Astronomy C

[mohona17]

Does anyone know how to do #31 on the MIT Initational 2016 test?

[Unome]

Does anyone know how to do #31 on the MIT Initational 2016 test?

There's no question 31 on the test (at least, not on the version online).

[Adi1008]

Does anyone know how to do #31 on the MIT Initational 2016 test?

There's no question 31 on the test (at least, not on the version online).

Yeah, MIT 2016 has 24 questions. Maybe you could post a screenshot of the problem so we know what you're talking about? There is an image 31 though, and it's mentioned in Question 20. Is that what you were talking about?

[Magikarpmaster629]

Does anyone know how to do #31 on the MIT Initational 2016 test?

There's no question 31 on the test (at least, not on the version online).

Yeah, MIT 2016 has 24 questions. Maybe you could post a screenshot of the problem so we know what you're talking about? There is an image 31 though, and it's mentioned in Question 20. Is that what you were talking about?

Maybe a typo? The key "2" is right next to "3" so they could have meant #21

[mohona17]

Sorry. I meant the 2015 test.

[Unome]

Sorry. I meant the 2015 test.

As far as I can tell it would depend on whether xxi is closer to or further away from the star than xx.
This is one extreme scenario:

Astro1.png (10.4 KiB) Viewed 5721 times

The other extreme would be to have the star on the other side of the planetary system.

Using law of sines & law of cosines there's a way to solve for A and C (I'm too lazy to do it right now).

Astro2.png (8.33 KiB) Viewed 5721 times

So the angle you're solving for is somewhere between arctan ( A / (1 parsec + C ) ) and arctan ( A / (1 parsec - C ) )

As far as I can tell, any answer within that range could be valid, depending on the angle between the axis of revolution of Earth around the sun and line going from the Sun to the star.

Hopefully I've got it right, but my reasoning could be completely wrong; Astro math is not my strong point.

Edit: I went through and attempted to calculate it, but got approximately 0.076 arcseconds for both extremes. Looks like I messed up somewhere...

[antoine_ego]

This is a question from the Yale Invitational. What we were given was the transit light curve of the host star, it's apparent magnitude (11.2), the period of the system (25 hours), the peak wavelength (408.5 nm), how much the wavelength varies by (0.592 pm). The first question was to find the temperature, which is a simple application of Wein's Law. However, we were then asked to find the luminosity in solar luminosities, as well as the radius and mass. The only way I've found is to use the HR diagram plotter here(Obviously they didn't expect us to be able to use this on the test).

Is there a way to determine one of these quantities with respect to the wavelength? Have I missed something obvious? (Is this even solvable?)

[Unome]

This is a question from the Yale Invitational. What we were given was the transit light curve of the host star, it's apparent magnitude (11.2), the period of the system (25 hours), the peak wavelength (408.5 nm), how much the wavelength varies by (0.592 pm). The first question was to find the temperature, which is a simple application of Wein's Law. However, we were then asked to find the luminosity in solar luminosities, as well as the radius and mass. The only way I've found is to use the HR diagram plotter here(Obviously they didn't expect us to be able to use this on the test).

Is there a way to determine one of these quantities with respect to the wavelength? Have I missed something obvious? (Is this even solvable?)

My best guess is that they want us to use the light curve to find the size of the star (not entirely sure how to do that though).

[syo_astro]

I think it is doable, but the phrasing you describe is a bit vague, perhaps the question was more detailed? I'm just going to take a few guesses, and let's see. Also, in theory stars on in HR diagram should follow common formulas like the Stefan-Boltzmann law or the mass-luminosity relationship (unless it's not main sequence). There's usually some tricks, but you should always have an HR diagram handy because the HR diagram has all the observations applying those theories, so for a given star you might be able to approx. values more quickly just using an HR diagram (just make sure you're approximating is semi-accurate >.>).

Also, for Unome's response. I don't think you can use the transit light curve for that. I know you can use it to get star-planet size, period, but I don't know about other quantities unless this one was weird.

The first thing is I'm not fully sure what the delta lambda applies to, but I assume it works with the peak wavelength. If that's the case, we have an orbital velocity for the STAR. Orbital velocity is based on orbital radius and period (we have period). So we get orbital radius, and then we can apply Kepler's 3rd law to get the mass of the star! To be honest, from here if I was on the spot I would just assume it was main sequence, apply a mass-luminosity relation based on that mass -> luminosity. Now with luminosity, temperature -> radius. Not too shabby, eh ? If none of this makes sense/some of this is wrong (totally possible), we can definitely try another route! But this question does seem possible.

[antoine_ego]

I think it is doable, but the phrasing you describe is a bit vague, perhaps the question was more detailed? I'm just going to take a few guesses, and let's see. Also, in theory stars on in HR diagram should follow common formulas like the Stefan-Boltzmann law or the mass-luminosity relationship (unless it's not main sequence). There's usually some tricks, but you should always have an HR diagram handy because the HR diagram has all the observations applying those theories, so for a given star you might be able to approx. values more quickly just using an HR diagram (just make sure you're approximating is semi-accurate >.>).

Also, for Unome's response. I don't think you can use the transit light curve for that. I know you can use it to get star-planet size, period, but I don't know about other quantities unless this one was weird.

The first thing is I'm not fully sure what the delta lambda applies to, but I assume it works with the peak wavelength. If that's the case, we have an orbital velocity for the STAR. Orbital velocity is based on orbital radius and period (we have period). So we get orbital radius, and then we can apply Kepler's 3rd law to get the mass of the star! To be honest, from here if I was on the spot I would just assume it was main sequence, apply a mass-luminosity relation based on that mass -> luminosity. Now with luminosity, temperature -> radius. Not too shabby, eh ? If none of this makes sense/some of this is wrong (totally possible), we can definitely try another route! But this question does seem possible.

Thanks so much, I just did the calculations and it worked! I can't believe I didn't figure that out before. Yeah, I remember when I actually took the test I assumed it was main sequence. I ended up just looking at a table of mass-luminosity-temperature things I happened to have and guessed it.