Prove that if you could observe the disks of stars through a telescope, you would notice that their surface brightness

Prove that if you could observe the disks of stars through a telescope, you would notice that their surface brightness is determined only by the temperature of the star’s surface.

The luminosity of a star is proportional to R ^ 2T ^ 4, where R and T are its radius and temperature. The brightness of a star on Earth is proportional to R ^ 2T ^ 4 / L ^ 2, where L is the distance to the star. The area of the visible disk is proportional to R ^ 2 / L ^ 2 As a result, the brightness per unit of the visible area is proportional to T ^ 4.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.