How do we measure the distances in space

Measuring distances in space is not easy. Traditional methods can only give us the distances of our nearest neighbours. Other systems had to be devised to calculate distances in deep space. When we came to talk about the distance of the Moon we found that the way astronomers used to do this was to observe the Moon simultaneously from two different places on Earth.

It is this principle that surveyors have used for centuries to measure the distance of places they could not reach - across the other side of a river, for instance. From two given positions they measure the angle between the distant object and the even more distant background. Knowing - or measuring·- the actual distance between the two places, and subtracting the two angles they have measured, it is possible to determine the distance by simple trigonometry. In the case of a moving object like the Moon, observations from both observatories must be made at the same time (or a special calculation done to allow for any time difference there is). But can we apply the lunar distance method to the stars? We can apply the principle, but not precisely the same method because the stars are so far away that places on the Earth's surface are too close together to give us an angle which is large enough to be measured.

The solution is to make observations from only one observatory, and then to wait for the Earth to carry the observatory to the other side of its orbit, before making the observation again. This gives a separation between observing positions - a base-line - of twice the Earth-to-Sun distance, or 299 million kilometres. Even so, this very long base-line still only gives very small angles. The angle, which gives the shift of the star measured against the background of more distant stars, is only something like 1% arc seconds, and as one arc second is 1/60th of one arc minute which is itself 1160th of a degree, this angle is miniscule. Half this angle is used in calculating distance and is known as the star's parallax. So what astronomers measure in order to find the distances of the nearer stars is an angle. Thus they find that the nearest star, C1 Centauri, has a parallax of 0.76 arc seconds; converting this to a distance tells us that it is 4.3 light-years away. But to compare distances astronomers do not need to convert to light-years; they can save themselves time by merely comparing angles. Indeed, for distances astronomers usually use the terms parsec and megaparsec.

One parsec is that distance at which a star would have a parallax of one second of an arc. No star is as near as this, but that does not matter because all we are after is a comparison of angles. Because the distance in parsecs is equal to one divided by the parallax, a star of parallax 0.5 would lie at 110.5, or two parsecs. A megaparsec is one million parsecs. How useful this scheme is immediately becomes obvious. For example, C1 Centauri has a parallax of 0.76 arc seconds, so its distance is 1.3 parsecs, while the star Lalande 21185 has a parallax of 0.377 arc seconds and thus a distance of 2.6 parsecs. The direct angle measuring method for determining stellar distances, using the Earth's orbit as base-line, is known as 'trigonometrical parallax', but it is only of use for nearer stars.

Beyond 100 parsecs (some 300 light-years) the angles become too small to measure with sufficient accuracy. This method will therefore only give the distances of some 8,000 stars. What is to be done, then, for. more distant stars? One way out of this difficulty is to determine what have become known as 'cluster parallaxes'. Here, astronomers make use of the fact that some clusters of stars - the Pleiades or the Hyades, for example - are moving relative to the Sun. All the stars of such a cluster are moving with the same speed and appear to us on Earth as if they are converging on a particular point in space, just as cars on a motorway appear to converge into the distance. Now the technique of distance measurement here is to find how the cluster shifts across the background of more distant stars and compare this with the true space velocity of the stars. (The true velocity is found by measuring the movement directly away from us of the stars and knowing the position of the converging point of the cluster.) This method is, of course, limited to clusters and is only accurate up to distances of something like 800 parsecs (2,600 light-years).

Some other method is required for the majority of other stars. The alternative to ordinary parallax measurements and to cluster parallax depends on finding how truly bright particular stars are. Observation immediately tells us how bright a star appears to be but, of course, not its true brightness. The further off it is, the dimmer it will seem to be. For instance, the bright star Sirius appears over 13 thousand million (13 x 109) times dimmer than our Sun, but this is only because it is 2.6 parsecs away; its true brightness is 221/2 times greater than the Sun's. We know how brightness drops off with distance, so if we know the true brightness of a star as well as its apparent brightness, we could calculate the star's distance.

But how can we tell the true brightness of a star without knowing its distance? The answer to this was found by examining a diagram devised in 1914 by two astronomers, the Swede Ejnar Hertzsprung and the American Henry Norris Russell. This Hertzsprung-Russell or 'HR' diagram shows the relationship of true brightness compared with spectral class. Spectral class refers to the kind of spectrum a star shows when its light is spread out into a coloured band or spectrum. The class is determined by the dark lines which lie across the colours of the spectrum, their number and positions giving a clue to the star's temperature, and thus its colour. The true brightness is given on the diagram in 'absolute magnitudes'.

This is a measure of the magnitude (i.e. the brightness) a star would have if it were only ten parsecs away. What the HR diagram shows is that the hotter (and bluer) most stars are, the brighter they really are; the cooler and redder they happen to be, the dimmer they are. There are some exceptions - the red supergiants are one - but the 'main sequence' of stars follow the general rule. So we now have a new way to determine distance. Observing a star's spectrum gives us its spectral class and the HR diagram then gives its absolute magnitude. Direct observation provides us with the apparent magnitude - the brightness we see. By comparing the two - apparent magnitude and absolute magnitude - and knowing how brightness drops with distance, we can easily calculate the star's distance. This method of measuring distance is known as 'spectroscopic parallax'.