Why does the Doppler effect only find the radial velocity?

The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law. Calculate the peak wavelength of a bluish-white star that radiates at temperature 20000 K.   a) 145 nm b) 100 nm c) 114 nm d) 155 nm

answer for 3

Integrate the first equation over all wavelengths to find an expression for the total luminosity of a black body star. (See the second equation for a hint)

An interstellar cloud is observed at a wavelength of 2.898 µm. Estimate the temperature of the cloud.

find the temperature of the coolest star whose peak blackbody wavelength can be observed with the human eye (the exact range of visible light varies from publication to publication, so use 380nm to 750 nm).

The three most prominent spectral lines of hydrogen are H-α at 656 nm, H-β at 486 nm, and H-γ 434 nm. If we observe an object with H-α at a wavelength of 700 nm, what wavelength will we observe H-β and H-γ? Is the object moving toward or away from us, and how do you know? Suppose we observe another object with H-α at 585 nm. Is this object moving toward or away from us? Is it moving slower or faster than the first object?

I am unsure where f3 should go from the black dot and the length/direction should it be?

Show that, if the ratio of the blackbody fluxes from a star at two different frequencies (i.e., a color) is measured, then, in principle, the surface temperature of the star can be derived, even if the star's solid angle on the sky is unknown (e.g., if it is too distant to be resolved, and its distance and surface area are both unknown).

Consider a large interferometer that uses a lazer with the wavelength of 1,073.27 nm (1073.27 x 10-9m). What is the frequency of the photons emitted by this beam in hertz?