Astronomy C

[slowpoke]

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?

:( (Click to Show Hidden Text)

1. 452.8 nm
2. 1.7 e7 m/s
3. I suppose not
4. 2.4 solar radii
5. 76.2 pc

[Magikarpmaster629]

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?

:( (Click to Show Hidden Text)

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

[Unome]

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?

:( (Click to Show Hidden Text)

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.

[Magikarpmaster629]

:( (Click to Show Hidden Text)

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.

[Unome]

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.

[slowpoke]

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?

[Ashernoel]

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.....?

[slowpoke]

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...).

[Unome]

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) (Click to Show Hidden Text)

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

[Ashernoel]

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) (Click to Show Hidden Text)

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