A main-sequence star at a distance of 20 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?

Explanation:

The surface area of a star estimated by the energy emitted per sq meter yields the overall luminosity, which can be represented mathematically as:

where;

L ∝ R²T⁴

and;

R = radius of the sphere

σ = Stefans constant

T = temperature

Also; The following showcase the relationship between flux density as well as illuminated surface area as:

where

A = 4πd² and L ∝ R²T⁴

Given that:

distance d₁ = 20 pc

Then, using equation (2)

However, we are also being told that there is a temp. drop by a factor of 3;

So, the final temp. ; and the final radius is since there is increment by 100 folds.

Now;

SInce;

It implies that:

Replacing all our values, we have: