Astronomy C

[sciolymom]

Syo Astro said:
Now that I've been through that I really ask that you take the time to look up more about the planetary equilibrium temperature to concretely understand where this all comes from.


I am trying to find a formula for planetary equilibrium temperature and am having a hard time finding anything that is understandable. I am working with two kids who are not that advanced in math (but are doing pretty well with the other formulas for this event). I just can't seem to find a resource that explains equilibrium temperature as it applies to planets in any kind of understandable way. Do you have any links to share?

[syo_astro]

Apologies for not replying faster.

To s_aaron:
There exists a relationship between transit depth, system, flux, and the radii of both objects in the system for transit light curves. I earnestly don't want you to take any of this as offensive, but if you google somewhere along the lines of "transit light curve equations", then you should find some stuff very useful. I only say this because I really do think it is within the scope of something you can find yourself, and you are likely to get even more useful problems or equations by searching that up rather than me just giving out an equation.

To sciolymom:
Well, first thing that's obvious is just to have the formula down, and even http://en.wikipedia.org/wiki/Planetary_ ... ar_planets (wikipedia) has that. For actual understanding, which I agree is quite important, let's see what we can muster up here. For one, I would like to outline the general topics involved include flux and luminosity, the Stefan-Boltzmann Law (and therefore blackbodies). I agree stuff online doesn't exactly lay this all out together in a nice way from what I've been looking up, though I would gladly enjoy being proven wrong by people who have been rigorously studying. http://www.astro.princeton.edu/~strauss ... /writeup3/ coupled with http://burro.astr.cwru.edu/Academics/As ... ltemp.html I found sort of outlined the general procedure for how to think about derivation. Of course, if you have trouble even before that with flux, luminosity, and the Stefan-Boltzmann Law, then please ask!

That said, what is confusing about those websites? Is it what this whole P, T, R, or something else is? Do the kids not understand the whole inverse square law thing that happens with flux to the planet from the star's luminosity? In my derivation back there did something confuse you? If there's an exact step somewhere that makes no sense, then that'd probably be the most useful to point out. Generally I think the variables involved are defined well, but I did find it annoying not much online seemed to really go through where the equation comes from.

A last note on this is fear not on the kids not being in advanced math, scioly has an unstated rule to never include advanced math. I, along with other test writers, do sometimes try to throw in questions that can be tricky to think about, but it should never involve any kind of true calculus. If I ever asked for a derivative, I would make it such a way that it'd be asking for the slope of a line (in some reasonable phrasing). The formulas themselves aren't impossible either, I started astronomy in sophomore year in HS (and no, I never skipped ahead in math). I think for the event a lack of understanding terminology and basic concepts (this is outside general necessary preparation of organizing notes, DSOs, formula, etc) really leads down the worst path (ie. using "plug and chug", overlying relying on notes, etc).

[sciolymom]

How do you solve for the star's effective temperature?

Image C1 shows the blackbody spectrum of Star E, which is a main-sequence star with a
parallax of 0.1” and radius of 0.480 Solar Radii. Planet F orbits Star E, has the same mass
and radius as Earth, and lies at a distance of 0.176 AU from Star E. What is the equilibrium temperature of Planet F, in Kelvin, assuming it has 0 albedo?

Edited - Never mind. We are just some seriously messed up math people. Carry on.

[boomvroomshroom]

Do you guys get a lot of really complicated calculations on your tests? I feel that this year the calculations are much easier than the past few years, when they were more stars/supernovae focused.

[syo_astro]

So sciolymom, the explanations and all are good?

boomvroomshroom, technically the calculations are never "complicated". They never get to calculus or any sorts of super complex equations to solve. The calculations are no easier or harder than past years to be perfectly honest. That said, I haven't seen too much of the tests you may be talking about, but, if they're invites or a regional test, then maybe you aren't getting the full deal. Generally, the tests you get depends on who's writing, and all sorts of tests can have variable difficulty. Maybe if you've been doing it for a few years you've just used the equations enough so that you're used to the level of math/formula prep needed to understand.

[boomvroomshroom]

Maybe. I'm comparing invite to invite and regionals to regionals. At this point in time last year, I wasn't the best at the math. Then again, it was my first year doing astro and I let my partner, who was more experienced, do all that while I just memorized all the theory. This year I actually studied the math seriously since my partner graduated. I just went back and compared some invite tests from last year and this year (written by teh same people). For some reason I still found the stars much harder to figure out. Maybe it's just because exoplanets have a lot of set equations already there, whereas supernovae have a lot more error involved.

[syo_astro]

Maybe. I'm comparing invite to invite and regionals to regionals. At this point in time last year, I wasn't the best at the math. Then again, it was my first year doing astro and I let my partner, who was more experienced, do all that while I just memorized all the theory. This year I actually studied the math seriously since my partner graduated. I just went back and compared some invite tests from last year and this year (written by teh same people). For some reason I still found the stars much harder to figure out. Maybe it's just because exoplanets have a lot of set equations already there, whereas supernovae have a lot more error involved.

I wouldn't quite say that. I honestly can't reveal questions I've made for competitions, but I'd think if you saw them, then you'd think there can be some decently challenging math for this year . Exoplanets definitely have a lot of error involved, perhaps moreso than with stars or supernovae. Think how long we've been observing exoplanets vs. stars or supernovae. Of course, there still can be practical stellar evolution math and whatnot, but maybe the writer just didn't have the time to make the questions as hard. Rather than worry about the test writer, just make sure you have done your work, and you'll be fine (and have learned something!). Lastly, technically "all" equations you're talking about (as in for the astro event) are "set" (as in most stuff is pretty concrete...for the event at least, though it can still get tough).

[boomvroomshroom]

Maybe. I'm comparing invite to invite and regionals to regionals. At this point in time last year, I wasn't the best at the math. Then again, it was my first year doing astro and I let my partner, who was more experienced, do all that while I just memorized all the theory. This year I actually studied the math seriously since my partner graduated. I just went back and compared some invite tests from last year and this year (written by teh same people). For some reason I still found the stars much harder to figure out. Maybe it's just because exoplanets have a lot of set equations already there, whereas supernovae have a lot more error involved.

I wouldn't quite say that. I honestly can't reveal questions I've made for competitions, but I'd think if you saw them, then you'd think there can be some decently challenging math for this year . Exoplanets definitely have a lot of error involved, perhaps moreso than with stars or supernovae. Think how long we've been observing exoplanets vs. stars or supernovae. Of course, there still can be practical stellar evolution math and whatnot, but maybe the writer just didn't have the time to make the questions as hard. Rather than worry about the test writer, just make sure you have done your work, and you'll be fine (and have learned something!). Lastly, technically "all" equations you're talking about (as in for the astro event) are "set" (as in most stuff is pretty concrete...for the event at least, though it can still get tough).

Thanks for the info. Sorry for the bad wording above. When I said "error", I was referring to myself (wasn't thinking when I wrote and didn't bother to reread the post).
As for challenging, I'm pretty sure you know your stuff but it's hard to judge difficulty from person to person. I remember my partner got this really annoying Hohmann transfer orbit question done in like thirty seconds but then drew a total blank at this question that I thought was super easy (and then it turns out that no one else got it right).

Maybe I just had an easier time finding info on exoplanets. There hasn't been a single question so far that I couldn't answer/derive from my base list, but I do remember last year there was a question on using RR Lyraes to estimate distance like Cepheids at some point in the competition. The Cepheid-Luminosity equation was on the front page on the internet, but we couldn't find a single thing that had the constants for the RR Lyraes (our teacher ended up finding some really obscure thing in some really obscure paper).

[syo_astro]

Not as relevant, but the RR Lyrae question is not bad at all. They are a classic standard candle, even easier to use than cepheids. They always have a constant absolute magnitude, I believe the estimate off the top of my head is 0.6 - 0.75. I'm pretty sure if you googled something like rr lyrae absolute magnitude or standard candles or something you'd get it (or there's graphs of it online). Good luck, ask if there's any questions!

[sciolymom]

c) For this you need to use the binary star/system mass ratio (or at least I think that's the easiest way). You should derive it for practice, it also helps you understand Kepler's third law! To summarize, it states that m_a*v_a = m_b*v_b. Neatly, this also works for radius, but we use velocity here because you can get it from the graph (and it's more trouble than it's worth trying to find barycentric distances when you can just do something simpler given your data).

You answered this related to question 24 on the sample test. We are having a problem. We started out using the formula M_1 + M_2 = a^3 / p^2 . I see that is different from what you used. We got a wildly wrong answer...but why? If we had the variables - mass of star, semi-major axis (distance from star for a circular orbit) and orbital period. Why would we get the wrong answer using those variables, and how would we have known we should use the Mstar x Vstar = Mplanet x Vplanet?