What is the new maximum distance at which the star would still be visible in the same telescope?

A main-sequence star at a distance of 29 pc is barely visible through a certain telescope. The star subsequently ascends the giant branch, during which time its temperature drops by a factor of three and its radius increases a hundredfold.What is the new maximum distance at which the star would still be visible in the same telescope?L = A * 蟽 * T^4



So:



L2 / L1 = (A2 * 蟽 * T2^4) / (A1 * 蟽 * T1^4) = (A2 / A1) * (T2 / T1)^4



L2 / L1 = (100^2)* (1/3)^4 = 123



L2 / d2^2 = L1 / d1^2



d2^2 = (L2 / L1) *d1^2 = (123) * 29^2 = 103827



d2 = 322 parsec



Oops, I made a typo in the first formula, it's corrected now. The result is correct, but it should have been "*" intead of "/".What is the new maximum distance at which the star would still be visible in the same telescope?i have the same question... I know that L=R^2/ ( 1/T)^4. I do not see how this is equal to 123 however. The rest makes sense. 100^2/ ( 1/3)^4 =810 000. Could you please explain this katekbo?