## Astronomy C

boomvroomshroom
Member
Posts: 189
Joined: February 19th, 2015, 5:10 pm
Division: C
State: CA

### Re: Astronomy C

Okay! Thanks guys.

sciolymom
Member
Posts: 45
Joined: May 3rd, 2013, 1:06 pm
Division: C
State: CO

### Re: Astronomy C

I am having trouble finding a formula or method for determining information such as diameter from a light curve. There is a test on the test exchange, the Fayetteville test, with this question. It has a light curve diagram below, which I'm not able to copy.

8. Star J is the primary yellow star shown below and Star K is the secondary red dwarf. The time between the
two blue lines on the light curve is 15.00 minutes and Star K is moving at 1770. km/s, what is the diameter
of Star J in km? [4]

How do you approach this type of question? I don't think I'm entering the right search terms in Google. Is there a formula that relates size to period and/or speed?

Again, thank you for all the help here..
Mom/Event Coach

finagle29
Exalted Member
Posts: 51
Joined: January 28th, 2013, 11:37 am
State: PA
Location: Caltech

### Re: Astronomy C

sciolymom wrote:8. Star J is the primary yellow star shown below and Star K is the secondary red dwarf. The time between the
two blue lines on the light curve is 15.00 minutes and Star K is moving at 1770. km/s, what is the diameter
of Star J in km? [4]

Assuming that the blue lines on the light curve are at the first and third contacts (exterior ingress and egress) or second and fourth contacts (interior ingress and egress), the time it takes for the Star K to move the distance of Star J's diameter is the time between the two blue lines. This gives the following equation:
$D_\mathrm{J}=v_\mathrm{K}\Delta t=1770.\,\mathrm{\frac{km}{s}}\times 15.00\,\mathrm{min} \times \frac{60\,\mathrm{s}}{1\,\mathrm{min}}=1.593\times 10^6 \,\mathrm{km}$
Bayard Rustin HS Alum

2013 Events: Thermo, Circuit Lab, Experiment, Robot Arm
2014 Events: Circuit Lab, Experiment, TPS, Mat Sci, Astro
2015 Events: Astro, Chem Lab, Compound Machines, Experiment, Time, TPS
2016 Events: Astro, Cell Bio, Chem Lab, Electric Vehicle, Time, Protein Modeling, Wind Power

syo_astro
Exalted Member
Posts: 564
Joined: December 3rd, 2011, 9:45 pm
State: NY
Contact:

### Re: Astronomy C

Important vocab to use when googling: Eclipsing Binary Variable Stars, First/Second/etc Contact, Transit Light Curves

I would like to frame this further. This goes along perfectly with the idea of how eclipsing works. My problem is actually the blue lines look like the second and third contacts to me. Also, a note is that ingress is the period where the planet begins to cover the star (aka going from first to second contact, first = first side of planet begins to touch star and is where we see a BEGIN to the drop in intensity, second = where the circle of the planet fully passes over the star, so the first point of the light curve where we get the new "flat bar"). Egress is the opposite. I would personally say the question was poorly made, unless the FM people want to come on here and explain it themselves (I want to clarify no offense meant, it could be a fantastic question for all I know, and I've actually made mistakes too...to me it's not so relevant as I'll explain).

http://mafija.fmf.uni-lj.si/seminar/fil ... _stars.pdf actually explains these variable stars fairly well and is what you're looking for. Found it last year, this year search terms were: "binary star transit light curve and velocity pdf" and looked through all the pdfs I had (unless my search history is just biased >.>). The essential concept going on is that how fast the transit occurs IS related to how fast the larger and smaller objects are orbiting around eachother. It is still important in that sense for this year. If you drew a diagram, you could see the two objects for the primary eclipse at least that object 1 goes velocity v_1 say to the right. Velocity v_2 would be the opposite to the left. If you looked, relatively, the velocities would actually add! This is just like look out the window of a car and seeing cars go in the same direction as you vs. opposite directions, except the eclipse basically allows us to see this relative motion ourselves. As I recall that formula also only works with edge-on cases (I can tell the inclination...won't explain why).

My opinion is people should not be worrying too much about that one specific formula (though, I'm not putting together the questions/practicing, so others would I guess know better). For exoplanets the analysis (I can't remember why off the top of my head) tends to be measurement of flux or intensity drop on the transit curve to get radius. My guess would be that it's more difficult to get the Doppler spectroscopy measurements for systems over time, which would be necessary for constructing radial velocity curves. This is why more often we use transit method, it is photometric (and you can think on why that's easier to measure ). With just photometric data alone, though, the flux drop ratio gives the radius pretty directly (I think this has been discussed).

This is part of the issue with trying to only go off past tests for this year, you have to judge carefully!
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

sciolymom
Member
Posts: 45
Joined: May 3rd, 2013, 1:06 pm
Division: C
State: CO

### Re: Astronomy C

Thank you Syo Astro! I found this also about exoplanet radius related to transit, which may be more related to this year's topic...but it looks like you would have to have the radius of the host star to start with.

http://www.baylor.edu/content/services/ ... 181811.pdf
Mom/Event Coach

syo_astro
Exalted Member
Posts: 564
Joined: December 3rd, 2011, 9:45 pm
State: NY
Contact:

### Re: Astronomy C

No problem, and radius of a star is actually easier to find out than you'd think, there are multiple ways to do it.

Formulas to look into for stellar radius: Small angle formula (if the star can be resolved with some angular size, and if you know the distance to it by trig parallax or distance modulus because you have spectra or it is a standard candle, then you can find the physical size of the object), binary star relationships (if you have a really funky planet system around a binary star...that may be tricky unless the problem is simplified), the Stefan-Boltzmann Law (you can find luminosity class and temperature from its spectra, and then with that you can directly solve for radius). Note that you could want to use all three methods to find errors between them, and that would be real science because what would cause the errors! These are all essentials to the event, if they're not mentioned in the rules (I think they are, but I don't feel like getting them up right now), then I believe at least the astro webinar and other resources mention this.

What is really appreciated in questions more than just "making stuff up" (not to anyone specific) is actually making it appropriate to how a real astronomer would find out and correct the data! To even start finding out about planets, you certainly need to know a thing or two about stars, among many other complexities. I could imagine MANY errors related to exoplanetary science in some way relates to errors in our understanding of stellar astro. Stars shine their light onto planets, have variability that can affect our interpretation of light curves, and are related even to transmission spectra as I recall. Why the year still involves stellar evolution and basic stellar math .
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

blindmewithscience
Member
Posts: 44
Joined: October 2nd, 2014, 8:57 pm
Division: C
State: NV

### Re: Astronomy C

Hi there everyone! Just thought I'd check in with y'all after my state competition down in Las Vegas.
So I'm really upset with the running of this event at my competition. I originally had TPS and Astronomy on consecutive shifts. During lunch, they decided to move every event forward--but then in the middle of TPS, they went back to the original schedule--so the two events overlapped, and so I ended up arriving 20 minutes late. And so even with all of the prep that you guys on this forum were able to give, I wasn't able to do well in this event . The test was around half about DSOs and facts, while the other half was mostly calculation oriented. Oh well, I hope we can do it next year!

I'd really like to thank all of you for the assistance and lessons you've given on this forum--it's been great to learn so much from the great community here at SciOly. I'll check in every now and then to see what help I can offer to any of you (though I'm sure some of you are much, much better at it than me ).
Thank you all, for helping to have a great SciOly experience this year!
Nevada state SO occurs on tau/2 day. Support the correct mathematical constant with all tauists.
http://www.tauday.com/tau-manifesto

Event: Regional/States
Astronomy: x/:(
Bungee: 3/3
Compound Machines: x/1
TPS: x/:(

sciolymom
Member
Posts: 45
Joined: May 3rd, 2013, 1:06 pm
Division: C
State: CO

### Re: Astronomy C

Sorry to hear about the scheduling problem at state. It's frustrating when something like that happens after working so hard. Glad your bungee went well. My daughter is on Astronomy and Bungee also (along with Chem Lab and Forensics).
Last edited by sciolymom on March 22nd, 2015, 3:39 pm, edited 1 time in total.
Mom/Event Coach

sciolymom
Member
Posts: 45
Joined: May 3rd, 2013, 1:06 pm
Division: C
State: CO

### Re: Astronomy C

Star A and star B are T Tauri stars with same luminosity. Star A is 0.7 sm and has a radius 3x that of star B. What is the mass of star B?

The mass/luminosity/radius formulas I'm finding are comparing the star to the Sun. How do I answer this question comparing two other stars to each other? Also, any significance of them being T Tauri stars?

Also, separate question...what is the relationship between the time a star spends on the main sequence to the time it spends as a protostar? Or is there a mass relationship?

Thanks again...!
Mom/Event Coach

syo_astro
Exalted Member
Posts: 564
Joined: December 3rd, 2011, 9:45 pm
State: NY
Contact:

### Re: Astronomy C

sciolymom wrote:Star A and star B are T Tauri stars with same luminosity. Star A is 0.7 sm and has a radius 3x that of star B. What is the mass of star B?

The mass/luminosity/radius formulas I'm finding are comparing the star to the Sun. How do I answer this question comparing two other stars to each other? Also, any significance of them being T Tauri stars?

Also, separate question...what is the relationship between the time a star spends on the main sequence to the time it spends as a protostar? Or is there a mass relationship?

Thanks again...!

I tried this in my spare time (hah, what's that) last night...let's see how far I got.

The first thing is to understand that proportionality and division of equations is EXTREMELY essential in physics and really in a lot of problem solving. I tried that here:
The Stefan-Boltzmann Law is $L = A \sigma T^4 = (4\pi R^2) \sigma T^4$
We thus have $L_A$ and $L_B$ , so $L_A = L_B$ and $L_A/L_B = (R_A/R_B)^2 * (T_A/T_B)^4 = 1$
We also know that $R_A/R_B = 3$ , $3^2 = 9$ , so $(T_A/T_B)^4 = 1/9$
Next we know $E = mc^2$ and $KE = 3/2kT$ , so $E_A/E_B = m_A / m_B$ and $E_A / E_B = T_A/T_B$
Now we can take the fourth root of 1/9 to get $T_A/T_B$
We can then say $m_B = m_A / (E_A/E_B) = m_A / (T_A/T_B)$ = 0.7 solar masses / (fourth root of 1/9), which is http://www.wolframalpha.com/input/?i=0. ... f+1%2F9%29

I fear greatly that I am missing some factors or am misusing proportionality. The issue with directly using the mass-luminosity relation is that it uses I think some assumptions surrounding hydrogen fusion usually, which we can't use here. Where was this question from? I don't think this is even the right answer to be honest, but it's my "first guess", and you at least get a gigantic lesson in how you can compare two quantities and ignore constants effectively. That's important because you don't need to compare everything to the Sun, it can be mightily useful, but knowing how this works in general is even better. I can't quite put my finger on why T Tauri stars...it seems like it is certainly more appropriate for this year (the part about involving early stellar evolution of stars). Do you have the answers or some reference or something?

As for relationships, I would recommend looking into the Hayashi (convective) and Henyey (radiative) tracks. They're important in understanding the evolution from a protostar to pre-main sequence star to main sequence star. The end result as I recall it is that massive stars do evolve faster from their protostar stage to the main sequence, in addition to evolving faster on the main sequence (this is how "mass determines everything" as some say). There are all sorts of timescales for protostar collapse and pre-main sequence evolution that you can look into.
Last edited by EastStroudsburg13 on March 29th, 2015, 6:20 pm, edited 1 time in total.
Reason: LaTeX is nice. :P
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

PatrickMcPherson
Member
Posts: 18
Joined: October 16th, 2014, 4:45 pm
State: NC
Location: Hickory Region, NC

### Re: Astronomy C

So I've been looking at deriving these radial velocity equations. They seem to be very important, I feel like I understand the concepts (I've been doing it since my sophomore year and I'm a senior now) but I've always had issues wrapping my head around the math parts. I'm in AB calculus this year, so I've seen all of the elements when changing around this "center of mass frame of reference;" I've never liked the polar coordinate system, and I don't remember it very well. Also, there was a lot of implicit differentiation which can get (and was) very complicated, particularly in the problems demonstrated. I don't see how I could really solve these sorts of problems in a competitive time (my state test is 4 8 min sections if it is the same as the past two years). Do any of you have suggestions to help me grasp a more comprehensive understanding of how the equations operate with the systems (in the problems) at hand?

syo_astro
Exalted Member
Posts: 564
Joined: December 3rd, 2011, 9:45 pm
State: NY
Contact:

### Re: Astronomy C

PatrickMcPherson wrote:So I've been looking at deriving these radial velocity equations. They seem to be very important, I feel like I understand the concepts (I've been doing it since my sophomore year and I'm a senior now) but I've always had issues wrapping my head around the math parts. I'm in AB calculus this year, so I've seen all of the elements when changing around this "center of mass frame of reference;" I've never liked the polar coordinate system, and I don't remember it very well. Also, there was a lot of implicit differentiation which can get (and was) very complicated, particularly in the problems demonstrated. I don't see how I could really solve these sorts of problems in a competitive time (my state test is 4 8 min sections if it is the same as the past two years). Do any of you have suggestions to help me grasp a more comprehensive understanding of how the equations operate with the systems (in the problems) at hand?

What exactly do you mean by "these radial velocity equations?" Literally just that velocity is the derivative of position with respect to time (deltax/deltat, the slope of a position-time graph), or do you mean like stuff involving the Doppler effect? Of course, there's other relevant formulas. To be honest, calculus alone only marginally helps in figuring out how the formulas work in my opinion. If you take a calc-based physics course, then that gives a bit more insight. But why do you care about center of mass frame of reference? Do you mean all the stuff I was doing before to try to help sciolymom? It is indeed an important concept, but one that is not tested as explicitly because the event, I believe, tries to really range in difficulty, unless this is more something you saw at states. Are you just trying to figure out how to conceptualize the center of mass of a system in relation to stuff like Kepler's third law? You definitely don't need polar for much of this stuff, and I don't see why you were doing implicit differentiation...usually formulas for this event can all be algebraically derived (and calculus would just be a small extra thing to make more sense of things like saying dx/dt instead of deltax/deltat).

For solving questions quickly first and foremost have a formula sheet, but then USE IT by practicing on as many tests as you can or making up questions. If you've taken physics, it is kind of similar in how once you practice enough times so it is all natural to do, then you will be able to (I guess obviously) get more done. Generally there's a limited number of equations you need to figure and know the derivation of (distance modulus, parallax, wien's law, etc), and once you do that you can be quite solid at the math.

Sorry that wasn't as helpful as it could be, but I'm a bit confused as I said. Could you clarify some of that?
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

cifutielu
Member
Posts: 63
Joined: March 2nd, 2013, 9:38 pm
Division: C
State: IL

### Re: Astronomy C

Hey syo_astro, can you help me out?

I tried solving this problem:

Star G has a radius of 30. Rsun and an effective temperature of 3000. K. If the sun has a temperature of 5778 K,
what is the luminosity of Star G in solar luminosities?

And using the equation L = 4*pi*r^2*stefanboltzmanconstant*temperature^4, I ended up getting 2.79 * 10^25 watts. Therefore, I got .07 solar luminosities. However, the answer is 65 SL. What did I do wrong?

syo_astro
Exalted Member
Posts: 564
Joined: December 3rd, 2011, 9:45 pm
State: NY
Contact:

### Re: Astronomy C

cifutielu wrote:Hey syo_astro, can you help me out?

I tried solving this problem:

Star G has a radius of 30. Rsun and an effective temperature of 3000. K. If the sun has a temperature of 5778 K,
what is the luminosity of Star G in solar luminosities?

And using the equation L = 4*pi*r^2*stefanboltzmanconstant*temperature^4, I ended up getting 2.79 * 10^25 watts. Therefore, I got .07 solar luminosities. However, the answer is 65 SL. What did I do wrong?

Help you out to where (har har har aren't I funny?) .

Oh, I know star G! Actually I don't, but I love me a Stefan-Boltzmann Law question. I think you are forgetting a trick of proportionality you can perform with the Stefan-Boltzmann Law (and anything in astronomy or physics). I actually did this a few posts ago, so I'll get to the point here:
L/Lsun = (R/Rsun)^2 * (T/Tsun)^4. Note: if you were given pure mks units you would probably have an easier time just stick to mks, but this hints you towards solar units (it depends on whatever you have to multiply/convert the least, though you can mess up the stefan-boltzmann constant and whatnot...so usually stars are made easier by this).
L/Lsun = (30 Rsun)^2 * (3000 K / 5778 K * Tsun)^4 = 65.41 Lsun. Multiplication, so by sig figs it simply indeed becomes 65 solar luminosities.

I am fairly confused because http://www.wolframalpha.com/input/?i=5. ... minosities gets it...I tried messing around with the radius and temperature, but I couldn't find what you did precisely. I suspect it's either solar radius conversion or mistyping the Stefan Boltzmann constant. If you give full work I can try to check it (could just PM you by that point).
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

cifutielu
Member
Posts: 63
Joined: March 2nd, 2013, 9:38 pm
Division: C
State: IL

### Re: Astronomy C

syo_astro wrote:
cifutielu wrote:Hey syo_astro, can you help me out?

I tried solving this problem:

Star G has a radius of 30. Rsun and an effective temperature of 3000. K. If the sun has a temperature of 5778 K,
what is the luminosity of Star G in solar luminosities?

And using the equation L = 4*pi*r^2*stefanboltzmanconstant*temperature^4, I ended up getting 2.79 * 10^25 watts. Therefore, I got .07 solar luminosities. However, the answer is 65 SL. What did I do wrong?

Help you out to where (har har har aren't I funny?) .

Oh, I know star G! Actually I don't, but I love me a Stefan-Boltzmann Law question. I think you are forgetting a trick of proportionality you can perform with the Stefan-Boltzmann Law (and anything in astronomy or physics). I actually did this a few posts ago, so I'll get to the point here:
L/Lsun = (R/Rsun)^2 * (T/Tsun)^4. Note: if you were given pure mks units you would probably have an easier time just stick to mks, but this hints you towards solar units (it depends on whatever you have to multiply/convert the least, though you can mess up the stefan-boltzmann constant and whatnot...so usually stars are made easier by this).
L/Lsun = (30 Rsun)^2 * (3000 K / 5778 K * Tsun)^4 = 65.41 Lsun. Multiplication, so by sig figs it simply indeed becomes 65 solar luminosities.

I am fairly confused because http://www.wolframalpha.com/input/?i=5. ... minosities gets it...I tried messing around with the radius and temperature, but I couldn't find what you did precisely. I suspect it's either solar radius conversion or mistyping the Stefan Boltzmann constant. If you give full work I can try to check it (could just PM you by that point).

I figured it out. I forgot to multiply the radius by 30 xD