1)
The space is filled with background radiation, remnant of the early age of the universe. Currently the distribution of this radiation is similar to the radiation of a blackbody at the temperature of 2.7 K. What is λmax corresponding to this radiation? What is its total intensity? Compare the intensity of the background radiation to the intensity of the Sun at the visual wavelengths.

2)
The temperature of a red giant is T = 2500 K and radius 100 times the solar radius. a) Find the total luminosity of the star, and the luminosity in the visual band 400 nm ≤ λ ≤ 700 nm. b) Compare the star with a 100 W lamp that radiates 5% of its energy in the visual band. What is the distance of the lamp if it looks as bright as the star?

The distance to the star is 10 pc.

3)
The effective temperature of Sirius is 10,000 K, apparent visual magnitude −1.5, distance 2.67 pc and bolometric correction 0.5. What is the radius of Sirius?

4)
a) The sun has a nominal surface temperature of 5778 K. Assuming the sun is a black-body emitter (which is mostly true), create a table with the [spectral] intensity as a function of wavelength across the near-visible range, 250–850 nm.
b) An ideal color filter is completely transparent for a range of wavelengths λ1 ≤ λ ≤ λ2 and completely opaque (no transmission) at all other wavelengths. An ideal camera is equally sensitive to all wavelengths. Suppose you have an ideal camera equipped with three ideal filters: a U filter that passes light between 320 and 400 nm, a B filter that passes 400–500 nm, and a V filter that passes 500–700 nm.
What are the color indices of the sun that you would measure with this camera (i.e., what are U − B and B − V )?
What would the color indices be for a red dwarf (T = 3500 K)? For a white dwarf (T = 17000 K)?

1) The space is filled with background radiation, remnant of the e...