects of buoyancy at high densities, and gave the example of planetary differentiation and the Earth's iron core as an example.
The spherical cloud that you appear to imagine, on the other hand, with most of the material in circular orbits around the gravitational center, seems almost miraculously organized and completely unphysical to me.
When talking about circular orbits, I was referring to the nature of the orbits in the subsequent disk, which is denser and rapidly rotating. The planets formed form this disk material, and they have remarkably circular orbits. Check out this simulation! (You have to scroll down a bit).
At equilibrium, will we see a uniform distribution of Xe atoms throughout the cloud, as we we did initially? I don't see how. If that were the case, the cloud could heat up more, and minimize its potential energy more (obeying the minimum total potential energy principle*) if the Xe atoms tended to be found more near the center. The segregation would not be total because thermal motions of the two types of atoms would tend to produce some mixing.
It seems like this is the crucial paragraph where you try to explain why the Xe and He spatial distributions should evolve differently from one another. No one I showed this to understood the logic here. A star eventually forms in the middle. By equilibrium, are you talking about stellar hydrostatic equilibrium, where the gravitational force is balanced by thermal pressure? By this point, the densities are high enough that buoyancy is important, as I noted above. But of course, looking at the system at this stage doesn't address the original poster's question of why the Sun is made mostly of Hydrogen. If you don't think it's futile to try to clarify, you can assume we know about the Second Law.
posted by pizzazz at 8:17 PM on April 3, 2009
If you don't think it's futile to try to clarify, you can assume we know about the Second Law.
I'm happy to make the acquaintance of a person on such free and easy terms with the 2nd Law; I've been introduced more than once, but the relationship has never become what I'd hoped it would, and Entropy has sometimes treated me very rudely in unexpected meetings.
I believe it is a mistake to think that what you are calling buoyancy begins or is important only when a cloud of gas stops contracting because of the build up of pressure within the cloud; at the micro level, where atoms of gas are exchanging energy and momentum in collision, that point would seem to be extremely hard to distinguish from what went before, and at the macro level it is a smooth and continuous process which amounts to the working out of the law of minimum potential energy in a particular instance. If anything, I think a point at which contraction in a gas cloud ceases could be seen as a milestone in the slowing down of the process of concentrating heavier elements toward the center. All that seems to me to be necessary for that principle of minimum potential energy to apply here from the very beginning is that the gaseous elements in the cloud collide and exchange kinetic energy and momentum, and as I said before, the only way I see for collisions to be avoided (in a cloud of more or less uniform density) is if the atoms are already in perfect non-intersecting orbits (I suppose the orbits could intersect as long as the atoms never collide), and in that case the cloud would never contract and heat up in the first place.
I think you're right to question any use of "at equilibrium" in the context of the solar system, though I think it does make sense for an isolated cloud of helium and xenon which is not too massive in the first place; if my argument is valid, such a cloud would end up at equilibrium spinning in space with the xenon more concentrated in the middle. For one thing, is the solar system at equilibrium right now? It may be in a steady state at present, but I've seen claims that chaos is so pervasive that the the solar system must ultimately fly apart altogether, in the very long run.
But in any case, invoking equilibrium is unnecessary, because the principle of minimum potential energy requires systems to move along a path that always reduces potential energy on the way toward equilibrium.
I knew that you have a Ph.D. in astronomy before I made my first comment, but not that you are a professional astronomer, and the thread has gone pretty much as I thought it would in the wake of my comment. I give your credentials great weight, actually, and I'd have to advise any readers who didn't for whatever reason want to try to go through the arguments for themselves that they should ignore me and listen to you (and your colleagues!).
Even so, I still think, at this point in time, that I am right, and more important, that Spoonman deserved my vote of support in celebration of what I saw as the excellence of his intuition, especially in the midst of the chorus telling him he was wrong.
posted by jamjam at 11:20 AM on April 6, 2009
I'm happy to make the acquaintance of a person on such free and easy terms with the 2nd Law; I've been introduced more than once, but the relationship has never become what I'd hoped it would, and Entropy has sometimes treated me very rudely in unexpected meetings.
I believe it is a mistake to think that what you are calling buoyancy begins or is important only when a cloud of gas stops contracting because of the build up of pressure within the cloud; at the micro level, where atoms of gas are exchanging energy and momentum in collision, that point would seem to be extremely hard to distinguish from what went before, and at the macro level it is a smooth and continuous process which amounts to the working out of the law of minimum potential energy in a particular instance. If anything, I think a point at which contraction in a gas cloud ceases could be seen as a milestone in the slowing down of the process of concentrating heavier elements toward the center. All that seems to me to be necessary for that principle of minimum potential energy to apply here from the very beginning is that the gaseous elements in the cloud collide and exchange kinetic energy and momentum, and as I said before, the only way I see for collisions to be avoided (in a cloud of more or less uniform density) is if the atoms are already in perfect non-intersecting orbits (I suppose the orbits could intersect as long as the atoms never collide), and in that case the cloud would never contract and heat up in the first place.
I think you're right to question any use of "at equilibrium" in the context of the solar system, though I think it does make sense for an isolated cloud of helium and xenon which is not too massive in the first place; if my argument is valid, such a cloud would end up at equilibrium spinning in space with the xenon more concentrated in the middle. For one thing, is the solar system at equilibrium right now? It may be in a steady state at present, but I've seen claims that chaos is so pervasive that the the solar system must ultimately fly apart altogether, in the very long run.
But in any case, invoking equilibrium is unnecessary, because the principle of minimum potential energy requires systems to move along a path that always reduces potential energy on the way toward equilibrium.
I knew that you have a Ph.D. in astronomy before I made my first comment, but not that you are a professional astronomer, and the thread has gone pretty much as I thought it would in the wake of my comment. I give your credentials great weight, actually, and I'd have to advise any readers who didn't for whatever reason want to try to go through the arguments for themselves that they should ignore me and listen to you (and your colleagues!).
Even so, I still think, at this point in time, that I am right, and more important, that Spoonman deserved my vote of support in celebration of what I saw as the excellence of his intuition, especially in the midst of the chorus telling him he was wrong.
posted by jamjam at 11:20 AM on April 6, 2009
law of minimum potential energy
Why do particles of different mass behave differently under this "law"? It seems that they should behave identically. Any particle, regardless of its mass, is at minimum potential energy conditions at the bottom of the gravity well.
posted by mr_roboto at 9:30 PM on April 6, 2009
Why do particles of different mass behave differently under this "law"? It seems that they should behave identically. Any particle, regardless of its mass, is at minimum potential energy conditions at the bottom of the gravity well.
posted by mr_roboto at 9:30 PM on April 6, 2009
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