25.2 Cosmology

Two stars, A and B, in a binary system move in an anti-clockwise direction around a common centre of mass, as shown in Fig. 1.1.

Fig. 1.1

On Fig. 1.2a and Fig. 1.2b below, mark the positions of stars A and B corresponding to their spectra as observed on Earth.

Fig. 1.2a                                                      Fig. 1.2b          

When measured in the laboratory, one of the spectral lines of hydrogen has a wavelength of 4.861 × 10⁻⁷ m. 

The same hydrogen line in the spectrum of one of the stars fluctuates from its laboratory wavelength by ± 0.420 × 10⁻⁷ m and the line in the spectrum of the other star fluctuates by ± 0.865 × 10⁻⁷ m. 

Calculate the velocity of each star in the binary system and identify the faster star and the slower star.

The orbital period of the binary system about the common centre of mass is 21 days.

Show that the orbital radius of star B is about twice the orbital radius of star A.

Newton assumed that the universe was infinite, uniform and static. The Big Bang model suggests space and time originated at one point around 14 billion years ago. At this time the temperature was very high.

In 1965, Penzias and Wilson discovered cosmic microwave background (CMB) radiation with a wavelength of around 1 mm.

Determine the current temperature of the CMB.

Surface temperature of the Sun = 5800 K

Peak wavelength emission of the Sun = 500 nm

Fig. 1.1 shows the map of microwave background radiation from the COBE satellite. It shows the variation in the mean temperature of the CMB in different parts of the sky.

Fig. 1.1

This radiation was first emitted around 300 000 years after the Big Bang, during a stage of the universe's history called the 'era of recombination'.

At this stage, the radiation was in the visible region of the spectrum and had a temperature of around 3000 K.

Determine the factor by which the universe has expanded since the universe was at a temperature of 3000 K.

Using Fig. 1.1, your answers to (a) and (b), and your knowledge of redshift and cosmology 

Fig. 1.1 shows the emission spectrum of some wavelengths of light that were observed using a source in a laboratory.

Fig. 1.1

The same wavelengths of light were observed on an emission spectrum from a distant galaxy but were found to be redshifted.

An astronomer observes that light from a galaxy has been shifted towards the blue end of an emission spectrum.

Hydrogen is an element of particular interest to cosmologists, as it can emit visible light waves.

A lot of useful information can be obtained by measuring the wavelength of the emitted light from the hydrogen in distant galaxies and comparing them to a laboratory sample. Some sample data is shown in Table 1.2.

Table 1.2

Compare the motions of galaxy 1a and galaxy 1b relative to Earth.

Use data from Table 1.2 to calculate the speed of galaxy 1b relative to Earth.

An astronomer analyses the light from a distant galaxy.

One of the observed spectral lines of hydrogen has a wavelength of 722 nm. The same spectral line has a wavelength of 656 nm when measured in the laboratory.

Explain how comparing the values of cosmological redshift for distant galaxies provides evidence for the Big Bang theory.

Cosmologists commonly quote the recessional velocity v of astronomical objects in relation to the speed of light c. This ratio is known as redshift z:

The Andromeda galaxy is the closest galaxy to our own Milky Way. Andromeda has a redshift value of z = −0.001.

Table 1.1 contains information about two galaxies.

Table 1.1