The Logarithmic Spiral

Now all you guys who are like “Yeah man the Fibonacci spiral is awesome” can just take a back seat here, because here we have the coolest of all spirals: the logarithmic spiral. Truth be told just about every time you’ve heard someone talk about the Fibonacci (or more accurately known Golden Spiral) they’ve been talking about this guy and just not realized it. The logarithmic spiral is given by the equation r=ae^(bθ) where r is the radius, a & b are positive constants and θ is the angle around the origin.

The logarithmic spiral also pops up quite often in nature, being the mathematical pattern behind such things as nautilus shells, Romanesco broccoli, spiral galaxies, the Mandelbrot set, storms, ferns and even sea horses.

The Life and Death of StarsI know tumblr is mostly filled of awe-inspiring, but physically quite dull nebulas, so here is a crash course in the life cycle of stars. Which are totally way cooler.ProtostarsStars begin their lives rather unassumingly as blobs of gas in molecular clouds that slowly grow in density even though they’re still less dense than vaccuum chambers on Earth. Slowly gravity pulls in more atoms and molecules, mostly hydrogen and helium until there’s a gravitational instability that causes this cloud to go over the tipping point and begin to collapse itself. This can be brought about by strong gravitational effects, such as the death of another star as a supernova. The collapse itself is known as a Jeans instability. As this happens the gravitational energy gives way to heat energy and the blob of gas rapidly begins to heat up and a protostellar core forms. This contraction typically takes between 10 and 15 million years.Main phaseThe star spends the majority of it’s lifetime in the main phase, what this is when the heat of the star reaches a high enough temperature to allow a fusion reaction of hydrogen into helium. The beginning of this phase is comprised of relatively small stars known as red and yellow dwarfs (our sun is a yellow dwarf). There is another type of object known as a brown dwarf and is essentially a star that did not reach enough mass or temperature to begin the fusion reaction. As the helium concentration of a star increases it gradually swells and increases in temperature. Stars can spend a range of time in the main sequence, our sun is predicted to last 10^10 years, while others may live much shorter or much longer. A red dwarf for example will last hundreds of billions of years, older than the universe is now.Post-main SequenceThis is the phase characterized by red giants which are stars that begin to expand and cool releasing shells of gas to form planetary nebula. Larger red giants however begin the next stage in their life, they then begin to heat up again in the layer around the core and begin the fusion of helium into heavier atoms like cosmic furnaces. It’s stars like this that are the reason you’re alive. Stars that are yet more massive, about 9 solar masses become what is imaginatively known as red supergiants in their helium fusing stage. Towards the end of their lives these stars are fusing different elements at different layers, helium on the outside and getting progressively larger elements as we head towards the center like an incredibly hot, giant onion.The collapse
Finally after billions of years we come to the death of a star. This can occur in many different ways, some relatively peaceful, others violent. Most average sized stars begin to shed their outer layers and the core compresses to form a white dwarf, with mass that of the sun and size that of the Earth these guys are pretty dense. They’re also made from electron-degenerative matter which can be thought of as atoms or molecules in which the electrons occupy higher than normal energy levels due to the high amount of pressure and energy concentrated in a small space.
Larger stars which have made it all the way to synthesizing iron have a more dramatic exit, the iron core of the center grows so dense and massive that the atoms the atoms themselves become crushed causing electrons to collapse into their protons. This itself causes the famous event known as a supernova. From here there are two other remaining options, most stars will remain as nothing more than incredibly dense neutron stars (such as pulsars) while even more massive ones will collapse until they occupy no space at all, becoming black holes.

The Life and Death of Stars

I know tumblr is mostly filled of awe-inspiring, but physically quite dull nebulas, so here is a crash course in the life cycle of stars. Which are totally way cooler.

Protostars

Stars begin their lives rather unassumingly as blobs of gas in molecular clouds that slowly grow in density even though they’re still less dense than vaccuum chambers on Earth. Slowly gravity pulls in more atoms and molecules, mostly hydrogen and helium until there’s a gravitational instability that causes this cloud to go over the tipping point and begin to collapse itself. This can be brought about by strong gravitational effects, such as the death of another star as a supernova. The collapse itself is known as a Jeans instability. As this happens the gravitational energy gives way to heat energy and the blob of gas rapidly begins to heat up and a protostellar core forms. This contraction typically takes between 10 and 15 million years.

Main phase

The star spends the majority of it’s lifetime in the main phase, what this is when the heat of the star reaches a high enough temperature to allow a fusion reaction of hydrogen into helium. The beginning of this phase is comprised of relatively small stars known as red and yellow dwarfs (our sun is a yellow dwarf). There is another type of object known as a brown dwarf and is essentially a star that did not reach enough mass or temperature to begin the fusion reaction. As the helium concentration of a star increases it gradually swells and increases in temperature. 

Stars can spend a range of time in the main sequence, our sun is predicted to last 10^10 years, while others may live much shorter or much longer. A red dwarf for example will last hundreds of billions of years, older than the universe is now.

Post-main Sequence

This is the phase characterized by red giants which are stars that begin to expand and cool releasing shells of gas to form planetary nebula. Larger red giants however begin the next stage in their life, they then begin to heat up again in the layer around the core and begin the fusion of helium into heavier atoms like cosmic furnaces. It’s stars like this that are the reason you’re alive. Stars that are yet more massive, about 9 solar masses become what is imaginatively known as red supergiants in their helium fusing stage. Towards the end of their lives these stars are fusing different elements at different layers, helium on the outside and getting progressively larger elements as we head towards the center like an incredibly hot, giant onion.

The collapse

Finally after billions of years we come to the death of a star. This can occur in many different ways, some relatively peaceful, others violent. Most average sized stars begin to shed their outer layers and the core compresses to form a white dwarf, with mass that of the sun and size that of the Earth these guys are pretty dense. They’re also made from electron-degenerative matter which can be thought of as atoms or molecules in which the electrons occupy higher than normal energy levels due to the high amount of pressure and energy concentrated in a small space.

Larger stars which have made it all the way to synthesizing iron have a more dramatic exit, the iron core of the center grows so dense and massive that the atoms the atoms themselves become crushed causing electrons to collapse into their protons. This itself causes the famous event known as a supernova. From here there are two other remaining options, most stars will remain as nothing more than incredibly dense neutron stars (such as pulsars) while even more massive ones will collapse until they occupy no space at all, becoming black holes.

Gravitational LensingFigured I should go into a bit more detail about this as it’s totally cool. As we know mass distorts spacetime we also know that the path light takes follows these contours. Well this can lead to a whole range of odd things such as the Einstein Cross up there (named because Einstein’s relativity theorized gravitational lensing). To the untrained eye it looks like 5 stars arranged in a cross shape, pretty cool I guess, but in reality it’s only one quasar (first of a quasar is a luminous galactic nucleus, not a star per se) and the light from it is being bent in such a way to give the appearance of multiple quasars which is TOTALLY FUCKING AWESOME GUYS. The quasar itself is also located 8 billion light years away while the mass doing the lensing is only 400 million light years away from us.

Gravitational Lensing

Figured I should go into a bit more detail about this as it’s totally cool. As we know mass distorts spacetime we also know that the path light takes follows these contours. Well this can lead to a whole range of odd things such as the Einstein Cross up there (named because Einstein’s relativity theorized gravitational lensing). To the untrained eye it looks like 5 stars arranged in a cross shape, pretty cool I guess, but in reality it’s only one quasar (first of a quasar is a luminous galactic nucleus, not a star per se) and the light from it is being bent in such a way to give the appearance of multiple quasars which is TOTALLY FUCKING AWESOME GUYS. The quasar itself is also located 8 billion light years away while the mass doing the lensing is only 400 million light years away from us.

Dark Matter and Dark EnergyThese are two words you often hear thrown around and more often that not I come across people who don’t know precisely what they are or even that they are two quite different things. So here we go.Dark MatterWhen you take a look at a galaxy you see a certain characteristic known as gravitational lensing where light is warped in a certain way by mass. From this you can deduce an estimate of the mass of the galaxy. However when we compare this to the mass we estimated based on the concentration, size and distribution of visible mass within the galaxy we find the two numbers to be at odds and not only this but the greatest curving of space time is found in the spaces between objects where nothing can be seen. The difference in masses is believed to be caused by the elusive dark matter, so called because it warps spacetime like regular matter but is completely invisible (hence the dark). All in all dark matter constitutes 23% of the mass-energy density of the universe and a worrying 83% of the total amount of matter. The universe is made chiefly of stuff you cannot see.Dark EnergyDark energy is also the answer to a problem, behaving somewhat like the x value in an algebraic equation we’re forced to solve. The problem lays in the fact that the universe is continuing to expand at an ever increasing rate and we have no idea why. When you think about it it really doesn’t make any sense, you would expect the universe’s expansion to slow down or at least stay constant but unfortunately this isn’t the case. Thus we call this mysterious energy that is causing the increasing the rate at which the universe expands “dark energy”.We really know so very little.

Dark Matter and Dark Energy

These are two words you often hear thrown around and more often that not I come across people who don’t know precisely what they are or even that they are two quite different things. So here we go.

Dark Matter

When you take a look at a galaxy you see a certain characteristic known as gravitational lensing where light is warped in a certain way by mass. From this you can deduce an estimate of the mass of the galaxy. However when we compare this to the mass we estimated based on the concentration, size and distribution of visible mass within the galaxy we find the two numbers to be at odds and not only this but the greatest curving of space time is found in the spaces between objects where nothing can be seen. The difference in masses is believed to be caused by the elusive dark matter, so called because it warps spacetime like regular matter but is completely invisible (hence the dark). All in all dark matter constitutes 23% of the mass-energy density of the universe and a worrying 83% of the total amount of matter. The universe is made chiefly of stuff you cannot see.

Dark Energy

Dark energy is also the answer to a problem, behaving somewhat like the x value in an algebraic equation we’re forced to solve. The problem lays in the fact that the universe is continuing to expand at an ever increasing rate and we have no idea why. When you think about it it really doesn’t make any sense, you would expect the universe’s expansion to slow down or at least stay constant but unfortunately this isn’t the case. Thus we call this mysterious energy that is causing the increasing the rate at which the universe expands “dark energy”.

We really know so very little.

I wanted to do a post on all the different types of subatomic particles, but determined it would be too lengthy and not nearly informative enough. As such I’ve decided to attempt a small series. Starting with QUARKS!Some of you may have heard that quarks make up all matter, this itself isn’t true, quarks only make up a group of particles known as hadrons (such as neutrons and protons). Quarks come in 6 varieties or “flavors” called: up, down, strange, charm, top and bottom. Protons are made of 2 down quarks and 1 up quark and when undergoing radioactive decay protons may change to a neutron and an electron. On the level of quarks what happens here is one of the down quarks converts itself to form an up quark (Neutrons are comprised of 2 up quarks and 1 down quark). There is also another group of particles known as mesons, mesons are made of 1 quark and it’s antiquark. These particles have incredibly short life spans and decay almost instantly. Quarks are also the only particles that have “fractional charge”. What this means is that instead of having integer charge (a proton has 1 charge) quarks can instead have charges of +2/3 such as observed in Up quarks.

I wanted to do a post on all the different types of subatomic particles, but determined it would be too lengthy and not nearly informative enough. As such I’ve decided to attempt a small series. Starting with QUARKS!

Some of you may have heard that quarks make up all matter, this itself isn’t true, quarks only make up a group of particles known as hadrons (such as neutrons and protons). Quarks come in 6 varieties or “flavors” called: up, down, strange, charm, top and bottom. Protons are made of 2 down quarks and 1 up quark and when undergoing radioactive decay protons may change to a neutron and an electron. On the level of quarks what happens here is one of the down quarks converts itself to form an up quark (Neutrons are comprised of 2 up quarks and 1 down quark). There is also another group of particles known as mesons, mesons are made of 1 quark and it’s antiquark. These particles have incredibly short life spans and decay almost instantly. Quarks are also the only particles that have “fractional charge”. What this means is that instead of having integer charge (a proton has 1 charge) quarks can instead have charges of +2/3 such as observed in Up quarks.


These three illustrations were made by an artist at the Jet Propulsion Laboratory in 1975 and reflect then-current ideas about our neighboring planet. Mars orbits the sun at a greater distance than Earth and is much colder. It has a thin atmosphere with a lot of carbon dioxide and is very dry. Not a good place for Earthly life.These images may have been influenced by scientists who thought Martian life might have been silicon-based, rather than carbon-based as on Earth. The stumpy life-forms are all fairly simple, and look a bit like 1970s-era home furnishings.

These three illustrations were made by an artist at the Jet Propulsion Laboratory in 1975 and reflect then-current ideas about our neighboring planet. Mars orbits the sun at a greater distance than Earth and is much colder. It has a thin atmosphere with a lot of carbon dioxide and is very dry. Not a good place for Earthly life.

These images may have been influenced by scientists who thought Martian life might have been silicon-based, rather than carbon-based as on Earth. The stumpy life-forms are all fairly simple, and look a bit like 1970s-era home furnishings.

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