Cosmology (Topic 10B)
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The Doppler effect refers to the change in frequency or wavelength of waves due to the motion of the source relative to an observer.
The Doppler effect is a very useful tool used in astrophysics for measuring the speed and position of stars and galaxies relative to Earth.
Redshift: When a light source moves away from the observer, the observed wavelength increases and the observed frequency decreases, shifting towards the red end of the spectrum.
Blueshift: When a light source moves towards the observer, the observed wavelength decreases and the observed frequency increases, shifting towards the blue end of the spectrum.
The Doppler equation relates the observed change in wavelength or frequency of electromagnetic radiation to the relative velocity of the source and the observer:
Where:
- is the source wavelength,
- is the source frequency,
- is the change in wavelength recorded by an observer,
- is the change in frequency recorded by an observer,
- is the magnitude of the relative velocity between the source and the observer, and
- is the speed of light in a vacuum,
It is important to note that symbols are used in the Doppler equation because it is a non-relativistic simplification, valid only when . For A-level you do not need to consider relativistic effects in this context.
Question walkthrough
Star Speed from Redshift
Use the Doppler wavelength-shift equation to calculate the speed of a distant star from a measured change in its absorption line wavelength, taking care to convert units consistently.
The quantity in the Doppler equation, is known as the redshift, can be represented using the symbol, Therefore, the Doppler equation may be written as:
Where the redshift may be represented more simply as . For sources moving away from the observer, is taken to be negative, so is positive.
Additionally, the Doppler equation in terms of frequency may be written in terms of :
Question walkthrough
Finding galaxy velocity from redshift
Uses Δλ/λ to find the redshift of a galaxy’s emission line from its emitted and observed wavelengths, then relates this to the galaxy’s recession velocity via the Doppler redshift approximation.
The red shift equations can be used to calculate both red shift and cosmological redshift as long as the velocity is much less than the speed of light . If the velocity is close to the speed of light, relativistic effects come into play, and the equations no longer work.
Astronomer Edwin Hubble determined that the more distant galaxies are moving away from us the faster. This suggests that the universe began as very hot and dense point, and is expanding at an increasing rate: this is known as the Big Bang theory.
In the late 1920s, Edwin Hubble examined the Doppler shift in the absorption spectra of various distant galaxies. His results confirmed that most galaxies exhibit redshift, indicating they are moving away from Earth.
Hubble also observed a correlation between distance and redshift. Specifically, more distant galaxies tend to have higher redshifts, suggesting they are moving away faster.
Hubble’s law states that the recessional velocity of a galaxy is directly proportional to its distance from Earth:
Where:
- is the recessional velocity of the galaxy in ,
- is Hubble’s constant in , and
- is the distance to the galaxy in megaparsecs,
The Hubble constant describes the rate of expansion of the Universe. It is approximately equal to:
The Hubble constant quantifies how quickly galaxies are receding from us, based on their distance. It is the rate of expansion per unit distance. For every megaparsec of distance from Earth, a galaxy’s recessional speed increases by kilometres per second.
The value of the Hubble constant is debated due to the difficulty of measuring distances to galaxies. This gives a range of values for typically in the range of:
The Big Bang theory states that the Universe began in an extremely hot, dense state called a singularity about 13.8 billion years ago and has been expanding ever since.
Hubble’s discovery that galaxies are moving away from each other, as evidenced by their cosmological redshift and their distances from the Milky Way, is one of the earliest pieces of evidence that the Universe is expanding, supporting the Big Bang theory.
Despite its name, the Big Bang was not an explosion in space, but rather the rapid expansion of space itself. Matter was not ejected outward; instead, space itself expanded, causing galaxies to move apart.
The age of the Universe can be estimated using the inverse of the Hubble constant . The Hubble constant describes the rate of the Universe’s expansion, and the inverse of the equation gives us a rough estimate of the Universe’s age:
However, due to the uncertainty in the exact value of the Hubble constant, there is uncertainty in the exact age of the universe.
Based on modern measurements of the Hubble constant, the estimated age of the Universe is approximately 13.8 billion years. This is a crucial number in cosmology, reflecting the time that has elapsed since the Big Bang.
It is important to note and recall the following key characteristics of ordinary matter and dark matter:
| Ordinary matter | Dark matter | |
|---|---|---|
| Definition | Matter composed of atoms (protons, neutrons and electrons); the “baryonic” matter that makes up everything visible. | A non-luminous form of matter that does not emit, absorb, or reflect electromagnetic radiation. |
| Role | Forms all luminous structures; stars, planets, interstellar gas, and living matter. | Provides the gravitational pull needed to hold galaxies together and drives large-scale structure formation. |
| % of the universe | |
|
| Detection | Directly observed via emitted or reflected electromagnetic radiation. | Inferred from gravitational effects; galactic rotation curves and gravitational lensing. |
It is useful to note that a mysterious form of energy called dark energy makes up the remaining of the universe. However, knowledge of this is not required for your exam.