## Astronomy C

slowpoke
Member
Posts: 21
Joined: May 3rd, 2016, 4:59 pm
State: TX
Has thanked: 0
Been thanked: 0

### Re: Astronomy C

Magikarpmaster629 wrote: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
5. 76.2 pc```
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
Exalted Member
Posts: 578
Joined: October 7th, 2014, 3:03 pm
State: MA
Location: No idea, but I can tell you exactly how fast I'm going
Has thanked: 0
Been thanked: 1 time

### Re: Astronomy C

slowpoke wrote:
Magikarpmaster629 wrote: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
5. 76.2 pc```
Yep, all good

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.

Unome
Moderator
Posts: 4250
Joined: January 26th, 2014, 12:48 pm
State: GA
Location: somewhere in the sciolyverse
Has thanked: 64 times
Been thanked: 29 times

### Re: Astronomy C

Magikarpmaster629 wrote:
slowpoke wrote:
Magikarpmaster629 wrote: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
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.
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.

Magikarpmaster629
Exalted Member
Posts: 578
Joined: October 7th, 2014, 3:03 pm
State: MA
Location: No idea, but I can tell you exactly how fast I'm going
Has thanked: 0
Been thanked: 1 time

### Re: Astronomy C

Unome wrote:
Magikarpmaster629 wrote:
slowpoke wrote:
```1. 452.8 nm
2. 1.7 e7 m/s
3. I suppose not
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.

A wild goose flies over a pond, leaving behind a voice in the wind.
A man passes through this world, leaving behind a name.

Unome
Moderator
Posts: 4250
Joined: January 26th, 2014, 12:48 pm
State: GA
Location: somewhere in the sciolyverse
Has thanked: 64 times
Been thanked: 29 times

### Re: Astronomy C

Magikarpmaster629 wrote:
Unome wrote:
Magikarpmaster629 wrote: 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.
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.

slowpoke
Member
Posts: 21
Joined: May 3rd, 2016, 4:59 pm
State: TX
Has thanked: 0
Been thanked: 0

### 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
Member
Posts: 345
Joined: January 27th, 2017, 1:31 pm
State: IL
Location: MA
Has thanked: 0
Been thanked: 1 time

### Re: Astronomy C

slowpoke wrote: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
Member
Posts: 21
Joined: May 3rd, 2016, 4:59 pm
State: TX
Has thanked: 0
Been thanked: 0

### Re: Astronomy C

Ashernoel wrote:
slowpoke wrote: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...).
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

Unome
Moderator
Posts: 4250
Joined: January 26th, 2014, 12:48 pm
State: GA
Location: somewhere in the sciolyverse
Has thanked: 64 times
Been thanked: 29 times

### Re: Astronomy C

slowpoke wrote: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?
```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```
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.

Ashernoel
Member
Posts: 345
Joined: January 27th, 2017, 1:31 pm
State: IL
Location: MA
Has thanked: 0
Been thanked: 1 time

### Re: Astronomy C

Unome wrote:
slowpoke wrote: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?
```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
NT '19
Harvard '23

### Who is online

Users browsing this forum: No registered users and 1 guest