Astronomy C

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Re: Astronomy C

Postby jonboyage » February 2nd, 2017, 10:04 am

Yeah you were right sorry, I checked online right after I posted just to make sure and I found that the dimmer ones drop faster.
Do you want to ask the next one?
Sure. Here's a tie-in math question.
A type Ia supernova is discovered in a distant galaxy. Its maximum apparent magnitude is measured at 18.4. After monitoring the supernova for 15 days, the B band magnitude drops by 1.2. 1. What is the theoretical absolute luminosity of a type Ia supernova originating from a single progenitor? 2. Calculate the distance to the supernova based on this theoretical absolute magnitude. 3. Determine the speed at which the galaxy containing the supernova is receding. Use a Hubble constant of 70 km^-1*Mpc^-1 4. Based on the luminosity decline, determine the actual absolute magnitude of the supernova. 5. Recalculate the distance and recessional velocity based on the actual absolute magnitude.
Answer
1. -19.3 2. 346.7mpc 3. 24271.6km/s 4. -18.4884 5. 238.6mpc; 16702.4km/s
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Re: Astronomy C

Postby Bob_117 » February 15th, 2017, 3:37 am

Yeah you were right sorry, I checked online right after I posted just to make sure and I found that the dimmer ones drop faster.
Do you want to ask the next one?
Sure. Here's a tie-in math question.
A type Ia supernova is discovered in a distant galaxy. Its maximum apparent magnitude is measured at 18.4. After monitoring the supernova for 15 days, the B band magnitude drops by 1.2. 1. What is the theoretical absolute luminosity of a type Ia supernova originating from a single progenitor? 2. Calculate the distance to the supernova based on this theoretical absolute magnitude. 3. Determine the speed at which the galaxy containing the supernova is receding. Use a Hubble constant of 70 km^-1*Mpc^-1 4. Based on the luminosity decline, determine the actual absolute magnitude of the supernova. 5. Recalculate the distance and recessional velocity based on the actual absolute magnitude.
Answer
1. -19.3 2. 346.7mpc 3. 24271.6km/s 4. -18.4884 5. 238.6mpc; 16702.4km/s
Sorry for jumping in but I have a question. How did you calculate the absolute magnitude in question 4? I've looked up luminosity decline rate and a couple other things and I haven't been able to find anything. Thanks in advance.
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Re: Astronomy C

Postby jonboyage » February 15th, 2017, 4:50 am

Sure. Here's a tie-in math question.
A type Ia supernova is discovered in a distant galaxy. Its maximum apparent magnitude is measured at 18.4. After monitoring the supernova for 15 days, the B band magnitude drops by 1.2. 1. What is the theoretical absolute luminosity of a type Ia supernova originating from a single progenitor? 2. Calculate the distance to the supernova based on this theoretical absolute magnitude. 3. Determine the speed at which the galaxy containing the supernova is receding. Use a Hubble constant of 70 km^-1*Mpc^-1 4. Based on the luminosity decline, determine the actual absolute magnitude of the supernova. 5. Recalculate the distance and recessional velocity based on the actual absolute magnitude.
Answer
1. -19.3 2. 346.7mpc 3. 24271.6km/s 4. -18.4884 5. 238.6mpc; 16702.4km/s
Sorry for jumping in but I have a question. How did you calculate the absolute magnitude in question 4? I've looked up luminosity decline rate and a couple other things and I haven't been able to find anything. Thanks in advance.
I simply used the formula for the Philips relationship which you can easily find the Wikipedia page for. The formula is this: M_max(B) = -21.726 + 2.698Δm_15(B). This formula is very specific to the scenario given here: after 15 days, the B-band magnitude drops by 1.2. Hope that helps!
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Re: Astronomy C

Postby Unome » February 15th, 2017, 5:16 am

Answer
1. -19.3 2. 346.7mpc 3. 24271.6km/s 4. -18.4884 5. 238.6mpc; 16702.4km/s
Sorry for jumping in but I have a question. How did you calculate the absolute magnitude in question 4? I've looked up luminosity decline rate and a couple other things and I haven't been able to find anything. Thanks in advance.
I simply used the formula for the Philips relationship which you can easily find the Wikipedia page for. The formula is this: M_max(B) = -21.726 + 2.698Δm_15(B). This formula is very specific to the scenario given here: after 15 days, the B-band magnitude drops by 1.2. Hope that helps!
Sorry, forgot about this during prep for regionals. Correct, your turn.
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Re: Astronomy C

Postby Magikarpmaster629 » February 17th, 2017, 2:47 pm

I'll pick this up then.

Some standard math:

Star A has a temperature of 6400 K.
1. Calculate its peak wavelength in nm.
2. The real wavelength is measured to be 480 nm. What is the recessional velocity of the star in m/s?
3. Is this number reasonable?
4. Star A is part of system AB, which has an apparent magnitude of 6.4 and an absolute magnitude of 1.99. Star B has a luminosity of 5.0 solar luminosities. What is the radius of star A in solar radii?
5. How far away is system AB in parsecs, light years, AU, and meters?
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Re: Astronomy C

Postby slowpoke » February 19th, 2017, 6:01 pm

I'll pick this up then.

Some standard math:

Star A has a temperature of 6400 K.
1. Calculate its peak wavelength in nm.
2. The real wavelength is measured to be 480 nm. What is the recessional velocity of the star in m/s?
3. Is this number reasonable?
4. Star A is part of system AB, which has an apparent magnitude of 6.4 and an absolute magnitude of 1.99. Star B has a luminosity of 5.0 solar luminosities. What is the radius of star A in solar radii?
5. How far away is system AB in parsecs, light years, AU, and meters?
:(
1. 452.8 nm 2. 1.7 e7 m/s 3. I suppose not 4. 2.4 solar radii 5. 76.2 pc
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Re: Astronomy C

Postby Magikarpmaster629 » February 20th, 2017, 5:49 am

I'll pick this up then.

Some standard math:

Star A has a temperature of 6400 K.
1. Calculate its peak wavelength in nm.
2. The real wavelength is measured to be 480 nm. What is the recessional velocity of the star in m/s?
3. Is this number reasonable?
4. Star A is part of system AB, which has an apparent magnitude of 6.4 and an absolute magnitude of 1.99. Star B has a luminosity of 5.0 solar luminosities. What is the radius of star A in solar radii?
5. How far away is system AB in parsecs, light years, AU, and meters?
:(
1. 452.8 nm 2. 1.7 e7 m/s 3. I suppose not 4. 2.4 solar radii 5. 76.2 pc
Yep, all good
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Re: Astronomy C

Postby Unome » February 20th, 2017, 7:27 am

I'll pick this up then.

Some standard math:

Star A has a temperature of 6400 K.
1. Calculate its peak wavelength in nm.
2. The real wavelength is measured to be 480 nm. What is the recessional velocity of the star in m/s?
3. Is this number reasonable?
4. Star A is part of system AB, which has an apparent magnitude of 6.4 and an absolute magnitude of 1.99. Star B has a luminosity of 5.0 solar luminosities. What is the radius of star A in solar radii?
5. How far away is system AB in parsecs, light years, AU, and meters?
:(
1. 452.8 nm 2. 1.7 e7 m/s 3. I suppose not 4. 2.4 solar radii 5. 76.2 pc
Yep, all good
Question: how does #4 work? Since it's before #5 in the order, it seems like it should be easier than it looks.
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Re: Astronomy C

Postby Magikarpmaster629 » February 20th, 2017, 9:57 am

:(
1. 452.8 nm 2. 1.7 e7 m/s 3. I suppose not 4. 2.4 solar radii 5. 76.2 pc
Yep, all good
Question: how does #4 work? Since it's before #5 in the order, it seems like it should be easier than it looks.
I'm guessing your problem was relating the luminosities of systems and stars. The luminosity of a system is the sum of the luminosities of each of the stars in the system.

First you must know the luminosity of star A to calculate its radius, since you already have its temperature. Convert the system's absolute magnitude to luminosity- 13 solar luminosities. Then subtract B's luminosity of 5.0 solar luminosities to get 8.0 solar luminosities. From there it's just Stephan-Boltzman Law- solve for R to get 2.3 solar radii, which is reasonably close to slowpoke's answer of 2.4.
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Re: Astronomy C

Postby Unome » February 20th, 2017, 10:03 am

Yep, all good
Question: how does #4 work? Since it's before #5 in the order, it seems like it should be easier than it looks.
I'm guessing your problem was relating the luminosities of systems and stars. The luminosity of a system is the sum of the luminosities of each of the stars in the system.

First you must know the luminosity of star A to calculate its radius, since you already have its temperature. Convert the system's absolute magnitude to luminosity- 13 solar luminosities. Then subtract B's luminosity of 5.0 solar luminosities to get 8.0 solar luminosities. From there it's just Stephan-Boltzman Law- solve for R to get 2.3 solar radii, which is reasonably close to slowpoke's answer of 2.4.
That's what I was thinking; it just seemed too complex in comparison to #5.
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Re: Astronomy C

Postby slowpoke » February 21st, 2017, 7:24 pm

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?
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Astronomy - 1/1/2
Chem Lab - 4/2/5
Hovercraft - 2/1/7
Materials Science - x/2/1

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Re: Astronomy C

Postby Ashernoel » February 21st, 2017, 8:17 pm

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?
Period (T): 70 hours.
M(system): 1.24
m(system): 2.3
d:16.29 pc from distance modulus
m(A): 3.5
M(A): 2.440 from distance modulus

A main sequence star should have around 6300K with this absolute magnitude.....?
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Re: Astronomy C

Postby slowpoke » February 21st, 2017, 10:02 pm

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?
Period (T): 70 hours.
M(system): 1.24
m(system): 2.3
d:16.29 pc from distance modulus
m(A): 3.5
M(A): 2.440 from distance modulus

A main sequence star should have around 6300K with this absolute magnitude.....?
Ah, I was mostly pulling these numbers out from my head rather than thinking of whether or not it was realistic :( . But, that wasn't really how I intended people to solve the problem. There should be a way to solve for these values without assuming anything (unless there is something horribly wrong with my reasoning...).
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Astronomy - 1/1/2
Chem Lab - 4/2/5
Hovercraft - 2/1/7
Materials Science - x/2/1

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Re: Astronomy C

Postby Unome » February 22nd, 2017, 5:23 am

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?
Assuming both stars eclipse fully (since as far as I know that can't really be derived from the problem without being stated)
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
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Re: Astronomy C

Postby Ashernoel » February 22nd, 2017, 7:11 am

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?
Assuming both stars eclipse fully (since as far as I know that can't really be derived from the problem without being stated)
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
nice work :D
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