Astronomy C

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syo_astro
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Re: Astronomy C

Post by syo_astro » March 3rd, 2016, 8:27 pm

Magikarpmaster629 wrote:The way I understand color-color diagrams is that they compare the fluxes of different wavelengths in the form of a graph. If that's the case, then why can't we just use the blackbody curve, which gives us fluxes at all wavelengths?
I will give a few questions that I hope helps out:

1) I presume by blackbody curve you might mean a spectrum. Spectra include blackbody curves, but blackbody spectra aren't the only type. A simple way to describe this is by "Kirchoff's Spectroscopy Laws" if you want a simple comprehensive way of thinking about it (I figure you knew this, but I might as well mention it).
2) Are spectra easy to get? How do we get fluxes, and how do we get spectra?
3) Say you did photometry and made just a batch of flux measurements. How easy would it be to quantify certain spectral features if you just plotted it on a graph as a function of wavelength? This is a useful method, but are there cases where you expect some behavior that you can quantify by comparing fluxes? Hint: Think about all the different spectral features there are. Also, they're useful for the same reason you use color-magnitude diagrams to classify stars.

I think that may define the questions better. Does that help? The summary is certainly it'd be nice to have better data, but can you always realistically? A super important thing is astronomers have gotten pretty good over the times with this exact issue of getting a lot of information from few observations, and color-color diagrams are an example. Note this is mostly just explaining the "why bother", not necessarily the how it's used, which might also be enlightening to get ideas.
Last edited by syo_astro on March 3rd, 2016, 10:23 pm, edited 1 time in total.
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Re: Astronomy C

Post by asdfqwerzzz2 » March 3rd, 2016, 9:23 pm

On the topic of color, a question popped up on a recent regional test. The question asked how much less the U-B flux of a 7000K star is compared to how much it actually emits. Now, the question was pretty ambiguous, but I'm assuming it's asking about how much is emitted by the star in all wavelengths versus how much it emits in the range of wavelengths confined by U and V. How would I do this? I would assume I would integrate the blackbody curve, but I don't know the function that defines the curve. Could someone help out with this?

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Re: Astronomy C

Post by syo_astro » March 3rd, 2016, 10:28 pm

asdfqwerzzz2 wrote:On the topic of color, a question popped up on a recent regional test. The question asked how much less the U-B flux of a 7000K star is compared to how much it actually emits. Now, the question was pretty ambiguous, but I'm assuming it's asking about how much is emitted by the star in all wavelengths versus how much it emits in the range of wavelengths confined by U and V. How would I do this? I would assume I would integrate the blackbody curve, but I don't know the function that defines the curve. Could someone help out with this?
I would love for someone else to chime in with their POV...mine is very confused. Colors aren't fluxes, so I am a bit unclear on how you can have a U-B flux, could you be mis-remembering something (or more probably a typo on the writer's part)? Getting the total flux of a star isn't so bad, you apply the Stefan-Boltzmann Law (total emitted flux is only dictated by temperature). I am just a bit confused on the other bit...was there more to the question, like a diagram or table?

Maybe it was copied/paraphrased from some source and got muddled? Could you ask the test writer if you know him/her? A test writer really shouldn't be using integration I hope, and it'd be really REALLY nasty to do that with a blackbody distribution...
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Re: Astronomy C

Post by asdfqwerzzz2 » March 3rd, 2016, 10:41 pm

syo_astro wrote:
asdfqwerzzz2 wrote:On the topic of color, a question popped up on a recent regional test. The question asked how much less the U-B flux of a 7000K star is compared to how much it actually emits. Now, the question was pretty ambiguous, but I'm assuming it's asking about how much is emitted by the star in all wavelengths versus how much it emits in the range of wavelengths confined by U and V. How would I do this? I would assume I would integrate the blackbody curve, but I don't know the function that defines the curve. Could someone help out with this?
I would love for someone else to chime in with their POV...mine is very confused. Colors aren't fluxes, so I am a bit unclear on how you can have a U-B flux, could you be mis-remembering something (or more probably a typo on the writer's part)? Getting the total flux of a star isn't so bad, you apply the Stefan-Boltzmann Law (total emitted flux is only dictated by temperature). I am just a bit confused on the other bit...was there more to the question, like a diagram or table?

Maybe it was copied/paraphrased from some source and got muddled? Could you ask the test writer if you know him/her? A test writer really shouldn't be using integration I hope, and it'd be really REALLY nasty to do that with a blackbody distribution...
It may have asked to compare the U-B magnitude compared to the total magnitude, but that was the general idea of the question is the same. I'm just wondering if you can easily find the emissivity of a blackbody between two wavelengths, because that would probably solve for the question. The test was not written by the proctor, unfortunately.

I was thinking about using planck's equation, but it doesn't carry the same units as stefan-boltzmann's. Planck's also doesn't allow for a range of wavelengths as far as I know.

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Re: Astronomy C

Post by syo_astro » March 3rd, 2016, 10:49 pm

This is a bit advanced I guess for high school. The Planck distribution that defines blackbodies is where the Stefan-Boltzmann Law comes from. If you integrate a spectrum, you get the emitted flux from the body that emits it. Integrating across all wavelengths or frequencies as appropriate (from -inf to +inf) is more precisely where this comes from. But...that's a pretty annoying integral. Integrating between two wavelengths on the other hand gets the emitted flux between filtered those two wavelengths. The issue with this is that this is again a hard integral. One other thing is emissivity is not emitted flux (sorry about my typical semantics complaints).

A "neat" side note is that filters and colors are even more complicated than this in actuality. Really, filters have kinda weird shapes that are usually below your spectrum, and you have to do this annoying normalization with your integral to find out how much energy actually got passed through your filter. I have had to do this for research...but I had a program do that for me because it would probably be too hard for me to do otherwise. So I suspect it probably wouldn't go that far, which is why I figure it might involve some graph or table instead, maybe "estimate area under the curve". Still annoying, but somewhat understandable at least.

So...other ideas (to other users)? I know there's a difference between "temperature" and "color temperature", and maybe it has something to do with that. I'll see if I can think of anything easy/find something.
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Re: Astronomy C

Post by astro124 » March 4th, 2016, 5:57 pm

Hey everyone! It's been awhile since I've last been on here but I'm glad to see a lot of familiar names still around.

Anyways, I'm having a little bit of trouble with the Union County 2016 practice test (number 25a)

How would we go about solving the tangential velocity. For part b, I figured that we would use Newton's equation for gravitational force. Would the orbital radius be given based on our answer for tangential velocity in part A?

Thanks!
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Re: Astronomy C

Post by andrewwski » March 4th, 2016, 7:27 pm

That question cannot actually be answered as written.

You are given the masses of the two bodies and the mean separation between them. The mean separation is equal to the semimajor axis of an ellipse. In order to determine the tangential velocity, though, you need to know the position along the ellipse (or the distance "r" between the masses at the time in question).

IF and only if the orbit is circular, then the separation is constant and equal to "r", in which case all velocity is tangential and you can use the Vis-Viva equation, which would reduce to:



But the answer in the key (to part a) makes no sense in this case. Intuitively it doesn't make any sense - it says 0.119 m/s. This isn't even near the right order of magnitude! Consider that the earth orbits the sun at ~30 km/s, and in this problem the star is twice as massive and the separation is half!

Likewise, if (and only if) you were to assume the orbit is circular, then you can solve part (b) with the given information. But even then, the answer in the key is wrong (it's off by 6 orders of magnitude, should be ).

But since it was not stated to assume that the orbit is circular, there is not enough information to answer the question.

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Re: Astronomy C

Post by Skink » March 5th, 2016, 4:56 am

I'm back; this of this as part one of two, as I still have a list of National test images to ask about. This is higher priority, though. If anyone can help, my team and I would really appreciate it!

National Site NY Test #27
We've had difficulty locating the phrase "inclination derived" and are unclear how inclination, itself, relates to the rest, particularly what we're looking for.

National Site MIT Test #24(e)
There's clearly some relation we don't know about in order to find this ratio.

Thanks.

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Re: Astronomy C

Post by syo_astro » March 5th, 2016, 12:27 pm

Skink wrote:I'm back; this of this as part one of two, as I still have a list of National test images to ask about. This is higher priority, though. If anyone can help, my team and I would really appreciate it!

National Site NY Test #27
We've had difficulty locating the phrase "inclination derived" and are unclear how inclination, itself, relates to the rest, particularly what we're looking for.

National Site MIT Test #24(e)
There's clearly some relation we don't know about in order to find this ratio.

Thanks.
Hey, I wrote that first test, and sorry about the bad wording in retrospect. Most of the questions were meant to be straight-forward. Typically, though, I try to make the questions have some sense that they are coming from somewhere (eg. the inclination was derived or modeled somehow working with data and theory) rather than just saying the value is blah (and in retrospect again I failed at that considering how I just gave other values in those problems, but again this wasn't meant to be the most impossible questions >.>). The other thing I phrased admittedly badly was the ratio of velocities. This one I meant (but didn't express well) to write that the ratio of velocities were determined assuming no inclination. Accounting for inclination modifies it slightly because then we are actually viewing a component of the star's radial velocity in reality, so you have to multiply it by a factor of sin(i).

But the basis of this question relates well to your other problem in 24e on the MIT test. To summarize, it is based around conserving momentum (m1 * v1 = m2 * v2). It takes an extra step, but it's nothing too bad. Let's do it twice!
m_a * v_a = m_planet * v_planet_a; m_b * v_b = m_planet * v_planet_b

Dividing one equation by the other gets us that
(m_a / m_b) * (v_a / v_b) = (v_planet_a / v_planet_b)

Still confused how to get the velocities within the question? I think it should be clear at least you need the masses (given) and the velocities of the planets (I assume these aren't the same if you were to calculate them). It's not a relation that gives the answer outright, but it certainly involves fundamentals! Any questions about this?
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Re: Astronomy C

Post by Skink » March 6th, 2016, 5:51 am

Thank you. I solved your problem now and followed your algebra for the second. I'm not sure how to calculate the velocities of the planet for each star (the only things I need to get the requested ratio), but I'll see if the team can figure it out. :D

And, as a side note: that effort doesn't go unnoticed. We all strive to write questions and scenarios that have purpose (or, at least, more color) to them versus saying "27. Mass is this. Volume is that. Calculate density.". Riveting problem there.

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