Astronomical distances are expressed using three specialist units:

  1. Astronomical unit: average distance between the Earth and the Sun
  2. Light-year: distance travelled by light in a vacuum in a time of one year
  3. Parsec: the distance from which a base length (radius) of 1 AU subtends an angle of one arc second

 1 pc = 1/tan(1″) au

  for small , so 1 pc = 3600 AU

Stellar parallax is a technique used to measure the distance to stars that are within 100pc of the Earth. The position of a close star shifts relative to a backdrop of more distant stars as the Earth moves between opposite sides of its orbit around the Sun. Precise measurements can be used to determine the parallax angle. This can be used to measure the distance of the star from the Earth.


The Cosmological principle states three characteristics of the Universe:

It’s homogeneous: matter is uniformly distributed across the Universe, so the same type of structure (galaxies) is seen everywhere

It’s isotropic: the Universe looks the same in all directions to every observer. The Universe has no centre or edge. The laws of physics are universal: they can be applied across the Universe 

The Doppler effect can be used to determine the speed of moving objects. When a wave source moves relative to an observer, the frequency and wavelength of the waves received by the observer change compared to what would be observed without relative motion. 

frac{Delta }{lambda }approx frac{Delta f}{f}approx frac{v}{c}

The Doppler effect can be used to determine the relative velocity of a distant galaxy. 

  1. Measure the absorption spectrum of a specific element in the laboratory
  2. Measure the spectrum in light from a distant galaxy
  3. Measure any difference in observed wavelengths of the absorption lines due to relative motion
  4. Use the equation above to determine its velocity

Light can be blue-shifted or red-shifted depending on the direction of relative motion. 

Hubble’s law states that the recessional speed of a galaxy is (almost) directly proportional to its distance from the Earth.

vapprox Hod

0 is Hubble’s constant. Its SI unit is s−1, but kms−1Mpc−1, which has a more convenient magnitude, is also frequently used. 

The Big Bang Theory attempts to describe the origin and development of the early Universe. It suggests that at some moment in the past all the matter in the Universe was contained in a single point, or singularity. This was the beginning of space and time. The infinitely hot, dense point expanded outwards to become the dynamic Universe we see today (the expansion of space-time). The Big Bang Theory has two key pieces of evidence:

  1. Hubble’s Law shows that the Universe is expanding: galaxies are receding because space is expanding in all directions. So at some point in the past the Universe must have been much smaller, denser and hotter. And at some point it must have occupied a single point.
  2. Microwave background radiation: when the Universe was young and extremely hot, space was saturated with high energy gamma photons. The expansion of the Universe caused stretching of space, and therefore cosmological redshift. So this primordial electromagnetic radiation is now perceived as microwaves with a temperature of 2.7K (if the Universe is treated as a black body). The CMB is isotropic.

If we assume that the Universe has expanded at a constant rate since the Big Bang, we can estimate the age of the Universe.

tapprox frac{1}{H_{o}}

The evolution of the Universe: 

Big Bang Time and space are created. Universe is a singularity.
10−35 s The Universe expands rapidly (inflation). The Universe is full of EM radiation in the form of high-energy gamma photons. K


10−6 s First fundamental particles (quarks, leptons) gain mass through a mechanism not fully understood, involving the Higgs Boson
10−3 s Quarks combine to form hadrons (e.g. protons and neutrons). Pair production produces most of the Universe’s mass.
1 s        Creation of matter stops. K
100 s   Protons and neutrons fuse to deuterium and helium nuclei, as well as a small quantity of lithium and beryllium. Rapid expansion means that no heavier elements are created. 25% of the Universe’s matter is helium (primordial helium)

380,000 years   The Universe cools enough for the first atoms to form. The nuclei capture electrons. Universe becomes transparent and EM radiation present will later be detected as the CMB 30 million years     First stars appear. Fusion produces heavier elements.

200 million        Galaxies form as gravitational forces pull clouds of hydrogen and stars together years

9 billion years     Solar system forms from the nebula left by a supernova. After the Sun forms, the remaining material forms the Earth and other planets (about 1bn years later). Life begins on Earth 11bn years after BB.

13.7 billion years  200,000 years ago modern humans evolved. = 2.7. (now)

Current ideas:

  1. The expansion of the Universe is accelerating. This implies that some “dark energy” is present – a mysterious expansionist force that makes up most of the Universe’s mass-energy.
  2. Some extra mass must be present in galaxies and galaxy clusters to explain the physical phenomena we observe – “dark matter”. It neither absorbs nor emit light and only interacts via gravity and the weak nuclear force.

Only a small percentage of matter is “ordinary”, i.e. part of the standard model.