Astronomy C

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antoine_ego
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Re: Astronomy C

Post by antoine_ego »

genew wrote:Hi! This is my first year in astronomy and I'm struggling a bit to understand all of these new concepts, especially since my physics, chemistry, etc. knowledge is still a bit limited. I have a couple of questions:
I was looking at example questions on scioly forums and I was wondering how you would identify which element is causing the largest emission line here. Image
Is there a type of element related to a certain wavelength or would it depend on the type of star?

Also, how would you find the angular size of a semi-major axis without knowing the period first?

Sorry if these questions are poorly worded or don't make sense, I'm still really confused about the overall topic of astronomy.
The 4650 line implies a carbon line (CIII/IV I think). Combining this information with the relatively small peaks on the Balmer lines (6563 ish), I'm guessing that this is WC Wolf-Rayet star. To match the lines with the element, you just need to have a list somewhere to reference.

For angular size if given the semi-major axis, I'm presuming you'd be given the distance. I'd use the small angle formula to determine the angular size.

Don't worry if you're confused, everyone started off that way! :)
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Re: Astronomy C

Post by Yackback »

The MIT Invitational has posted the astro test from this year at https://www.soinc.org/sites/default/fil ... y_Test.pdf.

e: This appears to be Astronomy specific, since the couple other events I checked are not up on the official website.
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Re: Astronomy C

Post by c0c05w311y »

The astro question marathon is a bit dead. I've been checking it frequently but since the beginning of the year it only came back to life for like a week between me, jonboyage, and PM2017. Anyone want to revive it?
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Re: Astronomy C

Post by PM2017 »

c0c05w311y wrote:The astro question marathon is a bit dead. I've been checking it frequently but since the beginning of the year it only came back to life for like a week between me, jonboyage, and PM2017. Anyone want to revive it?
Done, but my answer is very "mehhhhh"
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Re: Astronomy C

Post by andrewwski »

themightyweeaboo wrote:Also, does anyone know a formula I could use to solve this?

The ratio of orbital velocities for a star to its planet is 0.0083. The system has an inclination derived of
75 degrees, and the mass of the star is 0.66 solar masses. What is the mass of the planet in Jupiter
masses?
A bit late on this (astronomy isn't really my thing, but astrodynamics is), but if you're still stuck on this:

Two bodies exerting gravitational influence on each other orbit about their common center of mass. The center of mass is the point at which all of the mass balances. In this case, if the masses of the star and planet are and , respectively, and their distances from the center of mass are and , then the center of mass can be found by setting



We know the mass of the star, so if we can determine the distances from the center of mass, we can solve for the mass of the planet.

Now, given only the ratio of orbital velocities, we will need to assume that the objects are in circular orbits in order to do this. If the planets were in eccentric orbit, the ratio of velocities would be meaningless unless it was stated at which points in the orbit this occurs - as in an eccentric orbit, the velocity (including its magnitude) is always changing. However, in a circular orbit the magnitude of the velocity (also known as speed) is constant (although the direction of the velocity is changing). For the purposes of this problem I am going to proceed with this assumption, however this question is poorly written as it should state the orbits are circular. This cannot be assumed in general - for example, Mercury's orbit has an eccentricity of ~0.2, which means it is ~50% closer to the sun at perihelion than at aphelion. Saturn's orbit has an eccentricity of ~0.055, which puts it about 11% closer at perihelion than aphelion. This is non-negligible. Anyway, if we continue with the circular assumption, we can find the velocity of an orbit as a function of its radius and orbital period.

We know that velocity is distance traveled over time, and if the orbit is circular then the magnitude of velocity will be constant. The circumference of a circle is given by , where is the radius. So if we denote the orbital period - or time it takes to complete one orbit - as , then the velocity is given by:

.

Now, let's write this for both the star and the planet:




Now, let's appeal to Kepler's 3rd law: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Here, since the orbit is circular, the square of the period, , is proportional to the the cube of the radius, . So we know that is a constant.

Now, since we're only concerned about ratios, not absolute values, we can say that velocity is proportional to the radius over the period. If denotes "is proportional to", then




Now, since we know that the square of the period is proportional to the cube of velocity, we can take the square root of this and write . If we sub this in, we find that




Now, since we know , we can divide these out and sub in. Note that since we are actually taking the ratio of to when we do this, this becomes an equivalency, not a proportion.



or



But wait! This doesn't seem right at all! How can the radius of the planet's orbit be much smaller than the star's? If you continued solving, you'd see that the mass of the planet would be much larger than that of the star, which isn't realistic. In reality, the star would be traveling much faster about the center of mass (which it will be much closer to). So let's assume they mean the planet's orbital velocity magnitude is 0.0083 of that of the star, and



Now, we can rewrite the first equation (center of mass) as



and get



If kg, then

kg

which is 0.0447 Jupiter masses.

All in all - this is a poor question due to its lack of stating that the orbits are circular, and its (likely inadvertent) assertion that the planet is heavier than the star.
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Re: Astronomy C

Post by grandgesture »

Does anyone have recommendations as to how to study for the math section? What are some problem sources?
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Re: Astronomy C

Post by jonboyage »

grandgesture wrote:Does anyone have recommendations as to how to study for the math section? What are some problem sources?
The question marathon :D
But also looking at some tests can give a good idea of what to start studying for math.
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Re: Astronomy C

Post by Adi1008 »

jonboyage wrote:
grandgesture wrote:Does anyone have recommendations as to how to study for the math section? What are some problem sources?
The question marathon :D
But also looking at some tests can give a good idea of what to start studying for math.
I second using the question marathon. When I first began Astronomy, it was one of the most helpful resources, especially for practicing math.
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Re: Astronomy C

Post by PM2017 »

So I was thinking for the questions that involve G, that give solar units (AU, solar masses), to just convert G to those units, put in my notes, and use that instead. Do you think the event supervisors will ding this if they ask to show work, and they don't understand what I've done?
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Re: Astronomy C

Post by Adi1008 »

PM2017 wrote:So I was thinking for the questions that involve G, that give solar units (AU, solar masses), to just convert G to those units, put in my notes, and use that instead. Do you think the event supervisors will ding this if they ask to show work, and they don't understand what I've done?
I personally think that it might be easier to convert units back to SI unit as opposed to converting G to units of AU, solar masses, etc. Memorizing the conversion from solar masses to kg, solar luminosities to Watts, etc can help you in numerous types of problems, while knowing G in different units might be useful less often. I also think it could be faster

However, I think that as long you write the units out when you're showing your work/plugging stuff in, then the ES would be able to tell you're just using G, just with different units. If you end up getting the right answer in the end, I think the ES might not even care about units and they'd assume you knew what you were doing. You could also write a note saying something like "converted G's units" but doing that would probably waste too much time
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