9.3.1

# Doppler Effect

Test yourself

## Doppler Effect

The Doppler effect, applied to electromagnetic radiation, is very useful in astrophysics and cosmology.

### Formula

• For electromagnetic radiation, the following formula holds providing that the velocity of the source of the radiation is significantly lower than the speed of light.
• $\frac{\Delta f}{f} \approx \frac{v}{c}$
• Where f is the frequency of light, and v is the speed of the emitting source.

### Moving star

• For a single star moving away from the Earth at a constant speed, the light from the star decreases in frequency.
• If the star is moving away at 0.01c (one hundredth of the speed of light), then the frequency of any given wavelength (typically one of the hydrogen lines) will be lower by 1%.

## Binary Stars

Binary stars are systems where two similar stars orbit around their combined centre of gravity.

### Spectral line splitting

• In a binary system, in which two stars orbit around a common centre of gravity, then the spectral line splits into two.

### Explanation

• This is explained by one star moving away from the Earth slightly less quickly and the other star moving away from the Earth slightly more quickly than in the single star case.

### Orbital velocity

• The orbital velocity can be found by finding the recession speeds of the two stars (the speed the stars are moving away from us) and finding the difference.
• Half of that difference is the orbital speed of the star (assuming the two stars to be identical).

## Galaxies and Quasars

Galaxies are vast collections of stars in space. Quasars are very massive, high energy objects found in deep space.

### Cosmological redshift

• For galaxies and quasars, there is also a cosmological redshift, z, which is due to the expansion of the Universe itself.
• For low velocities:
• $z = \frac{v}{c}$

### Very distant objects

• Very distant galaxies and quasars can have enormous z-values which can only really be explained by general relativity calculations.