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Physics Dad
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I have made an effort to answer this question, and would like to know if my thinking is correct. I would appreciate any feedback.
Thank you!
Two stars in the sky have similar effective temperatures, masses and apparent brightness. However, star 1 has a surface gravity which is 10 times higher than star 2. If star 1 is 1pc away, what is the distance to star 2?
i) g*=GM*/R*2
ii) f*=L*/4πd*2
iii) L*=4πR*2σT*eff4
iv) m*1-m*2=-2.5log(f*1/f*2)
Based upon the question, I can assume that the mass (M*), the effective temperature (T*eff) and the apparent magnitude (m*) of both stars is the same.
First of all, I will start with the gravity which tells me that:
g*1=10g*2
so using equation i) I can say that:
GM/R*12=10GM/R*22
I can then rearrange to get a ratio of radii which will tell me that...
R*12/R*22=10-1
I can then calculate the ratio of fluxes by substituting equation iii) into equation ii),= and doing some cancelling to find that...
f*1/f*2=d*22(R*12/R*22)
I know that the value of R*12/R*22=10-1 so I can sub this value in
as I know that both apparent magnitudes are the same, I can say that m*1-m*2=0 and then sub in my ratio of fluxes to equation 4 to get...
0=-2.5log(d*22/10)
I can then solve this equation for d*2 and I get...
d*2=3.16pc
This seems feasible given that star two would have a radius 10 times bigger than star 1, but I would appreciate any help or advice anyone can offer.
Thank you!
Thank you!
Homework Statement
Two stars in the sky have similar effective temperatures, masses and apparent brightness. However, star 1 has a surface gravity which is 10 times higher than star 2. If star 1 is 1pc away, what is the distance to star 2?
Homework Equations
i) g*=GM*/R*2
ii) f*=L*/4πd*2
iii) L*=4πR*2σT*eff4
iv) m*1-m*2=-2.5log(f*1/f*2)
The Attempt at a Solution
Based upon the question, I can assume that the mass (M*), the effective temperature (T*eff) and the apparent magnitude (m*) of both stars is the same.
First of all, I will start with the gravity which tells me that:
g*1=10g*2
so using equation i) I can say that:
GM/R*12=10GM/R*22
I can then rearrange to get a ratio of radii which will tell me that...
R*12/R*22=10-1
I can then calculate the ratio of fluxes by substituting equation iii) into equation ii),= and doing some cancelling to find that...
f*1/f*2=d*22(R*12/R*22)
I know that the value of R*12/R*22=10-1 so I can sub this value in
as I know that both apparent magnitudes are the same, I can say that m*1-m*2=0 and then sub in my ratio of fluxes to equation 4 to get...
0=-2.5log(d*22/10)
I can then solve this equation for d*2 and I get...
d*2=3.16pc
This seems feasible given that star two would have a radius 10 times bigger than star 1, but I would appreciate any help or advice anyone can offer.
Thank you!