Distances on Earth are usually measured in kilometres. However, in astronomy, this unit of measurement is too small since the distances are gigantic. Astronomers, therefore, use units of measurement that are better suited to the dimensions of the universe.
The astronomical unit (au) is the unit of measurement corresponding to the average distance between the Earth and the Sun, or approximately 150 million km (exactly 149 597 870.7 km).
Astronomers use the astronomical unit to measure distances within our solar system, for example, between different planets or between planets and the Sun. Since an astronomical unit corresponds to the average distance between the Earth and the Sun, we consider that:
|1\, \text {au} = \text {150 million km} = \text {150 000 000 km} = 150 \times 10^{6}\, \text{km}|
Thus, the Earth is |\text {1 au}| from the Sun whereas Neptune, for example, is approximately |\text {30 au}| from the Sun. Also, the distance between the planet Mars and the Sun is |\text {1.5 au}|, which means that the distance between Mars and the Sun is 1.5 times greater than the distance between the Earth and the Sun.
What is the distance between Jupiter and the Sun in astronomical units?
Jupiter is approximately at |778\,300\,000\ \text{km},| so by writing a proportion (and then doing a cross multiplication) it is possible to find this distance in astronomical units.||\dfrac{1\ \text{au}}{x}=\dfrac{150\,000\,000\ \text{km}}{778\,300\,000\ \text{km}}||So the calculation will be:||\begin{align}x&=\frac{778\,300\,000\ \text{km}\times 1\ \text{au}}{150\,000\,000\ \text{km}}\\[3pt] x&=5.2\ \text{au}\end{align}||
Mars revolves around the Sun at a distance of |\text{1.52 au}|. What is the value of the radius of this orbit expressed in kilometres?
We know that |\text{1 au} = 150\,000\,000\ \text{km}.|The calculation will be: ||1.52\ \text{au} \times \dfrac{150\,000\,000\ \text{km}}{1\ \text{au}} = 228\,000\,000\ \text{km}||The orbit of Mars, therefore, has a radius of |228\,000\,000\ \text{km}.|
Une erreur s'est glissée dans cette vidéo.
À 0 min 44 s, on devrait lire 150 000 000 km.
The light year (ly) is the unit of measurement corresponding to the distance that light travels in a vacuum in a year, i.e. 9460 billion kilometres or 63 240 au.
Beyond our solar system, the distances are so great that even the astronomical unit is too small to be capable of expressing them. Thus, another unit of measurement, based on the speed of light, exists. This is the light year. It is used to assess the distances between celestial bodies located outside our solar system, for example between stars or between galaxies. Since light travels at a speed of 300 000 km/s, the value of one light year is:
|1\ \text {ly} = \text {9 460 billion km} = \text {9 460 000 000 000 km} = 9.46 \times 10^{12}\, \text {km}|
|1\ \text {ly} = 63\,240\, \text {au}|
We can thus evaluate different distances in the universe. For example, our galaxy, the Milky Way, is almost 75 000 ly in diameter. The Andromeda Galaxy, which is the closest galaxy to us, is more than 2 500 000 ly from Earth. The closest star to the Sun, Proxima Centauri, is 4.22 ly from Earth. Thus, the light radiated by Proxima Centauri is estimated to travel for 4.22 years before reaching Earth.
Proxima Centauri is located at |4.22\ \text{ly}| from the Sun. What is this distance in astronomical units and in kilometres?
For the measurement in astronomical units, we calculate a proportion: ||\dfrac{1\ \text{ly}}{4.22\ \text{ly}}=\dfrac{63\,240\ \text{au}}{x}||And we solve: ||\begin{align}x&=\dfrac{4.22\ \text{ly}\times 63\ 240\ \text{au}}{1\ \text{ly}}\\[3pt] x&=266\,872.8\ \text{au}\end{align}||Since the distance between Proxima Centauri and the Sun in astronomical units is known, it is possible to redo another proportion to calculate the distance in kilometres. ||\begin{align} \dfrac{1\ \text{au}}{266\ 872.8\ \text{au}}&= \dfrac{150\ 000\ 000\ \text{km}}{x}\\\\ x&= \dfrac{266\,872.8\ \text{au}\times 150\,000\,000\ \text{km}}{1\ \text{au}}\\ x&=4 \times 10^{13}\ \text{km}\end{align}||
The Orion Nebula is located at |14\,200\,000\,000\,000\,000\ \text{km}| (or |1.42 \times 10^{16} \ \text{km}|) from Earth. How many light years from Earth is the Orion Nebula?
We know that |\text{1 ly} = \text{9 460 billion km}.|
The calculation will therefore be: ||1.42\times 10^{16}\ \text{km} \times \dfrac{1\ \text{ly}}{9.46 \times 10^{12}\ \text{km}} \approx 1501\ \text{ly}||The Orion Nebula is about |1501\ \text{ly}| from Earth.
There are other, even larger units of measurement for determining distances in the galaxy. Parsec (pc) is one of them. When the distances are even greater, it is possible to use kiloparsec (kpc) or even megaparsec (Mpc).||1\ \text{pc} = 206\,265\ \text{au}||