## Astronomy C

Alex-RCHS
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### Re: Astronomy C

In this paper, I notice the use of $R_*$ - does anyone know what this symbol means? I think it's an "effective radius" of sorts, but I can't figure out where it comes from.
I’m not sure either. The paper says that the symbol is proportional to rotational velocity via the conservation of angular momentum. The phrase “rotational velocity” always annoys me because I never know what exactly it’s referring to. Is it the same thing as angular velocity, or is it recessional velocity?
Rotational velocity is typically the maximum linear velocity at the edge of the star (for whatever measure of "edge" is being used), since that's most relevant to spectral redshift and such.
Sorry if this is a dumb question, but maximum linear velocity of what?
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### Re: Astronomy C

I’m not sure either. The paper says that the symbol is proportional to rotational velocity via the conservation of angular momentum. The phrase “rotational velocity” always annoys me because I never know what exactly it’s referring to. Is it the same thing as angular velocity, or is it recessional velocity?
Rotational velocity is typically the maximum linear velocity at the edge of the star (for whatever measure of "edge" is being used), since that's most relevant to spectral redshift and such.
Sorry if this is a dumb question, but maximum linear velocity of what?
I think in this context it means the tangential velocity ($v_t = \omega r$) of a point on the surface of the star
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Unome
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### Re: Astronomy C

Rotational velocity is typically the maximum linear velocity at the edge of the star (for whatever measure of "edge" is being used), since that's most relevant to spectral redshift and such.
Sorry if this is a dumb question, but maximum linear velocity of what?
I think in this context it means the tangential velocity ($v_t = \omega r$) of a point on the surface of the star
Thanks - for some reason I forgot the word entirely.
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### Re: Astronomy C

In this paper, I notice the use of $R_*$ - does anyone know what this symbol means? I think it's an "effective radius" of sorts, but I can't figure out where it comes from.
I think it just means stellar radius.
Essentially, yes but with a major "but". In the paper they say it is the "hydrostatic radius"...which has some specifics, but it's basically a more mathematical / physics-y (read:consistent) way of describing a star's radius. The formality comes in because of asking "Is this the radius to surface of the star, somewhere inside?" This is actually a very interesting thing to think about: What is the surface of a star?

If I were to be very formal, I would suspect this is the the radius of the star out to "where we can observe most of the star's radiation"...which is somewhere pretty close to the surface. Can't guarantee I'm right, the original paper discussing the physics doesn't really mention this, but that's what I'd suspect anyway. Some other relevant radii I guess would be the core radius or the radius where winds come off of from the star, but those don't seem as directly relevant for what the paper was talking about.
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### Re: Astronomy C

I also wrote this test! (syo also helped with this one.)

I think I made it a bit too difficult for a Regionals... again. Sorry.
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### Re: Astronomy C

I also wrote this test! (syo also helped with this one.)

I think I made it a bit too difficult for a Regionals... again. Sorry.
Scored 71-74 depending on credit for ambiguous answers. This test was significantly harder than MIT.

How does #73 work? I came up with all sorts of nonsensical answers but couldn't figure out what to do to combine the orbits.

Also what's going on with #35? Pretty sure those are supernovae spectra
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### Re: Astronomy C

Scored 71-74 depending on credit for ambiguous answers. This test was significantly harder than MIT.
Not every invite has to be impossible, you know :P (Honestly, I think Tad/Donna do a much better job of difficulty than I do.)
How does #73 work? I came up with all sorts of nonsensical answers but couldn't figure out what to do to combine the orbits.
Find the radii of both orbits around the center of mass via $v = 2\pi R/T$ (I should have specified circular orbits), and average them to get half the major axis.
Also what's going on with #35? Pretty sure those are supernovae spectra
I derped and put the wrong image on the image sheet. ("Oh right, the spectra question. Must be this picture, right?") I'll upload a fixed version...

Edit: Fixed.
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Unome
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### Re: Astronomy C

Scored 71-74 depending on credit for ambiguous answers. This test was significantly harder than MIT.
Not every invite has to be impossible, you know (Honestly, I think Tad/Donna do a much better job of difficulty than I do.)
Agreed, but we also didn't need ~15% of the teams over 80%.
How does #73 work? I came up with all sorts of nonsensical answers but couldn't figure out what to do to combine the orbits.
Find the radii of both orbits around the center of mass via $v = 2\pi R/T$ (I should have specified circular orbits), and average them to get half the major axis.
Oh I forgot to half it... ;-; rip 6 points
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Magikarpmaster629
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### Re: Astronomy C

Scored 71-74 depending on credit for ambiguous answers. This test was significantly harder than MIT.
Not every invite has to be impossible, you know (Honestly, I think Tad/Donna do a much better job of difficulty than I do.)
Tbh your tests are the best, period (including nats) (well besides maybe nats 2016 that one was really good) (but other than that I've learned way more from yours than any others).

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### Re: Astronomy C

Scored 71-74 depending on credit for ambiguous answers. This test was significantly harder than MIT.
Not every invite has to be impossible, you know (Honestly, I think Tad/Donna do a much better job of difficulty than I do.)
Tbh your tests are the best, period (including nats) (well besides maybe nats 2016 that one was really good) (but other than that I've learned way more from yours than any others).
Hm, I thought the Nationals and MIT tests were of slightly better quality, but also generally easier than this one. The use of images and interpretation that they build into their math is probably part of it - although, can't really go hard on math for a regional. On this one it did seem like there was almost nothing between questions 51-70 below mid-difficulty though.
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