- #1

Physics Dad

- 55

- 1

*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!

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

_{*}

^{2}σT

_{*eff}

^{4}

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

_{*1}

^{2}=10GM/R

_{*2}

^{2}

I can then rearrange to get a ratio of radii which will tell me that...

R

_{*1}2/R

_{*2}2=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

_{*2}

^{2}(R

_{*1}

^{2}/R

_{*2}

^{2})

I know that the value of R

_{*1}

^{2}/R

_{*2}

^{2}=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

_{*2}

^{2}/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!