Cosmology (5.5.3)
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Astronomical unit (AU)
- Definition: An astronomical unit is the average distance between Earth and the sun.
- Value: Approximately
- Usage: Primarily used to describe distances within the Solar System, such as the distance between planets.
Light year (ly)
- Definition: The distance that light travels in one year in a vacuum.
- Value: Approximately
- Usage: Used to measure distances to stars and galaxies beyond the Solar System. For example, the Andromeda Galaxy is about 2.54 million light years away from Earth.
The arcsecond is a unit of angular measurement. The symbol for arcsecond is () and the symbol for arcminute is ():
- Value: An arcsecond is equivalent to of a degree.
- Usage: Arcseconds are commonly used in astronomy to measure very small angles, such as the apparent size of distant stars or the angular separation between celestial objects. They are also fundamental in defining a parsec.
The Parsec (pc) is the distance at which one astronomical unit subtends an angle of one arcsecond:
- Value: Approximately
- Usage: Commonly used in astronomy to measure stellar and galactic distances. For instance, the nearest star system, Alpha Centauri, is about away from Earth.
Stellar parallax refers to the apparent shift in the position of a nearby star against the backdrop of distant stars as the Earth orbits the sun:
- This shift is due to observing the star from two different points in Earth’s orbit, six months apart.
- Stellar parallax is used to measure distance to the nearby star from Earth.
You can more intuitively understand stellar parallax by holding your finger in front of you and alternately closing one eye, then the other.
The apparent ‘shift’ in your finger’s position mimics how a nearby star appears to shift against distant stars as Earth orbits the sun. The closer the star, the larger the shift (i.e. the parallax angle).
There are limitations to the stellar parallax method. It is effective for stars within only . Beyond this, parallax angles become too small to measure accurately.
Even with advanced instrumentation, distant stars remain difficult to measure; alternative methods, such as standard candles or Doppler-shift analysis of absorption spectra, are used instead.
The parallax angle is half the total angular shift of the star, measured in arcseconds:
- The parallax angle is inversely proportional to the distance to the star
- A larger parallax angle means the star is closer to the observer.
The parallax angle is half the total angular shift of the star against the backdrop of distant stars over a time period of six months as observed from Earth. The formula to calculate the parallax angle is:
Where:
- is the parallax angle in arcseconds, and
- is the distance to a star in parsecs.
A larger parallax angle means the star is closer to the observer.
The universe looks the same no matter the direction of observation: this is known as the cosmological principle.
The cosmological principle states that, on a large scale, the universe is both homogeneous and isotropic.
- Homogeneous: A universe where the matter is distributed uniformly such that the average density remains consistent.
- Isotropic: A universe that appears the same in all directions, no matter the point of observation.
Before the 1930s, it was believed that the universe was infinite in space and time and static: neither expanding nor contracting. This model seemed to be the only way the universe could be stable according to Newton’s law of gravitation.
A homogeneous Universe means that matter is distributed uniformly across large scales. This implies that:
- over vast distances, the average density of the Universe remains consistent,
- similar structures (like galaxies) can be found throughout the Universe, regardless of location.
The laws of physics are universal, meaning they apply uniformly across the entire Universe. This implies that physical laws (e.g. gravity, electromagnetism) are consistent and apply everywhere in the Universe.
It also suggests the universe has temporal consistency, whereby laws remain unchanged over time, meaning that the same physical principles that governed the Universe in the past are also applicable in the present and will continue to apply in the future. This concept allows for the reliable extrapolation of data and theories across different epochs of cosmic history.
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.
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 model of the expanding Universe posits that the fabric of space itself is stretching in all directions, so the space between galaxies is expanding, rather than galaxies merely moving away from each other.
This model emerged from Hubble’s observations of redshifts in distant galaxies. The further apart two galaxies are, the more pronounced the redshift, indicating faster recessional speeds.
When plotting a graph of the distance of galaxies from Earth against their recessional speed, the Hubble constant is represented by the gradient of a straight line. However, the spread of data points makes it difficult to plot an accurate line of best fit, suggesting some uncertainty in the exact value of .
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.
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.
Cosmic microwave background radiation (CMBR) serves as another critical piece of evidence for the Big Bang theory. CMBR is the afterglow of the early Universe; high-energy gamma photons from the early Universe have stretched into microwaves over time due to the expansion of space.
The picture of the cosmic microwave background above is a snapshot of the oldest light in our Universe, when the Universe was only years old. It shows small temperature fluctuations, and warmer areas are represented in red. These correspond to regions of slightly higher density, which are the areas where star clusters and galaxies eventually formed.
When the Universe was very young and extremely hot, space was filled with high-energy gamma photons. As the Universe expanded, the fabric of space stretched, which lengthened the wavelength of these photons to what we now observe as microwaves.
The Universe’s expansion over billions of years has cooled the initially hot, dense Universe to about At this temperature, the Universe acts as a black-body radiator, peaking at a wavelength around 1 in the microwave region of the spectrum.
The Big Bang theory is the most widely accepted explanation for the Universe’s origin. Competing theories have failed to explain this phenomenon, which has solidified the Big Bang theory’s standing in the scientific community. Penzias and Wilson’s discovery of the CMBR in 1964 formed the foundation of the Big Bang theory, earning them the Nobel Prize in Physics in 1978.
The Big Bang represents the starting point of the Universe, marking the creation of spacetime itself. This event initiated the expansion of spacetime, which continues to influence the structure of the Universe today.
The continuous expansion of spacetime affects how galaxies form and evolve over billions of years. Understanding this expansion is essential for predicting the future of the Universe and its eventual fate.
Einstein’s theory of general relativity predicted that spacetime could expand or contract, contradicting the previously accepted idea of a static Universe. Solutions to his equations, found by Alexander Friedmann, predicted that the Universe could expand from a single point, which later aligned with the Big Bang theory.
This expansion model was further supported when Edwin Hubble observed galaxies moving away from each other, confirming that the Universe is expanding.
Familiarise yourself with the key phases of the Universe’s evolution:
The Big Bang
Marks the beginning of the Universe, when all matter, energy, space, and time originated from an extremely hot and dense singularity.
At this moment, the Universe was a single point of infinite density, with no structures. This event occurred approximately 13.8 billion years ago and led to the rapid expansion of spacetime.
Inflation
Refers to the rapid and exponential expansion of the Universe that occurred within the first fraction of a second.
During this period, the Universe expanded faster than the speed of light, growing by a tremendous factor in a tiny fraction of time. Only high-energy gamma photons and electromagnetic radiation existed; no forms of matter had come into existence yet.
It is important to note that nothing can travel through space faster than light. But the expansion of space itself is not bound by this limit. This is why Hubble’s Law, , can give a recession speed greater than for sufficiently distant galaxies, without contradicting special relativity.
First particles
The Universe had cooled enough for fundamental particles to form. At this time, quarks – the building blocks of protons and neutrons – began to combine to form protons and neutrons. The energy present was still extremely high, but the Universe had expanded enough for these particles to exist in stable forms.
This period marks the beginning of the formation of the first atomic nuclei in the process that would later become known as nucleosynthesis.
First nuclei
The Universe had cooled enough for protons and neutrons to combine and form the first atomic nuclei: primarily hydrogen and helium.
This process, known as Big Bang nucleosynthesis, resulted in the creation of about hydrogen and helium nuclei, with trace amounts of deuterium (heavy hydrogen) and lithium.
The Universe’s temperature at this stage was around It was still too hot for electrons to combine with nuclei and form neutral atoms.
First light
The Universe cooled enough for electrons to combine with protons and form neutral atoms, in a process called recombination. This allowed photons (light) to travel freely through space for the first time, as they were no longer scattered by free electrons.
The electromagnetic radiation released during this period is what we observe today as cosmic microwave background radiation (CMBR).
First stars
The Universe had cooled sufficiently for gas clouds, primarily made of hydrogen and helium, to collapse under gravity and form the first stars. This period is known as the cosmic dawn.
These early stars were much larger and hotter than modern stars and emitted intense ultraviolet radiation. Their formation marked the beginning of stellar nucleosynthesis, which produced heavier elements like carbon, oxygen, and nitrogen, which would later contribute to the formation of planets and more complex structures.
The light from these first stars also began to ionise the surrounding gas, contributing to the epoch of reionisation, which ended the ‘cosmic dark ages’.
Galaxies and dark matter
The first galaxies began to form as stars clustered together under the influence of gravity.
At this time, dark matter played a crucial role in shaping the Universe’s structure. Dark matter, interacting with matter via gravity, acted as a scaffold for ordinary matter, helping to pull gas and stars together to form galaxies.
Though invisible, dark matter’s existence has been inferred by its gravitational effects on visible matter, providing the necessary mass to stabilise galaxies and clusters. This period marks the start of galaxy formation that would eventually lead to the vast, large-scale cosmic structures observed today.
Dark energy
The expansion of the Universe began to accelerate due to the influence of dark energy, which is a mysterious force that makes up approximately of the Universe. Dark energy counteracts gravity and drives the accelerating expansion of space.
Prior to this, expansion was slowing down due to gravitational attraction between the matter and dark matter in the universe. However, dark energy eventually began to dominate, overpowering gravity and accelerating the expansion. This marked a critical shift in the Universe’s evolution, and it continues to drive the accelerating expansion observed today.
Today
The Universe is currently billion years old. Over this vast timespan, the Universe has continued to expand. Galaxies, stars, and planetary systems, including our own Solar System, have formed.
Earth’s formation occurred about billion years ago, and life on Earth began around billion years ago. Human beings evolved relatively recently, with the first modern humans emerging around years.
The Universe’s expansion continues to accelerate due to dark energy, and current observations suggest it will keep expanding indefinitely.
It is important to note and recall the following key characteristics of ordinary matter, dark matter, and dark energy for your exams:
| Ordinary matter | Dark matter | Dark energy | |
|---|---|---|---|
| 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. | A form of energy proposed to explain the observed accelerating expansion of the universe. Its exact nature is unknown. |
| 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. | Acts as a repulsive influence on cosmological scales, driving the accelerating expansion of space. |
| % of the universe | |
|
|
| Detection | Directly observed via emitted or reflected electromagnetic radiation. | Inferred from gravitational effects; galactic rotation curves and gravitational lensing. | Inferred from Type Ia supernova redshifts, the cosmic microwave background, and large-scale structure surveys. |
This pie chart illustrates the composition of the Universe. It shows that most of the Universe is not ordinary matter, but is largely composed of invisible components that significantly influence its structure and behaviour. This highlights the importance of understanding dark energy and dark matter in cosmology.
