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.
- Answer
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.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.
- Answer
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 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.
- Sure. Here's a tie-in math question.
- Answer
Sorry, forgot about this during prep for regionals. Correct, your turn.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 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.
- Answer
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 goodI'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?
- :(
Question: how does #4 work? Since it's before #5 in the order, it seems like it should be easier than it looks.Yep, all goodI'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?
- :(
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.Question: how does #4 work? Since it's before #5 in the order, it seems like it should be easier than it looks.Yep, all good
- :(
That's what I was thinking; it just seemed too complex in comparison to #5.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.Question: how does #4 work? Since it's before #5 in the order, it seems like it should be easier than it looks.Yep, all good
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.
Period (T): 70 hours.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?
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...).Period (T): 70 hours.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?
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.....?
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?
nice workAlright. 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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