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Marko S.
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27 Aug 2017 12:18

Watsisname wrote:
Source of the post So, yeah, this situation would not only "look like" a black hole, but must actually be a black hole.

Okay, thanks! But, can we make Earth so small within the radius of 1 km? Earth looks like Earth. but is so small that has big density. Would that make any difference?  
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27 Aug 2017 14:28

Watsisname wrote:
Source of the post I think you didn't convert the kilometers to meters

Sorry. I kept the comma at 6,772 for the mass at 30000 km range for a decimal point. In German the comma is the decimal point.
 
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28 Aug 2017 02:47

FastFourierTransform wrote:
PlutonianEmpire wrote:
Source of the post 1. Knowing the Moon gradually recedes from Earth as the planet's rotation slows down thanks to the mutual tidal interactions; does the rate the moon recedes get slower as Earth's rotation get slower?

You are totally right. 4.5 billion years ago the Moon was born at just 3.8 earth-radii of distance, 2.5 billion years ago is was 52 earth-radii of distance, and now the Moon is located 60.3 earth-radii away from us. This means that for the first 2 billion years the Moon moved 48.2 earth-radii but for the last 2.5 billion years it has only made 8.3 earth-radii (a huge decrease in receding velocity).

This effect is summarized by the equation (2) of page 601 of this research paper. The a refers to the semi-major axis of the lunar orbit (a.k.a it's distance to Earth) and the dotted a refers to the increase in a (a.k.a the speed at which the Moon recedes from Earth). As you can see the dependence of one another is to the 5.5 power. This means that if the moon recedes at a speed v while been at a distance x from earth, then by the time it has receded to a distance 2x it is receding just a mere 2.2% of the initial receding rate v (45 times slower).


Wow, thanks! So two more moon questions:

With your answer in mind, how likely is it that the Moon will stay with us until the Sun expands after the end of the main sequence phase?

Secondly, I was googling shadow snakes, and noticed that this eclipse effect still seems unsolved. What's the likelihood that in addition to the effects from our atmsphere, it is also from the *moon's* atmosphere as well, since the light would be travelling through that first right before reaching the Earth?
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28 Aug 2017 03:20

PlutonianEmpire wrote:
Source of the post Secondly, I was googling shadow snakes, and noticed that this eclipse effect still seems unsolved. What's the likelihood that in addition to the effects from our atmsphere, it is also from the *moon's* atmosphere as well, since the light would be travelling through that first right before reaching the Earth?

The Moon's atmosphere is so thin as to be completely negligible here.  The effect is instead related to scintillation of the remaining crescent of sunlight through atmospheric turbulence -- the same effect that causes stars to twinkle at night.  Which should make some sense, as in the moments right before and after totality the remaining crescent is very thin and prone to being distorted like that -- just like the shimmering appearance of planets or the Moon in a telescope under unsteady air, or seeing something through heat haze.

It is notable that in the 2015 eclipse at Svalbard, very strong shadowbands were observed, and the solar crescent also twinkled strongly.  But in the 2017 eclipse at Madras, no shadowbands were observed, and the remaining crescent did not appear to twinkle at all.

An alternative theory has proposed that the effect is related to supersonic movements of the atmosphere, related to the cooling effect of the shadow which is itself supersonic.  But I think observations refute this, since the strong bands at Svalbard were associated with very weak cooling, while there was very strong cooling at Madras with no bands at all.
 
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28 Aug 2017 03:26

Somebody asked me today (somewhat jokingly) whether I think it's a coincidence that the Sun and the Moon have almost precisely the same apparent size.  Of course it's a coincidence, but the question becomes more complicated the more thought it's given.  The Moon seems to have had an important role in the evolution of the Earth including the evolution of life.  Had there been no moon, or a moon either significantly different in size or distance, we wouldn't be here (true even for small differences in the early history of Earth), but could we at all be here?  Do planets which have a moon and star of roughly the same apparent sizes have better conditions for life?  I.e. do favourable tidal forces and solar heating coincide with similar apparent sizes?
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28 Aug 2017 03:38

Watsisname wrote:
Source of the post But in the 2017 eclipse at Madras, no shadowbands were observed, and the remaining crescent did not appear to twinkle at all.

I didn't see any shadow bands at all, but YouTube is full of videos of shadow bands recorded during last week's eclipse.  Haven't seen one from Madras, though, and they're only visible on bright surfaces:


Still, watching this effect on a small sheet versus around your feed and everywhere around you are two different stories. :)
Also, the videos from this year's eclipse seem to show more random bands, whereas in Svalbard they could be seen drifting, a bit like shadows moving over a shallow seafloor.  It may just be that the movement is hard to see on only a small white patch, though.
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28 Aug 2017 07:10

PlutonianEmpire wrote:
Source of the post With your answer in mind, how likely is it that the Moon will stay with us until the Sun expands after the end of the main sequence phase?

It is very likely. The moon moves off the earth by 38 millimeters a year. (According to Wikipedia). In 10 billion years this would be only 380000 km, which is about a doubling of the distance. But still far within the hill sphere of the earth.

(As the tidal forces become weaker with increasing distance, I suppose that the speed decreases with which the moon moves away from the earth.)

Also that the earth will be tidal locked to the moon, happens long after the sun becomes a Red Giant.
 
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28 Aug 2017 08:14

midtskogen wrote:
Source of the post I didn't see any shadow bands at all, but YouTube is full of videos of shadow bands recorded during last week's eclipse.  Haven't seen one from Madras, though, and they're only visible on bright surfaces:

A small group of people nearby where I was had a sheet on the ground for catching the crescent shape and there were visible shadow bands.  It was very interesting to see.
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29 Aug 2017 16:37

Watsisname wrote:
A-L-E-X wrote:
Source of the post The funny thing is that the universe does expand at faster than the speed of light (it's the basis for the Alcubierre drive).

The expansion actually doesn't have a speed in that kind of sense. This is a very common confusion and might be worth spending a few moments on.

Suppose you look at a galaxy which is 100 Mpc away, and you find that it is receding at 7,000 km/s.  Then you choose another galaxy that is 200 Mpc away (twice as far).  You will find that it is receding at 14,000 km/s (twice as fast).  Indeed, for a wide range of distances, you'll find recession velocities that increase according to their distance from you (Hubble's Law).  

So, what would you call the universe's expansion speed in this example?  Is it faster than light?  How do you know?

It turns out we cannot define an expansion speed at all, but rather a speed per distance.  That is, the speed depends on distance!  The measure of expansion cosmologists use is called Hubble's Constant, and has units of km/s/Mpc.  

What this means is that no matter how small the Hubble's Constant is (provided it is not zero) there will always be a distance for which things are receding from us faster than the speed of light.  So the notion that the expansion is "faster than light" is totally meaningless. 

Things moving away from us due to expansion is a very different type of motion than things literally moving through the space.  It's not the things that are moving through space, but the space itself expanding between them, so the speed of light is not being violated (the rule is that things cannot move through the space faster than light).

Alcubierre's drive is based on a similar idea. While it is impossible to move something through space faster than light, it might be possible to distort the space-time such that some patch of it can be transported through the universe faster than light.  But to do this, the space-time must be distorted in a very strange way which is most likely impossible -- even if it satisfies the equations of general relativity.

Good point, Wat.  Another way of stating this is that the universe with its own space-time is expanding into something which we can call null space-time. In other words, speed is undefined since in this null space-time, our sense of space and time have no meaning.
That is my eventual hope for "FTL" drives-wormholes, etc., Einstein never accounted for the possibilities of anything outside our own universe, and Relativity only deals with the 4 dimensions of space-time.  Whenever we get a workable theory of quantum gravity, we might learn that our universe (and Relativity) is but a subset of something much greater.  Einstein himself was working on a multidimensional theory of everything in his later years, but of course back then we did not have the supercollider technology that we have today that would have shown him how the EM force and weak force can be united at very high energies.
A good indication that dimensionality changes at very high energy levels (like those present at the BB) is how very high energy cosmic rays have only two degrees of freedom (they move in 2D), another interesting aspect of this is that gravity ceases to be an attractive force in 2D space (this shows how a collapsing universe can re-expand.)
 
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29 Aug 2017 16:41

Watsisname wrote:
JackDole wrote:
Source of the post I assume it is a write error. When I apply your formula I get 1.52913392 solar masses. (Approximately 1.530)

I think you didn't convert the kilometers to meters (necessary for dimensional consistency, e.g. if speed of light is 3x108 m/s and G is 6.67x10-11 m3kg-1s-2).  So it must be multiplied by a thousand.

Marko S., I think there would be no object other than a black hole that could make light orbit around it by gravity.  A neutron star is closest possible object to a black hole, yet still has not quite strong enough gravity to do this. (Typical mass is 1 to 2 solar masses, within a radius of about 10km, yet the computed size of the photon orbit would be smaller than that radius, so it doesn't exist.)  

So, yeah, this situation would not only "look like" a black hole, but must actually be a black hole.

Quark stars and cosmic strings, if they exist might also be able to do this :-)
 
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29 Aug 2017 16:44

midtskogen wrote:
Somebody asked me today (somewhat jokingly) whether I think it's a coincidence that the Sun and the Moon have almost precisely the same apparent size.  Of course it's a coincidence, but the question becomes more complicated the more thought it's given.  The Moon seems to have had an important role in the evolution of the Earth including the evolution of life.  Had there been no moon, or a moon either significantly different in size or distance, we wouldn't be here (true even for small differences in the early history of Earth), but could we at all be here?  Do planets which have a moon and star of roughly the same apparent sizes have better conditions for life?  I.e. do favourable tidal forces and solar heating coincide with similar apparent sizes?

Yes I have been thinking of this also.  You need tides for sea life to move onto land and I'm not sure the sun alone would've been enough.  Not only that, but the moon was a celestial pin-cushion for many an asteroid that could have hit Earth.  The aftermath of an asteroid collision accelerates evolution, but the impact itself kills off up to 90% of all life, so without the moon evolution might have been in a perpetual start-stop-start-stop sequence.
 
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29 Aug 2017 19:32

A-L-E-X wrote:
Source of the post Good point, Wat.  Another way of stating this is that the universe with its own space-time is expanding into something which we can call null space-time. In other words, speed is undefined since in this null space-time, our sense of space and time have no meaning.

For sure, there's a helpful analogy for the expansion as a 3D space expanding into some higher dimensional space we can't perceive.  It's also possible (actually preferred teaching among most cosmological texts) to just treat it as a 3D expansion with no higher dimension at all.  This is necessary and sufficient to explain it with math (basically you have three spatial dimensions in the space-time metric, and the "scale" of them is a function of time.)  This fits into general relativity and gives the right predictions, but conceptually it can be a bit difficult to imagine how it works that way.  

It's also a bit limiting -- although it correctly predicts everything we can observe and currently understand with the universe, it doesn't let you go much further.  It's when you get into the deeper models of gravitation and cosmology that the interesting speculative stuff comes into play, like the higher dimensions, multiple universes, colliding branes, and so forth. :)


A-L-E-X wrote:
Source of the post Quark stars and cosmic strings, if they exist might also be able to do this

Good point, I forgot about those!  Strings in particular could cause some really weird and strong distortions of the space and light around them.

midtskogen wrote:
Source of the post Somebody asked me today (somewhat jokingly) whether I think it's a coincidence that the Sun and the Moon have almost precisely the same apparent size.  Of course it's a coincidence, but the question becomes more complicated the more thought it's given. 

This is a fascinating question!  Some years ago my astrobiology professor raised the same question for the class, and he seemed to be a big proponent of the idea.  I'm a bit doubtful but think there's definitely aspects which are important.  It is a very difficult thing to research and find robust answers for.

A-L-E-X wrote:
Source of the post Not only that, but the moon was a celestial pin-cushion for many an asteroid that could have hit Earth.

I've heard people suggest this before and it sounds appealing, but when we run through the numbers I think it's pretty doubtful.  The Moon currently covers only about 0.0005% of the sky.  (Yes, really!  I find this a surprising and neat bit of trivia).  The full "solid angle" of the sky is 4*pi steradians, and the Moon is about a half degree wide, or a solid angle of about pi*(0.25deg*pi/180)^2 = 0.000019*pi steradians.  The ratio of the two is about 5x10-6, or 0.0005%.

Expressed another way, that means it would take about 200,000 full moons to fill the sky!  It also means that out of a million asteroids that would hit Earth, only about FIVE of them would be blocked by the Moon.

Even if we look very far into the past the Moon's shielding ability wouldn't improve much.  There are large uncertainties in the evolution of the Moon's orbit since its formation, but even assuming it was just 1/4th of its current distance 3 billion years ago (probably way too generous), its screening ability would be about 80 out of a million.  And at the Roche limit of ~9500km, it still blocks less than 1% of them.

So I don't think the Moon could ever have done much to protect Earth from asteroids, but it certainly does do a lot for producing tides and keeping the Earth's obliquity in check.  It's an interesting question whether this naturally leads to an expectation that a complex life arises when Moon and Sun are of similar angular size, but I haven't seen a lot of strong research on it.
 
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29 Aug 2017 21:54

Watsisname wrote:
A-L-E-X wrote:
Source of the post Good point, Wat.  Another way of stating this is that the universe with its own space-time is expanding into something which we can call null space-time. In other words, speed is undefined since in this null space-time, our sense of space and time have no meaning.

For sure, there's a helpful analogy for the expansion as a 3D space expanding into some higher dimensional space we can't perceive.  It's also possible (actually preferred teaching among most cosmological texts) to just treat it as a 3D expansion with no higher dimension at all.  This is necessary and sufficient to explain it with math (basically you have three spatial dimensions in the space-time metric, and the "scale" of them is a function of time.)  This fits into general relativity and gives the right predictions, but conceptually it can be a bit difficult to imagine how it works that way.  

It's also a bit limiting -- although it correctly predicts everything we can observe and currently understand with the universe, it doesn't let you go much further.  It's when you get into the deeper models of gravitation and cosmology that the interesting speculative stuff comes into play, like the higher dimensions, multiple universes, colliding branes, and so forth. :)


A-L-E-X wrote:
Source of the post Quark stars and cosmic strings, if they exist might also be able to do this

Good point, I forgot about those!  Strings in particular could cause some really weird and strong distortions of the space and light around them.

midtskogen wrote:
Source of the post Somebody asked me today (somewhat jokingly) whether I think it's a coincidence that the Sun and the Moon have almost precisely the same apparent size.  Of course it's a coincidence, but the question becomes more complicated the more thought it's given. 

This is a fascinating question!  Some years ago my astrobiology professor raised the same question for the class, and he seemed to be a big proponent of the idea.  I'm a bit doubtful but think there's definitely aspects which are important.  It is a very difficult thing to research and find robust answers for.

A-L-E-X wrote:
Source of the post Not only that, but the moon was a celestial pin-cushion for many an asteroid that could have hit Earth.

I've heard people suggest this before and it sounds appealing, but when we run through the numbers I think it's pretty doubtful.  The Moon currently covers only about 0.0005% of the sky.  (Yes, really!  I find this a surprising and neat bit of trivia).  The full "solid angle" of the sky is 4*pi steradians, and the Moon is about a half degree wide, or a solid angle of about pi*(0.25deg*pi/180)^2 = 0.000019*pi steradians.  The ratio of the two is about 5x10-6, or 0.0005%.

Expressed another way, that means it would take about 200,000 full moons to fill the sky!  It also means that out of a million asteroids that would hit Earth, only about FIVE of them would be blocked by the Moon.

Even if we look very far into the past the Moon's shielding ability wouldn't improve much.  There are large uncertainties in the evolution of the Moon's orbit since its formation, but even assuming it was just 1/4th of its current distance 3 billion years ago (probably way too generous), its screening ability would be about 80 out of a million.  And at the Roche limit of ~9500km, it still blocks less than 1% of them.

So I don't think the Moon could ever have done much to protect Earth from asteroids, but it certainly does do a lot for producing tides and keeping the Earth's obliquity in check.  It's an interesting question whether this naturally leads to an expectation that a complex life arises when Moon and Sun are of similar angular size, but I haven't seen a lot of strong research on it.

Yes, and I don't know how much we can deduce from a sample size of one :P  I remember many years ago it was thought that every solar system we would find would have inner planets close to the sun and gas giants much farther out.  Of course, we now see that solar systems come in all shapes and sizes and varieties.  I would like to think that lifebearing planets possess a similar variety.
Wat, so it seems like the most basic model of the universe has it expanding into itself?  So basically speaking, the universe creates its own space and time is just a function of how quickly it creates that space?  So trying to ascribe a speed to that expansion is like asking where the "center" of the universe is- the answer is undefined because in a universe which creates its own space, that point no longer exists!
I think this is how Linde stated that it is possible for a universe to be created inside a black hole, it expands into the "spacetime" that it creates.  If we analogize to our spacetime, it's not as if our universe is expanding into hyperspacetime, null spacetime or the dimensions of a higher universe, but creating its own space and expanding into that which it is creating.  Our spacetime has no bearing or dimensionality in the spacetime of the parent universe (and vice versa.)
 
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29 Aug 2017 23:37

A-L-E-X wrote:
Source of the post I would like to think that lifebearing planets possess a similar variety.

Me, too. :)

A-L-E-X wrote:
Source of the post Wat, so it seems like the most basic model of the universe has it expanding into itself?  So basically speaking, the universe creates its own space and time is just a function of how quickly it creates that space?

I try not to think of it as the universe creating space -- that provokes a whole nest of difficult questions like "how does it create space?" or "where does that new space come from?".  There aren't meaningful answers to those questions, nor does describing it that way make the math any easier.

Instead, I like to think of the universe like a grid.  The grid is just an imaginary thing you slap onto the space to mark locations, just like street addresses.  Then to a very good approximation, the locations of things in the large scale universe (like clusters of galaxies) are fixed on that grid, since they don't move much through the space.  Now the question we're interested in is how does that grid evolve with time?  If the grid expands, then the physical distance between two locations gets larger, even though neither location is actually moving.

General relativity (GR) describes how the shape of space (and space-time) is affected by what the space contains -- the matter and energy.  Here's where things get a little weird, and possibly even surprising if you've heard some common descriptions about how GR works.

Most people have heard of the rubber sheet or trampoline analogy for gravitation in GR.  As it often goes "an empty space is like a flat rubber sheet.  Add a big mass to it, and the sheet gets curved."  That's sort of true, especially on a local scale, but the surprising bit is that in cosmology, empty space is actually not flat.  We call that a Milne Universe, which is totally empty and has negative curvature, meaning straight parallel lines will spread apart and the sum of angles in a triangle is less than 180°. 

That's probably pretty unintuitive.  The one thing about it that is intuitive is that such a universe will have a constant expansion rate.  There isn't anything trying to pull things apart or back together again, so there's no acceleration.  If it started out expanding it will stay expanding at the same rate forever.  

Now let's suppose we fill the space uniformly with matter.  A little bit at first, and then more and more.  This will add a gravitating effect, where everything is pulling on everything else and therefore the universe is pulled back in on itself.  If the universe started out static (a stationary grid), then it will start to shrink and collapse as a Big Crunch.  If it started out expanding, then the expansion rate will slow down.  The space also gets less and less curved -- closer and closer to "flat".  Eventually we'll reach a point called the "critical density" of the universe, which happens to be just a few hydrogen atoms per cubic meter, and this makes the geometry perfectly flat (straight parallel lines remain parallel, and sum of angles in a triangle is exactly 180°).  

A universe filled only with matter and exactly enough of it to make it "flat" is called an Einstein-de Sitter universe.  We don't live in such a universe.
The universe we do live in has some matter in it (obviously), but it isn't enough to make the space flat.  However, we also know that the space is close to flat.  So there must be something else.  Part of it is dark matter, which is just like adding more regular matter.  But the even bigger part is the dark energy.

The dark energy is kind of like adding a bit of something with antigravity everywhere.  It's a property of the space itself which makes it expand more.  A universe filled only with dark energy, and just enough of it to make it flat, is a de Sitter universe, and it expands exponentially faster.

The universe we live in seems to be somewhere between the de Sitter and Einstein-de Sitter universe type.  It is flat with a mixture of matter (regular and dark) and dark energy.  It started out expanding after the Big Bang, slowed down at first due to the matter, but now speeds up due to the dark energy, since the effect of matter weakens as it gets diluted while dark energy does not.

Okay, that's probably a lot to digest.  What's the take-home message?  The point is that in GR, matter and energy don't just cause gravity, but they also affect the shape of space itself -- the shape of the grid I was talking about.  It also says that the size of the grid can change, and the way it changes depends on what the space contains.  Matter will try to slow it down by pulling things together.  Dark energy will try to speed it up by spreading everything apart.

A-L-E-X wrote:
Source of the post So trying to ascribe a speed to that expansion is like asking where the "center" of the universe is- the answer is undefined because in a universe which creates its own space, that point no longer exists!

It's more like the problem of comparing velocity with acceleration.  The units don't work.  There is definitely a "rate" to the expansion of the universe (e.g. it seems to be about 70 km/s/Mpc), but it is not a "speed".  It is a "speed per distance".  Something twice as far away recedes twice as fast.  Because space itself expands, the farther away two things are, the faster they move away, so you can't ascribe a unique speed to the whole thing.  Instead you ascribe a speed per distance to the whole thing, but that's incomparable to plain "speed" as in speed of light.

What making the expansion rate faster will do is cause the cosmological horizon to shrink closer to you.  Objects may slip past the horizon and lose all further causal contact with you.  This is what happened with inflation, when nearby regions of space that had been able to "talk" to each other were suddenly driven apart so quickly that the causal connection was lost, and now they are no longer in the same observable universe as each other.  This is what resolves the Horizon Problem, which asked how distant parts of the universe could look so remarkably similar, as if they had actually been in contact with each other and established thermal equilibrium.
 
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30 Aug 2017 00:23

Wat, is there some limited evidence for quark stars and cosmic strings and other topological defects left over from the BB?  If so (more specifically the latter) might be able to account for the clumping we see in superclusters.  I remember reading that it's been difficult to account for superclusters forming so quickly in a universe that's only around 14 billion years old.

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