TLE to something useful?

Hello bloggers! How are you all doing today? I’m a little bit frustrated. Right now I’m trying to experiment with what I’ve been learning in diff geo. What I want to do is take statelier reentry data and make it into a curve of its position and platitude with respect to time. That way I can get its equation. You see, when a satellite or comet falls towards Earth it’s free falling and the only force excreted on it is gravity (if we ignore winds, which we can do if we go high enough in the atmosphere). And according to general relativity gravity isn’t a force at all but a shape. The gravity around earth is shaped a certain way and that makes things like balls and satellites travel towards the earth. I’ve included a picture of what I think the gravity around Earth looks like (this is only a slice). I’m managed to secure some satellite reentry data but it’s come in the form of a two line element (TLE) which I guess is standard for NASA. But I want longitude, latitude and altitude from this data. I’m having an impossibly hard time making the jump from Right Ascension to a longitude and altitude or whatever it supposed to be. Does anyone know how to do that? Or know anyone who would know?

Back in Black!

Wow. So my little world counter up there in the right corner has exploded with little red dots, so I think it might be beneficial for me to start this thing up again! Since I left the blog I've been hard at work trying to unravel the secrets of the universe. I've spent most of this summer teaching myself differential geometry. (The study of diff geo actually starts in kindergarten. Basically it's all about shapes, but the formal version is more concerned with their equations rather than their names.) And I have made a sincere effort to teach myself general relativity as well, but that hasn't gone so well, mainly because every time I start to read it all I want to do is throw the book across the room! General relativity (GR) is about the least formal, least elegant physical theory I have ever laid eyes on! I like the concepts: mass bending space, acceleration and gravity being the same thing, light bending, black holes and all that good stuff; but the math is positively atrocious! After reading all the formalized elegant diff geo it just makes me want to go throw up. Honestly I feel like GR needs to be redone! Now a question for you: has anyone ever tried to reformulate GR into a more mathematically elegant setup? If not I'm very tempted to try it!

With Regrets

Hello Bloggers. Hohenheim here with some unfortunate news. My health has been acting up lately and I (and my health advisor) have decided that it would be best to temporarily discontinue the blog. Hopefully by summer I'll be in better condition and will be able to pick it back up again. Thanks for all the support.

Cosmo 101 (a bit of math included)

Oh here is another interesting property of Hubble’s law that I don’t think I talked about last time. You can use it to set a minimum on the age of the universe. So to review, Hubble discovered that the universe is expanding and he found that the rate at which stuff (stars nebula etc.) is moving away from us is proportional to the distance they are away from us. The further they are away the fast they are receding. And then he graphed his results and found a line. The equation goes something like this: (the speed at which something is moving away from us) = (the Hubble parameter) X (the distance from us to them). This Hubble parameter is sometimes called the Hubble constant but it’s not really constant. It changes with time, that’s why we use the word parameter. There is another really cool aspect of the Hubble parameter, we can use it to tell how old the universe it.

(the Hubble parameter)= (the speed at which something is moving away from us)/ (the distance from us to them)

In math terms this is

H=S/d so if we invert this we get

1/H=d/S

and if you take any distance (say the distance that a car has travel) and you divide it by the speed that it went at they you know the time it took to get there. So from the inverse of the Hubble parameter give you the time that it took the stuff (stars nebula etc.) to get where is at, thus putting a minimum on the age of the universe. The current accepted value for H is 70.8 ± 4.0 (km/s)/Mpc which give the age of the universe to be 13.8 billion years.

Suggestions?

Hello Bloggers! Well since we only have class on Monday, Wednesday and Friday we still haven't learned anything new this week so I still have nothing to report. But I do have a question for you all. We have to do a project and a presentation for the final exam in this class. So I was wondering if you guys have any suggestions? What do you want to know more about? What deep questions have to been staying up at night trying to solve?

GOD! ?

So we had a test today....I think it went well for the most part. But consequentially we didn't learn anything new so here is a GOD!? post.

So first up we have an Onion article with an interview from God:

http://www.theonion.com/content/node/28151

Next we have an entire website dedicated to the question: Does God Exist?

http://www.doesgodexist.org/

And look there, I added a video!

Cosmo 101 Cepheid Variables

Hey bloggers! We’ve now made the transition to cosmology! And I have a test on General relativity tomorrow oh no! Anyway we’ve already gone over a lot of the stuff that we are talking about in class but I noticed that while I talked about Hubbles law and all (you can read about it here), I didn’t mention Cepheid variable stars. These stars a very interesting in that they blink. Their luminosity literally varies periodically like a lighthouse. But the cool thing is that there is a very linear relationship between it’s period (how fast it’s gets light and then light again) and it’s luminosity (how bright it is). I’ve included a graph to show this relationship. The cool part is the since we know this, if we look out into the sky and see a variable star we can tell how far away it is. How? Well we can see measure it’s period and see how bright it comes across to us. If we know (from the graph) how bright it’s really suppose to be we can calculate how far it. Yay! You may have heard of these stars before but usually they are referred to as standerd candles.

lolfox?

I don't think I have anything to write about today. So I'm not going to write about anything. Here, have an lolcat...errr....fox.

Cosmo 101 Olber's Paradox

Hello bloggers! How are you all doing this fine day? Well I’m doing wonderfully. You know why? Because in my cosmology class we will actually start talking about cosmology and not just gravitation! (I will warn you now, some of this stuff we’ve already gone over in the background section of this blog). So first we’ve started off with Olber’s paradox. People before the 20^th century believed that the universe was infinite and static. And a consequence of an infinite universe was that if you looked out into the night sky any were you look you would see a star. So instead of being black and blotchy the night sky would be a uniform brightness. Like in the picture. But this is obviously not true. Why not? Well there are 3 main reasons quoted. Firstly is the finite speed of light. Secondly is the finite age of universe. Third is the fact that space expands. The first and second ones go together. If the universe was created a certain finite time ago then the light from the far away stars hasn’t reached us yet. The third one only adds to this effect because as the universe expands the light from really far away objects gets red-shifted into a wavelength we can’t see. So from all this we can concluded that the universe isn’t static or infinite.

Cosmo 101 Orbits (for that good clean feeling, no matter what)

Ok so what do general relativity orbits have to do with our solar system? Well for a long time the orbit of Mercury was a bit mystery. It doesn’t quite follow the prediction of Kepler’s laws. It is just a tad bit off. This issue was first observed in 1859. Scientist tried to account for it but they couldn’t figure it out. And then all of the sudden there was this other theory of gravity! So plugged all the numbers in for the orbit of Mercury and low and behold it explained the difference. And if you look at the graphs from yesterday you can see why. The Newtonian graph the Einsteinian graphs are rather different. And this accounts for the difference we see in the Mercury’s orbit. This was the first definitive test of the theory of relativity, and of course it came out positive. The moral of the story is that all of the gravity stuff we’ve been talking about doesn’t only apply to imaginary alien races that live on the surface of a black hole. It applies to our own solar system too.

Cosmo 101 Orbits (for that good clean feeling, no matter what)

Ok now that I’ve gotten that out of my system, back to black holes. There are a lot of different equations that I’ve not talked about here. They can get very complicated very fast and if I shared then it would be super confusing. But when you get an understanding of a certain number of equations it turns out that you can predict orbits around a black hole. And not just a black hole, one of the most famous applications of general relativity was an orbital prediction in our own solar system. Or bits in our own solar system?! you say. No! We already know those from Kepler and Newton, you say. But no! They are not quite right. I have a graphs here with two curved lines. They are both potential energy lines. Reading them is easy if you think about it right way. If you imagine putting a marble at the intersection of the straight line (the amount of energy in the system) and the potential energy curve and then letting it go then it’s going to go back and forth like a pendulum. But if we look at the horizontal axis we see that it is something corresponding to an orbital radius. From this we get a familiar looking orbit (the last picture). Now the first curve is what Newton and Kepler came up with, and the second curve is what general relativity predicts. You will notice there is a slight difference. When we get near the vertical axis the Newtonian curve just keeps going up. But when we get near the vertical axis in the general relativity curve we see that there is this sharp slope and the object falls off into the black hole. But the thing is that it doesn’t have to be a black hole. It can be any planet or star, including our own. Now, you say, what does this have to do with our own solar system? Well I shall explain that tomorrow!

a rant

Please forgive me in this post for it is a rant and nothing but a rant. I hate Ockham’s razor with a hatred that cannot be described in English. Perhaps in Russian Mat but not in English. It’s like the catholic school teacher’s ruler against the dreamer’s knuckles. I suppose this is a strange thing for me to say considering that most physicists swear by it. But just think about it for a moment. Going with the simplest, least contrived answer kills one’s imagination and deadens the soul. Very much akin to Ockham’s razor is the set of philosophical ‘rules’ that debaters and intellects have used for centuries. We treat philosophical arguments like mathematical proofs. I like mathematical proofs; they are challenging and intriguing puzzles that one can solve in an afternoon’s time. But I hardly think the deepest mysteries of the universe should be treated so flippantly. We view the wonders of the universe and the questions which our mind raises in response to those, why, we treat the very existence of God as things to be tackles. We have no reverence or respect. We are out to conquer. And this disgusts me to no end. This is why I dislike philosophers so much! I cannot stand their arrogance and their brutal treatment of things like truth and self awareness. It’s as if they have been handed a new born child and after pondering it and examining it for a bit, declare that they have understood the miracle of life and promptly disregard the babe. And these people are regarded as intellectual giants. On the other hand those that do not hold to Ockham’s razor, those that do not abide by the rules of the philosophical world, those that would have the universe and the human mind be infinitely more complicated and beautiful than we could begin to grasp, those that ponder possibilities far outside of the ‘normal’ realm of possibility, those either keep their speculations to themselves or are labeled new age spiritualist or crackpots. How this makes my soul cringe. Why does everything have to be intellectually conquered? Why does everything have to straight forward? We assume we have the universe under out thumbs but in my opinion we understand a mere speck of the actual knowledge there is to behold and, also in my opinion, if this history has shown how the human race treats knowledge, we don’t deserve to get any more.

Why I haven't been on.

Hey bloggers. You may have noticed that I have not been on since Tuesday. Well at the university I'm currently 'attending' we were informed that Westboro Baptist Church was going to come an protest our homosexual community. Don't go to their website, go to the Wikipedia article here. So we have been very busy organizing and planning in order to counter their efforts. My biggest part in all of this has been pointing out that Christians don't acctually believe this. Christians believe that God loves everyone and sent Jesus to die for everyone. Emphasis on the word 'everyone.' But anyway that's why I have written. Hopefully I'll be able to pick up on the blog again tonight.

Cosmo 101

Hey! Sorry I didn’t post yesterday. I said to myself, I said, “Self you gotta remember to post on the blog!” But then I started watching the finals for Olympics ice dancing. And they just got so exciting and I got so wrapped up in them that before I knew it, it was midnight and I hadn’t done any work! But I’m at a bit of a loss as to what to write about. In my class right now we are mainly doing a lot of calculations concerning the alterations one needs to make in order to compensate for the presence of a massive body such as a black hole. But I doubt these calculations are very interesting and in my opinion say very little about the concepts behind general relativity. So instead I think I’ll talk about the philosophical implications (and the implications to physics as a whole) of general relativity for a couple of entries. So let’s see, now we’ve done away with gravity and replaced it with a structural change in spacetime. What we’ve essential done is replaced gravity as one of the four fundamental forces. Now all we have left is magnetism /electricity, the weak force and the strong force. We have done away with gravity as a force and we have messed with time and space. They have become distorted. If we were to take a look out from out distorted place in the universe what do we see. We see things through a circus mirror. To me it feel like we have to question the way we see everything! It changes the whole playing field.

Cosmo 101

We interrupt the regularly scheduled programming to bring you the bigger picture. So we’ve been talking all about gravity, and we’ve been talking about it from the perspective of general relativity. In other words we’ve been looking at gravity as simply a bending in spacetime. It’s not a real force or anything it’s just a warping to the playing field. But there is a very different view on gravity that we haven’t talked about yet. It’s the particle view and it says that gravity is a force that is carried by a massless partial called the graviton. Yes I am aware that these two views are totally and completely in contradiction to one another. And everybody else knows it too. This is one of the great challenges facing physicists today. We have tried and tried again to fit two together. But we don’t have a straightforward answer yet. In fact string theory is one of the leading theories that people are trying to use to solve this conundrum. But if any of you young people out there (or old people for that matter) would like to give physics a go this could be an area you might check you.

GOD! ?

Hello there readers! I wanted to do a GOD!? entry today but I didn't want to just do pictures today. So to start things of here is the first paragraph of Wikipeida's entry on God:

God is a deity in theistic and deistic religions and other belief systems, representing either the sole deity in monotheism, or a principal deity inpolytheism.[1] God is most often conceived of as the supernatural creator and overseer of the universe. Theologians have ascribed a variety of attributes to the many different conceptions of God. The most common among these include omniscience, omnipotence, omnipresence, omnibenevolence (perfectgoodness), divine simplicity, and eternal and necessary existence. God has also been conceived as being incorporeal, a personal being, the source of all moral obligation, and the "greatest conceivable existent".[1] These attributes were all supported to varying degrees by the early Jewish,Christian and Muslim theologian philosophers, including Maimonides,[2] Augustine of Hippo,[2] and Al-Ghazali,[3] respectively. Many notablemedieval philosophers and modern philosophers developed arguments for the existence of God.[3] Many notable philosophers and intellectuals have, by contrast, developed arguments against the existence of God.

I have also been looking out for pop cultural views and references to God and have discovered that while American society isn't always interested in God there is a large interest in the supernatureal. So I googled that and the picture up top is the gist of the first 20 pages or so.

The last thing I've included for today is a picture of one of the most beautiful and moving buildings I have ever been in, the Hagia Sophia. It was originally a church (this is when I visited it), then it became a masque and now it is a museum but it is very closely associated with God (and it's just gosh darn pretty) so I thought I'd include a picture of it.

Cosmo 101 The Schwarzschild metric

Ok so here are two more strange effects of the Schwarzschild metric. One is the time. Let’s say we are attending the interstellar Olympics being held on our black hole alien friends home ‘planet.’ But a dispute arises with the speed skating. The fans in the stands measure the winning speed skater to have competed the required number of laps in 34 seconds. But the fans orbiting the planet from further out measure on 1.5 seconds. But there is no discrepancy. The time is warped by the curvature of spacetime alone. I think I’m going to leave the next item for tomorrow and got get some sleep. I’ve had a lot going on and I wouldn’t mind a bit of a break.

Cosmo 101 The Schwarzschild metric

Ok so equation 4 from yesterday is the Schwarzschild metric but we won’t use all of it. That last term, the one with r^2 and phi, has to do with angles so we don’t use it much. We mostly use the first two terms. The first term describes how time changes and the second term describes how space changes. You remember that alien race that thrives around black holes. Well they are used to this and know how to measure things around a black hole. And because this is so strange to us they give us an example. Let’s say we are very close to a 5,000 meter (that’s the mass) black hole. Let’s say we start out right above the horizon (which is at 2M or 10,000 meters) and want to measure 1 meter. Now we need more information than this. There are two viewpoints we could take with this measurement. We could take the viewpoint of someone outside the influence of the black hole or we look at this from the perspective of someone right here next to the horizon. Let’s say we want to measure one meter from the viewpoint of someone outside the influence of the black hole. Now what would that one meter look like from the perspective of someone right here next to the horizon? Well if you use just the second term of the metric you calculate a distance of about 83 meters! Quite strange. Ok this is all I have time to do tonight but I’ll see if I can’t explain this more tomorrow.

Cosmo 101 The Schwarzschild metric (math included)

Now I would like to take a moment to talk about the actual Schwarzschild metric. Now there will be a bit of math involved in this but hopefully it will be well worth it. First let’s talk about units again. In general relativity we like for things to be as simple as possible, so we make time and length have the same units. In my book we use meters. Well how do you make time go from seconds to meter? Well you multiply by the speed of light, c. So, now that we have everything in meters things will be pretty easy. We’ve seen the first equation up top (1). It’s the equation for the distance one travels. We’ve also seen the equation right below it (2). It tells us the distance one has traveled in spacetime. But the thing about equation 2 is that it only works for flat spacetime. But now we are dealing with a curved spacetime and we will have to change equation 2. What Schwarzschild discovered is that you can alter this equation to get a distance that works for curved space. But first we have to do some more unit changing. Now we are dealing with gravity and that means we have to deal with masses. Masses normally come in units of kg’s but now we want them in meters as well. So we multiply any mass we get by Newton’s gravitational constant, G, and then dividing it by the speed of light squared. This is in equation 3. Now our new equation for distance will look nice and neat. And there it is, equation 4. There is a lot more to talk about but I think I’ve given you enough already. We’ll talk about all that tomorrow.

Cosmo 101

I may not have a really sound answer to the question of why all this stuff is so strange but I do have a bit of an illustration that might help us think about it. Have you ever heard of the book flatland? Well it’s about this group of shapes that live in a 2D plane. Our protagonist is a fellow by the name of square. These shapes live in a 2D plane and have never experienced 3D. Now if our square were to travel into a vicinity of very high mass, as in the picture, he would dip down in be warped under the strange warped space. Strange things would happen. He would get distorted. Lengths and time would be distorted. And it would freak him out! Just like we do when we encounter strange things like this. He can’t imagine or see his space being twisted, just as we can’t see 4D spacetime being bent and twisted. But it is and that’s why all those strange things happen. It’s very hard to picture but I hope my illustration has given you a little bit of a better understanding of what is going on.