Two distant stars A and B are observed through a spectroscope. The wavelength at which star A shows maximum intensity is 580 nm, while for star B it is 290 nm. Assume both stars radiate approximately like perfect blackbodies.
a. (i) Using the appropriate physical relation, obtain the ratio of the surface temperatures T_B : T_A.
b. (ii) If the surface temperature of star A is 5000 K, calculate the surface temperature of star B.
c. (iii) If another star C has its peak at 970 nm, compare its surface temperature with that of star A by calculating T_C : T_A.