Astronomy C

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Magikarpmaster629
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Re: Astronomy C

Post by Magikarpmaster629 » February 22nd, 2017, 6:01 pm

Unome wrote:
slowpoke wrote:Alright. Sorry for more math whoops.

Image

Above is the light curve of an eclipsing binary system of Star A and Star B that is perfectly edge on. Star A, the primary and larger star, has a temperature of 3000 Kelvin and 2 times the radius of Star B. The absolute magnitude of the system is 1.24.

a. What is the temperature of Star B in Kelvin?
b. What is the luminosity of Star A in solar luminosities?
c. What is the luminosity of Star B in solar luminosities?
d. What are the radii of Stars A and B respectively in km?
a. 36,000 K
b. 6.72 L[sub]sun[/sub]
c. 20.15 L[sub]sun[/sub]
d. I have lost myself among the various luminosity/flux conversions
So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
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Re: Astronomy C

Post by Unome » February 22nd, 2017, 6:16 pm

Magikarpmaster629 wrote:
Unome wrote:
slowpoke wrote:Alright. Sorry for more math whoops.

Image

Above is the light curve of an eclipsing binary system of Star A and Star B that is perfectly edge on. Star A, the primary and larger star, has a temperature of 3000 Kelvin and 2 times the radius of Star B. The absolute magnitude of the system is 1.24.

a. What is the temperature of Star B in Kelvin?
b. What is the luminosity of Star A in solar luminosities?
c. What is the luminosity of Star B in solar luminosities?
d. What are the radii of Stars A and B respectively in km?
a. 36,000 K
b. 6.72 L[sub]sun[/sub]
c. 20.15 L[sub]sun[/sub]
d. I have lost myself among the various luminosity/flux conversions
So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
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Re: Astronomy C

Post by Ashernoel » February 22nd, 2017, 6:46 pm

Unome wrote:
Magikarpmaster629 wrote:
Unome wrote:
a. 36,000 K
b. 6.72 L[sub]sun[/sub]
c. 20.15 L[sub]sun[/sub]
d. I have lost myself among the various luminosity/flux conversions
So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
If you use the magnitude difference, doesn't that say that when there combined they are 3x brighter? Instead of just the second star?
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Re: Astronomy C

Post by Magikarpmaster629 » February 27th, 2017, 10:50 am

While we wait for slowpoke to return with an explanation, can you write a question Unome?
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Re: Astronomy C

Post by Tom_MS » February 27th, 2017, 1:21 pm

Ashernoel wrote:
Unome wrote:
Magikarpmaster629 wrote: So I solved this using what I remember from exoplanet transits. How do you start with solving for temperature, which is what I assume you're supposed to do since its problem a? I solved for A's radius first, which was 1.31*10^7 km.
I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
If you use the magnitude difference, doesn't that say that when there combined they are 3x brighter? Instead of just the second star?
I started by solving for distance using the apparent magnitude of the system and the given absolute magnitude. Using that, I solved for the luminosity of the larger star, and through subtraction, that of the smaller star. Once the luminosity of the larger star was found, its absolute radius could be found. Then, once that was found, the radius of the smaller star B could be found. Then, the temperature of the first star could be found, and in the process, the other 3 parts. I got 8.47 and 17.1 solar luminosities for the star, 5057K for B, and 5.4 and 10.8 solar radii for the stars.

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Re: Astronomy C

Post by Unome » February 27th, 2017, 1:22 pm

Tom_MS wrote:
Ashernoel wrote:
Unome wrote: I converted the magnitude difference of 1.2 to luminosity, giving me almost exactly 3 times. Assuming both stars fully eclipse each other, I solved for each temperature using (T1/T2)^4*(R1/R2)=(L1/L2)
If you use the magnitude difference, doesn't that say that when there combined they are 3x brighter? Instead of just the second star?
I started by solving for distance using the apparent magnitude of the system and the given absolute magnitude. Using that, I solved for the luminosity of the larger star, and through subtraction, that of the smaller star. Once the luminosity of the larger star was found, its absolute radius could be found. Then, once that was found, the radius of the smaller star B could be found. Then, the temperature of the first star could be found, and in the process, the other 3 parts. I got 8.47 and 17.1 solar luminosities for the star, 5057K for B, and 5.4 and 10.8 solar radii for the stars.
You got the expected ratio of radii (which I didn't get), so if you want to take the question instead of me go ahead.
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Re: Astronomy C

Post by Tom_MS » February 27th, 2017, 6:31 pm

A certain star A known to be on the main sequence is observed through spectral analysis as rotating around a companion B. Star A is known to be to have a parallactic angle of 4.848*10^-8 radians has an apparent magnitude of 13. The system is eclipsing.
a. Determine the approximate surface temperature of star A in Kelvin.
b. What distinctive spectral features can we expect to see from star A?
c. Given that the observable H-beta line (486.10 nm) of the Balmer series is observed to have a maximum shift in wavelength to 486.13 nm for star A, determine its radial velocity in the system.
d. Through spectral analysis, star B is determined to be a cool red dwarf. If the combined luminosity of the system is 5.1 solar luminosities, what is the angular diameter of the system in radians? Make sure to show your work.

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Re: Astronomy C

Post by Unome » March 1st, 2017, 7:47 am

a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K.
b. I think Hydrogen lines peak at around this temperature, not entirely sure though.
c. ~18.5 km/sec
d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
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Re: Astronomy C

Post by Magikarpmaster629 » March 1st, 2017, 1:59 pm

Unome wrote:
a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K.
b. I think Hydrogen lines peak at around this temperature, not entirely sure though.
c. ~18.5 km/sec
d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
Yeah, I'd say D is unsolvable. To Tom_MS: No offence, but these are pretty badly written questions. While there are charts and relations between luminosity and temperature and mass, typically I see tests avoid having these relations match up because the purpose of the math in this event isn't for the student to look up the answer in a table, but to use real math and solve for variables using Kepler's law, Wien's law, Stefan-Boltzmann law, etc. I'd suggest you look at some of the tests in the test exchange (https://scioly.org/wiki/index.php/2017_ ... #Astronomy) for past questions.

Unome, you should go next.
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Re: Astronomy C

Post by Unome » March 1st, 2017, 2:19 pm

Magikarpmaster629 wrote:
Unome wrote:
a. Absolute magnitude of 3, so I assume I'm supposed to look at an H-R diagram since it says main sequence? I get ~9000K.
b. I think Hydrogen lines peak at around this temperature, not entirely sure though.
c. ~18.5 km/sec
d. No idea. Does this have something to do with the size of star necessary to eclipse at a certain orbital distance?
Yeah, I'd say D is unsolvable. To Tom_MS: No offence, but these are pretty badly written questions. While there are charts and relations between luminosity and temperature and mass, typically I see tests avoid having these relations match up because the purpose of the math in this event isn't for the student to look up the answer in a table, but to use real math and solve for variables using Kepler's law, Wien's law, Stefan-Boltzmann law, etc. I'd suggest you look at some of the tests in the test exchange (https://scioly.org/wiki/index.php/2017_ ... #Astronomy) for past questions.

Unome, you should go next.
I don't know about D, but the rest seem pretty typical to me; I've seen plenty of questions like that (which I why I thought of doing it with an H-R diagram).
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