As a stars size increases, it’s luminosity
also increases. The relationship between a star's size and its luminosity is known as the Stefan-Boltzmann law. According to this law, the luminosity of a star is directly proportional to the fourth power of its radius.
In other words, if a star's size doubles (its radius doubles), its luminosity will increase by a factor of 2^4 = 16. Similarly, if a star's size triples (its radius triples), its luminosity will increase by a factor of 3^4 = 81.
This relationship holds true for main sequence stars, where the fusion of hydrogen into helium is the primary source of energy. However, for stars beyond the main sequence, such as red giants or white dwarfs, the relationship between size and luminosity may not follow the Stefan-Boltzmann law.
As a star's size increases, its luminosity also increases. The luminosity of a star refers to the total amount of energy it radiates per unit of time. It is directly related to the star's surface temperature and its size or radius.
One way to understand this relationship is through the Stefan-Boltzmann law, which states that the luminosity of a star is proportional to the fourth power of its surface temperature and the square of its radius. This means that if the star's size increases (i.e., its radius increases), its luminosity will increase exponentially.
To put it simply, larger stars have more surface area, which allows them to emit more energy. So, as a star gets bigger, it becomes more luminous and shines brighter.