ASTR 220 Homework 3

Use Wien's law [(peak wavelength) x (Temperature) = 3 x 10⁶ nanometers x Kelvins] and the Stefan-Boltzmann Law [(Luminosity) ~ (Radius)² x (Temperature)⁴] to answer the following questions:
- a) The peak wavelength of the spectrum of a star is found to occur at 1,000 nanometers. What is the star's surface temperature?
- b) Assume that this star has the same radius as the sun, and that the temperature of the sun is 6,000 K. How bright is this star compared to the sun?
- c) Now suppose that a star of this surface temperature is not the same size as the sun, but instead is a red giant whose radius is 64 times that of the sun. How does its luminosity compare now?
Below are the Hertzsprung Russell diagrams of two different star clusters, 47 Tuc and the Pleiades.
Which one is older?

Besides their age, in what other ways are these clusters visibly different?
Picture of 47 Tuc
Picture of the Pleiades