We Are All Born Superstars

Happy Monday! It’s thundering and raining up a storm here, so I’m pacing around the bottom floor of my apartment to try to get my steps for the day. Exciting stuff, what can I say.

Speaking of exciting stuff, today I got to practice differential equations! No, that’s not sarcasm, I actually really enjoy solving differential equations. It reminds me of the time I went to summer school in college. I took Diff Eqs so that I could free up some space in my academic year schedule (to take classes not at all required—yep, I have always been a huge nerd). I was still a fresh-faced third class midshipman, excited about not being a plebe anymore (the new class of plebes (Class of 2010, jeez I’m old) were there and calling me “ma’am” when they ran by me, which was…strange, to say the least), and loving getting to spend my time chilling and doing math. I gave up my summer leave to do so and never regretted it.

In any case, reminiscing aside, there’s just something very satisfying about it. Identifying the best way to solve it, doing some algebra, then some calculus, and somehow ending up with a solution. Quite good. Today’s chapter was limited to first-order ordinary differential equations, aka the easy ones.

On the astrophysics side, I continued my journey through stellar astrophysics to learn about protostars, star formation, and pre-main-sequence evolution. This was an interesting topic, and I liked how the book layered on the complexity. Start considering only gravity, then add gas pressure, then add magnetism…now you’re cooking with gas! There’s a whole host of interesting complications to consider, and the text frequently mentioned that it was an active area of research. Which makes me wonder what the status of it is now, 11 years later! I may have to do some digging just to say.

It was a good day for studying here, even if I did lag a little bit and not finish until 10 PM.

Playing Catch Up

I haven’t updated all week! But not because I haven’t been studying, dear readers. Never that! It’s just that I fell behind rather early on this week (Tuesday), and I kept telling myself I’d post when I caught up. But then I never caught up. At least, not until today! Had to devote some of my “weekend” time (as if I don’t have enough free time right now, but it’s nice to have designated days that I don’t stress myself out as much—plus I usually use the extra time for writing) to studying, but I finished my self-assigned studies for the week!

It was quite an interesting week, really. The Bob material ramped up really quickly and got very tough, but it’s all fascinating. I continued the section on stars, and I covered 4 chapters: The Classification of Stellar Spectra, Stellar Atmospheres, The Interiors of Stars, and The Sun. The chapter on atmospheres was a doozy and the one that got me behind on Tuesday. Really, these chapters had everything. Complicated math, analytical solutions, numerical solutions, searing temperatures, nuclear fusion. Super cool stuff. The proton-proton chains! I forgot that in astrophysics we just call everything that isn’t hydrogen or helium “metals”. Oxygen, carbon, nitrogen—all metals!

Speaking of complicated math, I had a couple chapters in Mathematical Methods this week as well. They covered Fourier series and integral transformations (primarily Fourier transforms, but also Laplace transforms). For some reason I was intimidated by the faint memory of Fourier series, but it actually ended up being relatively straightforward. I was able to follow along and work out the examples, and I only swore a couple times. Definitely useful material to review.

As if that weren’t enough, I also hit the Computation Physics book this week as well. I’m about halfway through the third chapter, which deals with graphing. This is totally new for me, as this type of visual coding wasn’t covered by Codecademy at all. It’s not super difficult, but the results are pretty awesome. I wrote a program in only a few lines that shows a diffraction pattern of circular waves! This type of thing is going to be super important for me in my research (I expect), so I’m glad to be getting a taste of it now. I’m starting to feel pretty comfortable in Python. I know it can (and will!) get a lot more complicated, but I’ve got the basics down well enough to be able to tackle the more complicated stuff.

So, all in all, it was a productive week for me! Now I shall take my shortened weekend and begin again on Monday. &9786;

You Spin My Star Right Round

I was so excited about the weekend that I just went ahead and decided to have it early! That’s the joy of a flexible schedule. I took all of Friday off and enjoyed it immensely. Of course, the work still had to be done. That’s the joy of being a stubborn goal-setter, I suppose. But I did a bit on Saturday and a bit today and still enjoyed the rest of my weekend.

Yesterday I tackled a Mathematical Methods chapter on line, surface, and volume integrals. The line integrals are straightforward enough, once I got the hang of proper parametrization and limits again. It got a bit trickier with the surface and line integrals, and I confess that by the end of the chapter I was sort of lost. Most of the examples in this section were proofs rather than working out samples, and I find that doesn’t help me grok the material as well. Divergence and curl manage to be more confusing in integral form, although I know it is quite practical. In any case, it was a solid chapter and had lots of physics applicability (Maxwell’s equations, anyone?).

Today I settled in for a good read in Bob. I finished Part I, so I got to start on Part II, which is all about stars. This chapter dealt with binary stars and how we can use their orbital characteristics to glean information about them. It’s quite an interesting topic and one of the biggest challenges of astrophysics. How can we, stuck on Earth or the immediate vicinity, gather meaningful data about things that are farther away than we could ever hope to directly observe? Luckily, smart people have come up with lots of methods over the years. This chapter briefly covered several of them, including light curves, spectrum shifts, and astrometric wobbles. It also gets into the angle of inclination and how we deal with the fact that, by sheer chance, we have to observe other systems from whatever angle we have, which may not be nicely head-on or side-on. Lastly, the discussion moved to extrasolar planets, which can be detected by many of the same methods, although their effects are much, much smaller because planets are a lot smaller and dimmer than stars! I had another chuckle about the ageing of this text. At the end of the chapter, it states, “Although Earth-sized planets have yet to be discovered around solar-type stars, […] it seems likely that such discoveries will occur soon.” Exoplanets as a field has been experiencing huge growth, and they were not wrong!

Go go exoplanets!

Photo: NASA Ames/JPL-CalTech/R. Hurt

Did You Make It to the Milky Way

I took a break from math today. In the morning, I got through another Bob chapter, this one on telescopes. This was very interesting information, applying many of the theoretical concepts (diffraction, refraction, etc.) into a practical form that enables us to gather information about the universe around us. Very interesting but it also sounds very frustrating! I have a lot of respect for people who do it, but instrumentation is absolutely not my thing. It was also interesting to read this chapter from a perspective over a decade after it was written. Talking about the upcoming JWST, other projects that have been canceled, and referencing projects that were upcoming at the time but are now ongoing (e.g. Gaia). In many ways, these things go fast but also they take so long! Who knows what observing instruments might be available for me before my astrophysics career (if I have one…) is over?

In the afternoon I returned to my Python environment. I had hoped to finish the rest of the second chapter, but it was a little slow going after I ran into a couple bugs, and so I only got through one section. Still, it was a helpful section (mostly dealing with for loops) and I made it through all the examples and exercises with a rather minimal amount of headaches. I am a little annoyed that my last program worked but was really inelegantly coded. I am quite sure there had to be a better way to it—but, it worked, so yay!

Looking forward to Friday tomorrow. As much as I love studying, I also love my breaks! The ones where I don’t let myself feel guilty for not opening a textbook. Still lots of other things to do!

All the Small Things

Today was a bit of strange day, mostly because there was no physics in the mix. Only had a couple of those days but they usually leave me feeling like I’ve forgotten something! But of course I have not, because I have my schedule all written out for the week. If you fail to plan, you plan to fail, after all. Or because I’m kind of ridiculous. (Like how my boyfriend teased me about writing up a packing list—complete with expected activities and weather forecast—for a 4 day trip. I swear that’s just conscientious, not crazy!)

Anyway, I started out bright and early (okay, it’s a lie, I didn’t get out of bed until 9, but I did get started right away after I got up!) and got Python running and waiting for some juicy new code. I worked through two more sections in the introductory chapter of the text, covering if/then/else and while loops, lists, arrays, and a few other items. The arrays were new to me, and I still mentally giggle at the “numpy” package, but they seem like they will be very useful indeed. I ran into a problem while trying to write a small program to display the first several Catalan numbers. This should have been straightforward, and I reviewed my logic a hundred times and it was impeccable. After much frustration and some poking around Stack Overflow, I realized I just had to move one of the calculations from outside the loop to inside it. I was ready to rage-quit, but it was so simple in the end! Writing code in a nutshell, I suppose.

After a break for some grocery shopping and a few chapters of the Wheel of Time (I’m re-reading, currently on the fourth book), I dove back into vector calculus. Today I was finishing up the chapter, and I got into the del operator, gradient, divergence, curl, etc. Aside from esoteric theory on curvilinear coordinates, this was pretty straightforward. It can get a bit tedious to work through the longer examples, but it is quite satisfying when it all comes together. And it’s nice to be able to follow what’s going on!

And in non-studying but sort of related news, the condo-buying process has been going pretty great. Inspection was done, no major red flags, attorney review is almost finished, and I may have a place to live for the fall soon! Which just makes me realize that this is all going to actually start happening very, very soon.

I Know My Calculus

Despite a rather strange schedule today, I pushed through some laziness and finished my studying for the day, so I’ll count it a success! It really was a success, as I actually followed the math today quite easily. Vector calculus > linear algebra. I did the first half of the vector calculus chapter, so I covered just basic integration and differentiation for vectors. It was definitely a relief to understand what was going on in all the examples. Even so, it took a couple tries to get through the sections, but that is because I went to the beach during my “lunch” today and that made me very sleepy for my afternoon studying! It was a lovely day, though, and I want to take advantage of my current schedule to do things like ride my bike to the beach on a Tuesday afternoon. I am, after all, paying for the privilege!

Prior to the beach, I read another chapter in Bob. This one was on light-matter interactions and, once again, was a retread of material I’ve already reviewed. Seeing things multiple times, especially from different authors/perspectives, is definitely helping me feel more comfortable just in the general arena of physics, which is good. That is one of the things I have lost the most in the intervening years. Topics ranged from Compton scattering to the Pauli exclusion principle and a lot in between. A good high-level view of quantum physics, especially as it relates to astrophysics—primarily in the area of spectroscopy.

Feeling energized going into tomorrow, ready to keep crushing and building my physics skills and confidence.

Bonus: Here is the (awful, awful) song that today’s title comes from!

I Don’t Want to Be a Stupid Girl

Happy Monday! I didn’t sleep well last night, so I was a bit surprised that I woke up relatively early and ready to go. I guess I’m just too excited about studying!

Today I had the short chapter in Mathematical Methods that I didn’t get to last week. It dealt with normal modes. Due to the length and the subject matter (oscillations, we meet again!), I thought it would be easy. I was wrong. This was mostly more advanced-level matrix manipulation. I don’t find this intuitive at all, so when the text claims that this is an “easier” way of doing the math, I have to scoff. I know that it is, really, but to me it just doesn’t quite click. Still, I did get through the chapter. I really hope that I can get better with matrices. I’ve always had a knack for math and enjoyed it, so it doesn’t sit right to be struggling here!

The afternoon was devoted to diving into some physics Python programming. I made it about halfway through the chapter I was working on, and got to write up several neat little programs to do things like calculate a planetary orbit, the probabilities of reflection and transmission of a particle wave function, and so on. I wrote a lot of code, and I was pretty pleased with it. For the examples, I didn’t even need to follow along with the author’s coding, I just took the prompt and did it. Of course, this chapter is intended for people who have no programming experience, so it should be easy for me with at least the basics under my belt.

Midnight, You Come and Pick Me Up, No Headlights

I didn’t post the past couple days because it’s been a little bit of a mess for my, studying-wise, but I’ve decided I’ve just got to own up to it and move on! So Thursday I had planned to work on Python (starting on the Computational Physics text as discussed in my previous post). That didn’t go quite as smoothly as I hoped! Before, I was using basically a faux-dev environment via the Codecademy course. Now, I need to get something set up to actually run Python on my own machine. This isn’t actually very difficult, but somehow I managed to have to do three different installations and several computer reboots and various mucking around that managed to frustrate me and waste a lot of time without actually even getting to the stuff I wanted to do. But at least I now have a working version of Python 2.7.13 and a vague sense of how to run modules through it. Success! Sort of.

Thursday afternoon I was supposed to finish up my chapter on matrices. However, I scheduled a call with a professor from my department that I had been procrastinating, and that basically took my entire afternoon. Not that it was a long call—it was not even 20 minutes—but because talking to people is a Big Weakness of mine. I know it sounds kind of silly, but I’ve always dreaded it. I remember crying as a little girl if my dad made me tell my order directly to the McDonald’s cashier. I handle it a little better now, but I’m still much much more likely to try to handle any business over email or text. Talking on the phone makes me nervous, and video calls can be downright terrifying. So once I knew I was committed to making a video call, it really wiped out my ability to concentrate for the rest of the day.

Of course, once I took the call, it was totally fine. These things never turn out to be as horrible as I worry they will, and yet I still worry every time. I also got to discuss some potential projects that sounded quite interesting, and he sent me some items to take a look at (including a Python program—I am so glad that I’ve been working on my coding already!!), so things are starting to feel almost Real in a scary but cool sort of way.

So anyway, I tackled the matrix stuff on Friday. And hoo boy was it a whopper. I’m pretty sure the last couple sections I was barely hanging on to understanding and definitely wasn’t able to complete the examples on my own. I’m sure singular value decompositions are child’s play to some, but my brain felt all stretched out trying to follow along. This was a little discouraging, but I am trying not to be too hard on myself. I can always revisit the material later!

I also read another chapter in Bob, this one on special relativity. This is now the third time that I’ve reviewed relativity, so it’s starting to feel pretty comfortable. Which is great! Even so, there managed to be some stuff in here that I hadn’t encountered in Tipler and Mosca. It’s a big topic, after all, and a crazy one no matter how familiar I am with it.

I intended to also do the next chapter in Mathematical Methods, this one on normal modes, but I ran out of energy/motivation/whatever. So I intended to do it yesterday. But I didn’t. Sooo I guess I’ll have to write it into my schedule for next week.

Today’s fun “new” fact: The relativistic headlight effect causes light emitted from a moving source to be concentrated into a cone to a stationary observer. This effect can be observed in synchrotron radiation from relativistic electrons

Photo by Georg-Johann / CC BY-SA 3.0

Too Hot (Hot Damn)

This morning I bid farewell to my boyfriend, as he is off on the Navy’s bidding for a few weeks. I also dealt with a malfunctioning air conditioner (a lizard fried himself on a capacitor, poor guy) in 90F+, extremely humid weather, a morass of bug bites on all my limbs, and the cavalcade of documents that go along with a mortgage. I also had to talk on the phone multiple times, which for me is super unfun. All in all, it was A Day, and I could be forgiven for letting my first day back at studying slide.

But! I did not! I guess I’m just stubborn enough. Or scared enough. Or I actually enjoy doing this enough. Well, a little bit of all of it, I suppose. In any case, once the internal temperature settled back down into the 70s, I was able to focus on learning more about matrices. In today’s sections, I got to the key part about determinants. No wonder I was having trouble remembering how to do this—they are, like many matrix-related things, supremely annoying to calculate. I am not sure if it the spatial element of it (if I am not careful I will get my rows and columns mixed up halfway through) or something else, but I have to go slow and frequently use my finger to point at the numbers I am trying to work with within a matrix. However, they are useful little beasties, and doing these sorts of calculations by hand is only for the theory of it and so a little painstaking is fine.

I read through another chapter in Bob today as well, this one on light and the electromagnetic spectrum. After having gone through this at least a little rigorously in my physics text, it was nice to get the astrophysics perspective here. A lot of focus on blackbodies, magnitude, and luminosity, which are key to our observations of the universe. Surface temperatures in the thousands of Kelvin! Distances in parsecs! I also re-learned some interesting info about color indices and getting a little bit into the practical side of things, with at least some attention given to correcting for instruments, atmospheric effects, etc.

One thing popped up that illustrates the downsides of using my old college textbooks for studying. For the most part, it’s quite adequate, as the things I am reviewing have been settled science for many decades, but sometimes the time gap rears its head. In this case, the text referenced an upcoming NASA mission called SIM PlanetQuest. It sounded quite interesting, and I was intrigued about a mission I had never heard of. So I pulled out my phone, googled it…aaaand it was canceled in 2010. Well damn. Better luck next time!

Back to the Grind!

But in this case, it’s not so bad, since the grind is just studying math and physics at my leisure. ☺ I’ve got it good right now and I know it!

I went up to Chicago this past week to attend my cousin’s wedding and do some house hunting. I was pretty worried about this, as I found out my current lender doesn’t finance co-ops, which wiped out like half my favorites list, and a lot of the units I liked had already gone off the market. But after a lot of visits, I ended up putting in an offer on the very first one we saw! And it was accepted today, so if I’m lucky it’ll go all the way to close and I can spend tons and tons of money having some place to live. Yay! It’s definitely nice to not have to keep stressing about the house hunt—although of course, it ain’t over til it’s over. While we were there, I stopped by the campus and showed my boyfriend around a little, but I felt too shy/nervous to go inside. Yep, introvert!

I gave myself a free day when we got back, but yesterday I put some things down on my study schedule and got back to it! I ran out of time before we left to finish my vector chapter, so I worked through the last sections of that. Then I broke open Bob, aka the Big Orange Book, aka An Introduction to Modern Astrophysics, 2nd Edition by Bradley Carroll and Dale Ostlie. I already ready chapter one a couple months back, so I hit up chapter two, which delved into heliocentric theories, Kepler’s laws (which we already know I love!), and the theory of gravity. Very interesting stuff, including a detailed derivation of Kepler’s laws from Newton’s laws and a basic breakdown of conic sections and orbits. This reminded me that I have been dallying in my reading of the Celestial Mechanics book I’ve been working on!

After that, it was back to Mathematical Methods to start on the chapter dealing with matrices. This is important stuff and I am definitely very rusty on it. It’s a long chapter, so I’ve broken it down over 3 different sessions. This first one mostly dealt with laying the groundwork (and making my brain hurt by trying to nail the concept of M-dimensional vector space) and some basic matrix math: addition (easy), subtraction (easy), and multiplication (painstaking).

In all, it felt good to get back to it! September is getting closer every day, and I am trying my best to get all the pieces to fall in place. I still don’t really have any clue what to expect/what I will be doing come fall. That’s making me a bit of a nervous wreck, but at least I am taking some proactive steps to help assuage my anxiety. That being said, it’s a holiday weekend, and my boyfriend is about to leave for some Navy crap for the rest of the summer, so I’ll be taking a few days off to chill with him! But Wednesday it will be ON again!