Astronomical Distances

The Techniques and Units Used to Describe Distance

As everybody knows distances in astronomy are vast with many people struggling to understand the extremely large numbers involved and the methods Astronomers use to calculate distances. It must be said here that there is no single method able to be used to calculate the distance to the entire Astronomical phenomena that have been discovered.

Let us just contemplate the time it would take to travel the distance to some of our neighbours and far off relatives if we were to travel at a variety of speeds:

 Destination ETA Travelling at 201 kms/second Birmingham to London201 kms in 1 second ETA Travelling at 2994 kms/s 6,696,000 mph 0.998% speed of light ETA Travelling at 299460 kms/s 186,000 miles/s 99.8% speed of light Earth’s Moon 31.7 minutes 2.13 minutes 1.28 seconds Planet Mars 4.51 days 7.28 hours 4.36 minutes Planet Saturn 2.45 months 4.94 days 1.18 hours Closest Star Proxima Centauri 6400 years 430 years 4.3 years Center of the Milky Way 44.6 million years 3,000,000 years 30,000 years Closest Galaxy Andromeda 3.72 billion years 250 million years 2.5 million years Edge of the observable Universe 22,300 billion years 1500 billion years 15 billion years

So it can be seen that there is a vast range of measurements to be made over a range approximately 1: 16.43 x 10 15. This is mathematical shorthand for 16.43 followed by 15 zeros; a very, very large number. Consequently Astronomers have developed a series of techniques and units to measure distances to far off objects. The most easy to understand is the “light year”, namely the distance light travels in one earth year and this is the unit most commonly used in popular Astronomical publications.

1 light year = 9.5 million million kilometres, or 6.0 million million miles

Within the solar system it is common to talk of distance measured in Astronomical Units defined as the distance between the Earth and the Sun.

1 AU = 150 x 10 9 metres, equivalent to 93 x 10 6 miles, i.e. 93 million miles.

Another local measure is the Lunar Unit, i.e. the distance from the Earth to the Moon. This is particularly useful in expressing the threat to the Earth of sizeable known “Near Earth Objects” describing their closest approach as multiples of LUs (hopefully!).

1 Lunar Unit =404x 10 3 km, equivalent to 250 x 10 3 miles, i.e. 250,000 miles

For relatively close objects, like stars in our local galaxy, the Milky Way; a method is usedwhich applies basic trigonometry to the Solar System. It uses as a baseline the observation of a star’s apparent position and measures the angle to the star from either side of a line running through the Sun to the Earth’s position diametrically opposite. This is known as the parallax method and gives rise to the unit of the “Parsec” from parallax arc second. In formal Astronomical papers it is normal to express distances in Parsecs, Mega Parsecs, Giga Parsecs, etc. The further away the star is the smaller the apparent movement is and thus other methods had to be developed.

1 Parsec = 3.26 Light Years, equivalent to 31 million, million kilometres,
or 30.857 x 10 12 Km or 19 million, million, miles;

and therefore using the conversion above:

1 AU = 4.85 x 10 -6 Parsecs

The cosmic distance ladder is the name given to a succession of techniques which allow progressively larger distances to be measured using a variety of sophisticated techniques not usually available to the amateur. Several of these methods have evolved from simple concepts used in light and time measurement for the last 400 hundred years. The idea of a Standard Candle which had a measurable luminosity and burnt for a consistent time has been around for a long time. Astronomers were able to use this idea to look for objects which had a known brightness and could be fitted on the Main sequence of star life. They then compared the luminosity of the object with its observed brightness, applied the inverse square law and computed its distance. Gradually a series of Standard Candles was developed, and is still being refined as measuring technology improves. These techniques have allowed astronomers to make measurements to the edge of the observable universe of 13.7 billion light years.

Whilst the ladder approach sounds rigorous it has two basic problems, a) Calibration; how standard is the Standard Candle and what is its absolute magnitude? and b) recognising other members of the class and applying the wrong calibration to them.

It has to be recognised that the further away an object is the greater the degree of error in its measurement, because of the combination of uncertainties. It is common in earth bound measurements that in any measuring procedure small instrumental errors or lack of sensitivity occurs and measurements are described as X units +or- 2% say. So too with astronomical measurements; typically in cosmological measurements all stated distances carry an accuracy or uncertainty factor e.g. the distance to the Virgo cluster expressed in Mega Parsecs using the Type 1a Supernovae method is 19.4 +/- 5.0! That is quite a health warning which should lead us to question the assumptions and accuracy of all distance measuring methods whilst still accepting that all methods and technologies will improve over time.