Post under review.
Please check back soon for update.
Thursday, 31 January 2013
Wednesday, 30 January 2013
Why the Sun is Hot (spoiler alert!)
Well, I never!
I have been left slightly flabbergasted this morning, since I have just had a lifelong belief, overturned by the course notes from my course S382, Astrophysics.
What do I mean?
Well, I had always assumed, nay, believed; that the reason why the sun and other stars, are so god-damn hot, was because of all that fusion energy going on within the star. I mean, just get too close to a 1 megaton H-bomb as it detonates, and you would feel the effects of why that assumption might seem correct.
However, If one explores the equations that govern luminosity, and work out, from the proton-proton chain fusion reactions that occur at the core of the sun; you would see that for each square meter of nuclear material that is available to 'burn', it only produces approximately 300W of power per cubic metre.
The course notes use the example of imagining three 100W light bulbs in a cupboard, as an equivalent amount of energy release per unit volume.
So then, why is the sun so damn hot?
Well, it turns out that the fusion energy only really prevents the sun from collapsing in on itself uncontrollably, due to the energy released from this reaction which counters the gravitational energy from the mass of all that material.
The Sun is hot, simply because, it is so massive, that it has a mindbending amount of gravitational potential energy. As all of this mass attracts itself and causes a contraction, the gravitational potential energy, is converted to kinetic energy. And, fast moving particles, are very hot.
So, the main source of heat for all stars is caused by this conversion of energy from gravitational to kinetic. The fusion reaction energy just seems to retard the gravitational collapse.
Well, it impressed me anyway....
I have been left slightly flabbergasted this morning, since I have just had a lifelong belief, overturned by the course notes from my course S382, Astrophysics.
What do I mean?
Well, I had always assumed, nay, believed; that the reason why the sun and other stars, are so god-damn hot, was because of all that fusion energy going on within the star. I mean, just get too close to a 1 megaton H-bomb as it detonates, and you would feel the effects of why that assumption might seem correct.
However, If one explores the equations that govern luminosity, and work out, from the proton-proton chain fusion reactions that occur at the core of the sun; you would see that for each square meter of nuclear material that is available to 'burn', it only produces approximately 300W of power per cubic metre.
The course notes use the example of imagining three 100W light bulbs in a cupboard, as an equivalent amount of energy release per unit volume.
So then, why is the sun so damn hot?
Well, it turns out that the fusion energy only really prevents the sun from collapsing in on itself uncontrollably, due to the energy released from this reaction which counters the gravitational energy from the mass of all that material.
The Sun is hot, simply because, it is so massive, that it has a mindbending amount of gravitational potential energy. As all of this mass attracts itself and causes a contraction, the gravitational potential energy, is converted to kinetic energy. And, fast moving particles, are very hot.
So, the main source of heat for all stars is caused by this conversion of energy from gravitational to kinetic. The fusion reaction energy just seems to retard the gravitational collapse.
Well, it impressed me anyway....
Sunday, 27 January 2013
From Newton to Lorentz, In Two Short Weeks...
Having now completed two weeks worth of OU study on Relativity and Astrophysics; I have found, to my surprise, that the astrophysics course seems to have far less reading in the early stages, than the relativity course.
If I were to gauge them in terms of study time taken; I would say that on average Astrophysics (S382) seems to take about 6hrs per week for each of the first two chapters. There were a few things that caught me out initially. Firstly, I had to spend some additional time on being thorough when calculating sums and using scientific notation. I also got tied up with a small bit about nucleosynthesis during the proton-proton chain. I felt that the question on that topic, didn't fully correlate with the preceding diagrams.
As for the relativity course, there are a lot of conceptual difficulties when one starts to delve into the algebraic manipulation of some of the Lorentz calculations. But, as with Pure mathematics, I found that a strategy of 'just keep reading' held me in good stead. This allowed me to gloss over any difficult passages and then come back to them at the end of the chapter, with a much better 'big-picture' view, from which to tackle them.
The relativity course (S383) did seem to take me about 10hrs of study per week for the first tranche. More than I expected, but then we have just covered the history and mathematics of motion, courtesy of Messrs Newton, Galileo and Lorentz.
No small feat in two weeks!
If I were to gauge them in terms of study time taken; I would say that on average Astrophysics (S382) seems to take about 6hrs per week for each of the first two chapters. There were a few things that caught me out initially. Firstly, I had to spend some additional time on being thorough when calculating sums and using scientific notation. I also got tied up with a small bit about nucleosynthesis during the proton-proton chain. I felt that the question on that topic, didn't fully correlate with the preceding diagrams.
As for the relativity course, there are a lot of conceptual difficulties when one starts to delve into the algebraic manipulation of some of the Lorentz calculations. But, as with Pure mathematics, I found that a strategy of 'just keep reading' held me in good stead. This allowed me to gloss over any difficult passages and then come back to them at the end of the chapter, with a much better 'big-picture' view, from which to tackle them.
The relativity course (S383) did seem to take me about 10hrs of study per week for the first tranche. More than I expected, but then we have just covered the history and mathematics of motion, courtesy of Messrs Newton, Galileo and Lorentz.
No small feat in two weeks!
Thursday, 10 January 2013
The Relativistic Universe
A quick post. I have delved into the first book of The Relativistic Universe (S383), from the Open University; and, well, I just can't put it down!
It is one of the most interesting, easy to understand and yet detailed enough presentations of Special Relativity, that I have seen so far (and I've thumbed a few books on the subject, in the last two months).
The book is typical O.U fare, with less dense text, examples with clearly defined answers, leaving very few jumps in Algebraic manipulation to cope with; and a clean look that is sometimes missing from traditional textbooks.
I like the way that the coordinate system for Lorentz transformations is also presented; for example, using
ct (the speed of light in a vacuum multiplied by time), to allow the first coordinate of the Lorentz equation to be stated as a distance (since distance is velocity multiplied by time). It certainly makes things easier to handle when lugging about all of those values.
Also, the use of S and S' as the two inertial time frames in standard configuration, rather than the sometimes confusing use of A and B, in some texts, is a breath of fresh air and certainly allows one to better visualize a Lorentz transformation problem.
So far, so good.
It is one of the most interesting, easy to understand and yet detailed enough presentations of Special Relativity, that I have seen so far (and I've thumbed a few books on the subject, in the last two months).
The book is typical O.U fare, with less dense text, examples with clearly defined answers, leaving very few jumps in Algebraic manipulation to cope with; and a clean look that is sometimes missing from traditional textbooks.
I like the way that the coordinate system for Lorentz transformations is also presented; for example, using
ct (the speed of light in a vacuum multiplied by time), to allow the first coordinate of the Lorentz equation to be stated as a distance (since distance is velocity multiplied by time). It certainly makes things easier to handle when lugging about all of those values.
Also, the use of S and S' as the two inertial time frames in standard configuration, rather than the sometimes confusing use of A and B, in some texts, is a breath of fresh air and certainly allows one to better visualize a Lorentz transformation problem.
So far, so good.
Wednesday, 9 January 2013
The Smell of Fresh Books!
They arrived this morning. I now have 9 months of Astrophysics and Cosmology to look forward to.
First impressions on flicking through the books? Very doable and, dare I say it, they look rather enjoyable. The cosmology course (The Relativistic Universe), starts off by dipping straight into Lorentz transformations and tensors. However, I feel suitably prepared having now self-studied the Special Relativity section of S207 (The Physical World) and also a book on tensors! (Fleisch).
I have also finalized my study of the prep material for these two courses, that the O.U provides as a bridge, to those who may not have followed a traditional study route (like moi)!
I found it, for the large part, more wordy than I am use to, coming from a year of pure mathematics; but a welcome diversion, none-the-less.
The Astrophysics books actually look the more taxing of the two courses, which surprises me, since I was expecting the opposite, based on my little knowledge of the previous presentations of these two courses.
Anyway, tomorrow, I am dipping my toe into both courses. I have the books, I might as well just get on with it!
Great.
First impressions on flicking through the books? Very doable and, dare I say it, they look rather enjoyable. The cosmology course (The Relativistic Universe), starts off by dipping straight into Lorentz transformations and tensors. However, I feel suitably prepared having now self-studied the Special Relativity section of S207 (The Physical World) and also a book on tensors! (Fleisch).
I have also finalized my study of the prep material for these two courses, that the O.U provides as a bridge, to those who may not have followed a traditional study route (like moi)!
I found it, for the large part, more wordy than I am use to, coming from a year of pure mathematics; but a welcome diversion, none-the-less.
The Astrophysics books actually look the more taxing of the two courses, which surprises me, since I was expecting the opposite, based on my little knowledge of the previous presentations of these two courses.
Anyway, tomorrow, I am dipping my toe into both courses. I have the books, I might as well just get on with it!
Great.
Thursday, 3 January 2013
Astrophysics and Cosmology
As promised, I made my decision today, regarding whether to take two courses starting in Feb, or just the one.
Well, I chose two; both the courses Astrophysics (S382) and The Relativistic Universe (S383).
They both start on the 2nd of Feb and each have different challenges, in their own right. Having self studied the 'Book 0', prep material that the O.U provides as a brush up on the prerequisite knowledge for both of these courses; I have already noted some teeny-tiny elements of these courses, that will probably drive me insane, by October.
I suspect that they wouldn't bother most people; but combine my recent drilling in pure-mathematical rigour, my dyslexia and a general bit of miserable old git; these little issues are surely going to send me 'round the bend'.
I guess that the issue for me, is the rather unclear and nonsensical way that astrophysicists and cosmologists appear to throw around mathematical and unit notations with wild abandonment, not dissimilar to the experience that I had this afternoon, pouring my Alphabetti Spaghetti onto two pieces of burnt toast.
For example, in mathematics, we could use the letter r for the radius of a circle. But if you are a 'telescope-anorak', (as my wife has now taken to calling me! hmm), then you will have created your own symbols, just for the hell of it.
Hey, why not let d be the radius of an imaginary sphere when working out how bright a star appears in space? Or, better still, lets use the symbol R on the same page, to describe the radius of that star.
This is a heady world where F is flux, not force; m is magnitude, not mass and i is an angle of inclination; which has nothing to do with complex numbers, I can assure you.
I think it's going to take some 'parrot-fashion' wrote learning, for me to grasp all of these different uses of the same symbols, within the same texts.
So, if you ever hear on the news, of a crazy man being committed to an institution after being found walking around Birmingham town centre shouting, 'Come back Group Theory, all is forgiven!'
Then please, think of me ;-)
Well, I chose two; both the courses Astrophysics (S382) and The Relativistic Universe (S383).
They both start on the 2nd of Feb and each have different challenges, in their own right. Having self studied the 'Book 0', prep material that the O.U provides as a brush up on the prerequisite knowledge for both of these courses; I have already noted some teeny-tiny elements of these courses, that will probably drive me insane, by October.
I suspect that they wouldn't bother most people; but combine my recent drilling in pure-mathematical rigour, my dyslexia and a general bit of miserable old git; these little issues are surely going to send me 'round the bend'.
I guess that the issue for me, is the rather unclear and nonsensical way that astrophysicists and cosmologists appear to throw around mathematical and unit notations with wild abandonment, not dissimilar to the experience that I had this afternoon, pouring my Alphabetti Spaghetti onto two pieces of burnt toast.
For example, in mathematics, we could use the letter r for the radius of a circle. But if you are a 'telescope-anorak', (as my wife has now taken to calling me! hmm), then you will have created your own symbols, just for the hell of it.
Hey, why not let d be the radius of an imaginary sphere when working out how bright a star appears in space? Or, better still, lets use the symbol R on the same page, to describe the radius of that star.
This is a heady world where F is flux, not force; m is magnitude, not mass and i is an angle of inclination; which has nothing to do with complex numbers, I can assure you.
I think it's going to take some 'parrot-fashion' wrote learning, for me to grasp all of these different uses of the same symbols, within the same texts.
So, if you ever hear on the news, of a crazy man being committed to an institution after being found walking around Birmingham town centre shouting, 'Come back Group Theory, all is forgiven!'
Then please, think of me ;-)
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