Measuring distances in astronomy is difficult: we cannot simply take a metre stick and pace out the distance to a star or galaxy. Instead we have to find indirect ways of estimating the distance, from other quantities which can be measured directly. A powerful method for estimating distances is the idea of a standard candle - i.e. a particular type of star whose intrinsic brightness is known, rather like knowing the wattage of a household light bulb. By comparing the intrinsic brightness (or luminosity) with how bright the star appears to be, one can estimate its distance. Two examples of standard candles commonly used by cosmologists to measure distances are Cepheids and Supernovae; together with measurements of galaxy redshifts, these distance estimates tell us a great deal about the distribution and motions of galaxies - and the dynamics of the Universe itself.
 
 

Cepheids

Cepheids are variable stars which pulsate regularly, changing their size and intrinsic brightness over a period ranging from a few days to a few weeks. In the early 1900s Henrietta Leavitt studied Cepheids in the Large Magellanic Cloud (the small satellite galaxy of the Milky Way) and found a relationship between their period and the luminosity. This meant that, simply by measuring the period of a more distant Cepheid, astronomers could immediately determine its luminosity - and hence its distance. Now, almost a century later, Cepheids remain the backbone of the cosmological distance scale. The Hubble Space Telescope can observe Cepheids in galaxies many tens of millions of light years away, such as the giant Spiral galaxy M100 in the Virgo Cluster. (The images below show some Cepheids in M100). During the past decade the HST Distance Scale Key Project has used Cepheids to map out our "Local Neighbourhood" of the Universe.

Supernovae

Even with the Hubble Space Telescope, it is only possible to observe Cepheids out to a distance of about 100 million light years. Beyond this point cosmologists need to find alternative methods to estimate galaxy distances. One such method is another standard candle: a supernova. Supernovae are massive stars which, as they reach the end of their lives, undergo a cataclysmic explosion, making them almost as bright as entire galaxy. Cosmologists can now observe supernovae in galaxies at distances of billions of light years; we are seeing these exploding stars at a time when the Universe was less than half its present age. Measuring galaxy distances with supernovae has helped us to understand the past evolution - and even the future fate - of the Universe (see below).
 
 
 
 

Hubble's Law and the Redshift

In the 1920s the American cosmologist Edwin Hubble (pictured here second from the left) measured the distances and velocities of many nearby galaxies using the 100 inch Hooker reflector on Mount Wilson, and realised that galaxies generally appeared to be moving away from us. Their recession velocity caused a shift in the spectrum of light towards redder colours - analogous to the Doppler shift in the pitch of an ambulance siren as it passes by - and is known as the redshift. Cosmologists proposed that the redshift of galaxies was due not to their motions through space, but rather to the expansion of space itself - a dramatic conclusion, but one which is nonetheless in agreement with the predictions of the 'Big Bang' theory for the origin of the Universe, and Einstein's (pictured third from right, above) general theory of relativity.
 

Hubble's law states that the recession velocity (or equivalently the redshift) of a galaxy is proportional to its distance, and the constant of proportionality - known today as the Hubble constant - measures the present expansion rate of the  Universe. Today, more than seventy years after Hubble's original work, cosmologists still debate the precise value of the Hubble constant - although the launch of the Hubble Space Telescope, and the work of the HST Distance Scale Key Project, has led to a wide degree of consensus. The Hubble constant can also now be measured from data on even larger scales, by studying the microwave background and gravitational lenses, yielding results consistent with traditional "standard candle" methods.
 
 
 

The Runaway Universe

Recently, cosmologists have switched focus from measuring the present expansion rate of the Universe to determining the expansion rate in the very distant past. These observations can tell us whether the Universe is speeding up or slowing down - a question closely related to the curvature of space - and so predict whether or not the expansion of the Universe will continue forever. We can determine the expansion rate when the Universe was around half its present age by measuring the distances of supernovae observed at high redshift, and comparing their estimated distance with the predicted distance in model Universes with different curvature. Two research groups (the Supernova Cosmology Project and SN High-z Team) have both reached the startling conclusion that the Universe is accelerating, so that the expansion will indeed continue forever. The energy driving the acceleration appears to come from fluctuations in the vacuum of space itself - which somewhat resurrects the idea of a "cosmological constant" proposed, but later rejected, by Einstein himself. Studies of the microwave background confirm the existence of this vacuum energy, and suggest that the Universe has zero curvature - which means its geometry is essentially the same as a flat piece of paper. Now cosmologists are working hard to understand more clearly what is the precise nature of the vacuum energy driving the acceleration of the Universe.