Question
A star size increases its luminosity blank as a star's temperature blank its luminosity increases
Answers
GPT-4o mini
A star's size increases its luminosity **dramatically** as a star's temperature **increases** its luminosity.
To elaborate:
- When a star's size increases (specifically, its radius), its luminosity can increase dramatically because luminosity is proportional to the surface area of a star, which is a function of the radius squared (Luminosity ∝ R²).
- When a star's temperature increases, its luminosity also increases, following the Stefan-Boltzmann Law, which states that luminosity is proportional to the fourth power of the temperature (Luminosity ∝ T⁴).
Thus, both increasing size and increasing temperature lead to a significant increase in a star's luminosity.
To elaborate:
- When a star's size increases (specifically, its radius), its luminosity can increase dramatically because luminosity is proportional to the surface area of a star, which is a function of the radius squared (Luminosity ∝ R²).
- When a star's temperature increases, its luminosity also increases, following the Stefan-Boltzmann Law, which states that luminosity is proportional to the fourth power of the temperature (Luminosity ∝ T⁴).
Thus, both increasing size and increasing temperature lead to a significant increase in a star's luminosity.