Calculating Luminosity of a Star at Different Stages

[kelseymclean]

The question is A main sequence star is barely visible at a distance of 20 pc with a certain telescope. The star subsequently
ascends the red giant branch, during which time its surface temperature drops by a factor of 3 and its radius increases by a factor of 50.
a) Determine the how luminous the star is now compared to its original luminosity, that is, determine
LRED GIANT/LORIGINAL
b) Determine how far away this star could be seen now by the same telescope.

So far, I have, L=R^2 * T^4. and that Radius is proportional to $$\sqrt{luminosity}$$/temperature.
and Apparent magnitude - absolute magnitude = 5 log(base 10) (Distance/ 10 pc).
I am stuck at determining the radius and luminosity of the star before it ascends.
Any hints/ help would be greatly appreciated.

 

[phyzguy]

You don't need to know the radius and luminosity before it goes red giant. You are only asked to determine the ratio of the luminosity after it expands to the luminosity before it expands. The formulas you wrote have everything you need. If the radius increases by 50 and the temperature decreases by 3 and L~R^2*T^4, what happens to the luminosity?

 

[kelseymclean]

The luminosity increases by 50^2/(3^4) Because temperature drops by a factor of 3?

 

[phyzguy]

Sounds good to me!

 

[kelseymclean]

So this value, 30.86 is LRedGiant/ L original? how do i go about finding out how far it can be seen from?

 

[phyzguy]

Do you know how to relate luminosity, distance, and magnitude?