## Astronomy C

Skink
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### Re: Astronomy C

I'm not sure, really; it's hard to gauge that when I can't find cut-and-dry explanations of these 'tools' (versus, say, if you were in a chemistry event and had to learn about different instruments used and the resultant spectra generated by them...that would be a rather easy assignment despite the complexity of the material). Yeah, Wikipedia has a page on light curves and things, but it's often skeletal and devoid of enough examples. Related, consider all of those figures on the National test from last season (if you have it). Where are the event supervisors pulling them from? It's hard to practice reading these graphs and images (many of which are the DSOs, granted) without knowing from where they're coming. It's not hard to find what they are, but SO isn't so interested in what things are but how to use and interpret them. Similarly, then, I can find 'multiwavelength image' explanations; heck, I have one posted on my wall! But, I can't generate practice questions with any of that, especially without new examples on hand. Does that make sense?

sciolymom
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### Re: Astronomy C

Question about evolutionary sequence of high mass stars:

Most sources indicate a sequence like this:
main sequence - cepheid variable (which I guess would technically be instability strip of horizontal branch?) - then supergiant. I'm not seeing anything in that sequence about red giant or AGB.

But another source gave this sequence:
• Subgiant Branch (SGB) - hydrogen shell burning - outer layers swell
• Red Giant Branch - helium ash core compresses - increased hydrogen shell burning
• First Dredge Up - expanding atmosphere cools star - stirs carbon, nitrogen and oxygen upward - star heats up
• Core Helium Flash - continued compression with added helium ash ignites helium - lots of neutrinos
• Horizontal Branch - helium burning core - hydrogen burning shell
• Pre AGB (Asymptotic Giant Branch) - outer layers expand cooling the star - hydrogen shell becomes dormant
• AGB - re-ignited hydrogen shell burning (like a second Red Giant phase)
• Several stages of dredge up - nucleosynthesis creates numerous elements (F, Ne, Mg, Al, Li, Ne, Na)

How can a massive star go through the Red Giant branch?? And based on where the Red Giant branch and the AGB are located on the HR diagram, it doesn't *look* like a massive star goes through that area on the diagram. I'm confused! (This came up because we are trying to understand the horizontal and AG branches better).
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syo_astro
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### Re: Astronomy C

Skink, it makes a lot of sense, but I think you know that it is hard to help without isolating problems. You named a few in that last post that I hope to resolve. Also, I put it as "tools" because as you say it is very much about understanding the USE of these various diagrams. Certain things are confusing, though. For example, I always had trouble doing spectroscopy and how much one had to know about specific spectral lines.

Light curves always plot intensity of light (which if you know astronomy, is aka flux or brightness or our crazy magnitude system) vs. time. What does it mean? You should see that stars/pre-main seq stars change their light output over time. But why? The answer is...variable, so to say. There are MANY reasons for this changing light output, and it shows how simple observations give a physical understanding of some object. There are technical terms here, like intrinsic, extrinsic, etc, etc, but we need to put it in context like you say. About exoplanets + young stars, where do we see variability? If we look up the light curve for each type of object we see patterns. Like if you do it for a brown dwarf, T Tauri, Herbig Ae/Be star, and some exoplanet-y ones (namely transit light curves). With that, given any light curve you should simply know it from the pattern and what causes that pattern (superficially).

If you look at specific DSOs, then you'll better understand what they are and how we know what they're doing physically based on the light curve. You can get these images from many sources. From google (I recommend checking the web page to make sure the image goes with the object you searched for), or better Hubble/Chandra/Spitzer/AAVSO work well. I mean, even for multi-wavelength images, the DSOs have tons online sometimes from papers too that act as good sources for questions. Sorry that there is no magic answer, but if you go between finding images for DSOs and finding images for random objects, you should get why the multi-wavelength images are different or why the light curves have their pattern or lack of one. I myself have googled "T Tauri light curve" or "brown dwarf light curve". Are you not able to find key features when you look them up? Typically they are listed, especially on AAVSO. But this is just one useful diagram.

I have two main points: The event gives you free examples if you can't find any (the DSOs, though you should find random general examples as backup if you google say "object" + "light curve"), and actually having an understanding of a physical basis behind the different tools, features, and images helps you to understand why they look the way they do. I hope that helps to some extent, and if you have more questions please ask.

Remember if you run out of practice, there are tests on the test exchange for astro, and part of the rules tends to not change much (okay, except the color-color diagrams thing...but it's very appropriate for pre-main sequence stars, I promise). Another resource is also the question marathons, which hey make this forum as active as possible!

On a side note about the images on last year's national exam. I am curious which ones you found to seem tough to come up with as an example (here it is for ref: https://www.aavso.org/sites/default/fil ... Images.pdf). I guess I am biased, but I don't see question writing as so complex because for me it was always just like studying in reverse. In studying I would amass large quantities of information, systematically organize it, and understand the scientific connections so I could say discuss about it. In question writing I do the same information amassing, but I ask for someone to tell me about it leaving out a few key bits that reflect understanding or require putting together the information.

------------------------------------------

Now for sciolymom...I feel bad if people ask about high mass stellar evo when that's not really the emphasis. I can answer you question pretty directly, though. High-mass stars follow different post-main sequence tracks from low-mass stars that follow the track you discussed with the RGB and all. Where did it say high-mass stars go through those evolutionary steps? Here's a neat little table from wiki that might help to summarize how high-mass is quite different: https://en.wikipedia.org/wiki/Wolf%E2%8 ... ent_models (by schematic evolution...).
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sciolymom
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### Re: Astronomy C

SYO, this was the link. Actually, the first one that came up under high mass star evolution. It sounded off to me, that is why I wanted to clarify.
http://astronomyonline.org/Stars/HighMassEvolution.asp

Stellar evolution is part of the topic, no?
"stellar evolution and star formation and exoplanets"
We aren't spending a ton of time on it, just brushing up. We were looking at what tracks different things follow on the HR diagram.
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syo_astro
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### Re: Astronomy C

Stellar evolution is DEFINITELY a part of the event, but that's not what I mean. The event at least in my perspective focuses on stellar evolution in conjunction with the other topics, so it should emphasize pre-main sequence evolution and understanding of planets. Admittedly, I have seen many tests ask about some general stuff as you are studying, so it is what it is. Also, for sure if one is interested in the topic it never hurts, it's quite fun!

I think http://casswww.ucsd.edu/archive/physics ... ass_ev.pdf would serve as a better summary. It's longer, slightly more detailed, and gives details in case you want to search more up about parts of the evolution. Or if you just look up "high mass stellar evolution" on google you'll find more sources. It's funny because I remember using astronomyonline when starting out...but mistakes are mistakes, certainly good to ask.
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Skink
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### Re: Astronomy C

Good stuff, syo, thanks...tell you what, re: the National test images, I'll have to check in with my group to see where we had trouble when working through them and come back later. The test had a lot of 'Pick which image from all of these that I'm walking about...'-type of questions, so sometimes we were on target while, others, it was a guessing game. Like, speaking of light curves, there was 34. I think we reasoned through them working backwards but cannot remember offhand.

sciolymom
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### Re: Astronomy C

Regarding high mass versus low mass stars and their affect on planets:

First question - one of the objects connected a short orbital period with the low mass of the host star. I'm not understanding how that is connect.

Second question - I always thought that higher mass stars were more likely to have tidally locked planets due to their significant gravity. But I read this elsewhere:
On the opposite extreme, stars with less than half of Sol's mass are more likely to tidally lock planets that are orbiting close enough to have liquid water on their surface too quickly, before life can develop (Peale, 1977).

I have a feeling these two questions might be related... I would think that if low mass stars tend to have planets closer to the host, the closeness is what causes the tidal locking. But what is it that makes them end up closer to the low mass star than to a high mass star?
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jkim117
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### Re: Astronomy C

Has anybody else noticed that the DSO page for Astronomy 2016 appears to have a lot of mistakes?
Just a few examples:

M42 or the Orion Nebula is in the constellation Orion and not Lepus
51 Pegasi b is in the constellation Pegasus and not Hydra
51 Pegasi b is 50.9, not 176 ly away
51 Pegasi b's right ascension and declination is 22h 57m 28.0s/+20 degrees, 46', 08'' not 11h 01m 52s/-34 degrees, 42', 17''
55 Cancri is 40.3 ly, not 172 ly away
55 Cancri equatorial coordinates inaccurate
AB Aurigae equatorial coordinates inaccurate
AB Aurigae is in constellation Auriga, not Aquila
and so on.

I could be be wrong (though I'm pretty sure that the Orion nebula is in Orion) but could someone check this out?

Thanks!

syo_astro
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### Re: Astronomy C

Sorry for not replying to questions faster. I meant to, but I figured someone else would, and I was busy...

Considering that, sciolymom I will give it another week or two before putting together a response, unless you're hard-pressed for a response with some competition coming up or something.

To jkim, yeah, astro wiki...could use some edits. But that's where users like you come in . Or hey there's always the onwards blog har har...too bad nobody wanted to continue helping me edit it cough :/ (and nobody PM'd me or Alpha as I've heard to take it over totally?). Typically just go by the guidelines that editing information is okay as long as you're not just omitting it all without replacement. If you are confused with editing the wiki, I believe there are pages on it, or you could PM JohnRichardsim. Also, yes, M42 is most definitely in Orion!
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andrewwski
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### Re: Astronomy C

If you use the semimajor axis of an elliptical orbit, isn't it the same as using the radius of a circular orbit? I don't know why, but I've heard that it has something to do with the energy of an orbit staying constant. Not sure though, but thanks a ton!
Oops - neglected to check this thread, sorry! (Astronomy usually isn't my thing, but orbital dynamics is.)

The answer to your question is no - it isn't the same. If an elliptical orbit is circular (think of a circle as an ellipse with zero eccentricity), then the semimajor axis is equal to the radius of the circle. Moreover, however, the distance between the two masses is always constant and equal to the radius. For an elliptic orbit with nonzero eccentricity, however, the radius is not defined, but that distance (between the two masses) is changing continuously with time.

When you formulate the equation for energy in an orbit, it's the distance between the two bodies that you're concerned with, which happens to be constant and equal to the radius in the circular case - but not in the eccentric case. Let's look at the formulation:

Define $r$ to be the distance between the two bodies. Note that this is also equivalent to the radius of a circular orbit, but this is not the formal definition.

If we assume that mass $M$ is stationary (inertially fixed), then the total kinetic energy of the system is:

$T=\frac{1}{2}mv^2$

or just due to the motion of $m$. The potential energy is:

$U=-\frac{\mu m}{r}$

Note that here, I've used $\mu=G(M+m)$, which is known as the "gravitational parameter." This is common in astrodynamics use, as for any given body, $\mu$ can be determined much more precisely than G. If $M >> m$, as is the case the orbit of a planet around a star, etc, then we can say $\mu \approx GM$. I'll proceed with this definition, but analytically you could proceed forward with either. (Note: $\mu$ is more commonly used in astrodynamics than G, because for a given body, it can be determined to much greater precision than the universal constant G. I've never seen $\mu$ used in high school physics courses or the like - they usually stick to the formulation with G, but it's what orbital dynamics people use.)

Now, we can combine the two together to get the total energy:

$E_{mech}=T+U=\frac{1}{2}mv^2-\frac{\mu m}{r}$

Great, right? Well yes, but we still have $v$, or the velocity in the equation. We know that for an elliptic orbit, this is related to $r$ by other orbital parameters.

Let's now look at the Vis-Viva equation. Note that this is actually derived from the fact that energy and angular momentum must be constant throughout an orbit - so the energy at apogee is equal to the energy at perigee, and the angular momentum at apogee is equal to the angular momentum at perigee. I'll skip the derivation here, but Wikipedia's derivation is clear if you're interested. Anyway, the Vis-Viva equation:

$v^2=\mu(\frac{2}{r}-\frac{1}{a})$

where $a$ is the semimajor axis.

Now, let's substitute the Vis-Viva equation into the total energy equation:

$E_{mech}=-\frac{\mu m}{r}+\frac{1}{2}\mu m(\frac{2}{r}-\frac{1}{a})$

This simplifies to:

$E_{mech}=-\frac{\mu m}{2a}$

So total energy in an orbit is not a function of the current position $r$, but of the semimajor axis $a$! This makes sense, as we know the total energy cannot change in an orbit.

Now, if your orbit is circular, then this becomes $E_{mech}=-\frac{\mu m}{2r}$ as $r = a$ is constant (only for the circular orbit). Then, we know the potential energy at any point (since $r$ is constant!) is $U=-\frac{\mu m}{r}$ - or total energy is half the potential energy. So we've proven this for the circular case! But what happens in the elliptical case?

The answer is, since $r \neq a$, we can't say anything about the kinetic or potential energies for an arbitrary point, except that they must equal the total mechanical energy, unless we know $r$. If we're concerned about actually propagating the orbit, there are a few ways to determine $r$, using a choice of anomaly (true, eccentric, or mean) to determine the position vector, and then taking the magnitude of the position vector. For periapsis and apoapsis, however, we have the relations:

$r_p=a(1-e)$
$r_a=a(1+e)$

We can use these to determine the kinetic and potential energy components for periapsis and apoapsis. At periapsis, potential energy is

$U_p=-\frac{\mu m}{r_p}=-\frac{\mu m}{a(1-e)} = \frac{2E_{mech}}{1-e}$

and at apoapsis, potential energy is

$U_a=-\frac{\mu m}{r_a}=-\frac{\mu m}{a(1-e)} = \frac{2E_{mech}}{1+e}$

So yes, it has to do with the energy (and momentum) of an orbit being constant, which will give you the Vis-Viva equation. Substitute this into the definition of kinetic and potential energies, and the result follows.

Hope this makes sense!