## Astronomy C

jonboyage
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### Re: Astronomy C

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.
I was in a bin

Rustin '19
UPenn '23

Bob_117
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### Re: Astronomy C

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.
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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jonboyage
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State: PA

### Re: Astronomy C

Sure. Here's a tie-in math question.
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!
I was in a bin

Rustin '19
UPenn '23

Unome
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### Re: Astronomy C

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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Magikarpmaster629
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### Re: Astronomy C

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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slowpoke
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### Re: Astronomy C

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?
:(
2017 R/S/N
Astronomy - 1/1/2
Chem Lab - 4/2/5
Hovercraft - 2/1/7
Materials Science - x/2/1

William P. Clements HS '17

Magikarpmaster629
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### Re: Astronomy C

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?
:(
Yep, all good

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A man passes through this world, leaving behind a name.

Unome
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### Re: Astronomy C

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?
:(
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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Magikarpmaster629
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### Re: Astronomy C

:(
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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Unome
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### Re: Astronomy C

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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slowpoke
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### Re: Astronomy C

Alright. Sorry for more math whoops.

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?
2017 R/S/N
Astronomy - 1/1/2
Chem Lab - 4/2/5
Hovercraft - 2/1/7
Materials Science - x/2/1

William P. Clements HS '17

Ashernoel
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### Re: Astronomy C

Alright. Sorry for more math whoops.

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.....?
NT '19
Harvard '23

slowpoke
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State: TX

### Re: Astronomy C

Alright. Sorry for more math whoops.

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

William P. Clements HS '17

Unome
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### Re: Astronomy C

Alright. Sorry for more math whoops.

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)
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Ashernoel
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### Re: Astronomy C

Alright. Sorry for more math whoops.

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)
nice work
NT '19
Harvard '23