Question

Problem B.3: Mysterious Object (6 Points)
Your research team analysis the light of a mysterious object in space. By using a spectrometer,
you can observe the following spectrum of the object. The Hα line peak is clearly visible:
(a) Mark the first four spectral lines of hydrogen (Hα, Hβ, Hγ, Hδ) in the spectrum.
(b) Determine the radial velocity and the direction of the object’s movement.
(c) Calculate the distance to the observed object.
(d) What possible type of object is your team observing?

Answer 1

(a) The four spectral lines are below:

(b) The radial velocity and the direction of the object’s movement:

$$v=zc=(3\cdot10^5)\bigg(\frac{800}{656.28}-1\bigg)=65700\text{ km/s}.$$

The velocity is positive. The wavelengths elongate. Thus, the object moves away from us.

(c) According to Hubble's law, the distance is

$$D=\frac{v}{H_0}=\frac{65700\text{ km/s}}{72\text{ km/s/MPc}}=913\text{ MPc}.$$

(d) The type of object is a galaxy.