## Measuring Very Great Distances

In Chapter 17, "Of Giants and Dwarfs: Stepping Out into the Stars," we saw that the distance from us to the planets can be measured accurately by radar ranging, but that measuring the distance to farther objects, namely the nearer stars, requires measuring stellar parallax. But beyond about 100 parsecs parallax doesn't work well, because the apparent angular displacement becomes smaller than the angular resolution of our best telescopes.

Gas velocities and a model of the rotation of the Milky Way can be used to measure distances within our own Galaxy (out to about 30,000 light-years). Beyond this, and out to 10 to 20 million parsecs (30 to 60 million light-years), variable stars (the RR Lyrae and Cepheid variables discussed in Chapter 21) can be identified and observed in order to determine distance.

The trouble is, Cepheid variable stars farther than 15 million parsecs are difficult to resolve, and for most telescopes too faint to be detected. And many galaxies are well beyond 15 million parsecs away.

Two methods have been used to estimate inter-galactic distances greater than 15 million parsecs. One tool is called the Tully-Fisher relation, which uses an observed relationship between the rotational velocity of a spiral galaxy and its luminosity. By measuring how fast a galaxy rotates (astronomers use the 21 cm hydrogen line described earlier), we can calculate its luminosity with remarkable accuracy. Once we know the luminosity of a galaxy, we can measure its apparent brightness and easily calculate its distance out to several hundred million parsecs.

### Star Words

A standard candle is any object whose luminosity is well-known. Its measured brightness can then be used to determine how far away the object is. The brightest standard candles can be seen from the greatest distances.

### Star Words

A standard candle is any object whose luminosity is well-known. Its measured brightness can then be used to determine how far away the object is. The brightest standard candles can be seen from the greatest distances.

The other tool is more general and involves identifying various objects whose luminosity is known. Such objects are referred to as standard candles. If we truly know the brightness of a source, we can measure its apparent brightness and determine how distant it is. A 100-watt light bulb is an example of a standard candle. It will look fainter and fainter as it recedes from us, and in fact, we can determine how far it is by measuring its apparent brightness versus its known luminosity.

One very interesting standard candle is a Type I supernova. It is interesting because its peak luminosity is very regularâ€”and enormous (10 billion or 1010 solar luminosities!). We have discussed the Type II supernovae, the core collapse of a massive star. Type I supernovae occur when a white dwarf accretes enough material from its binary companion to exceed 1.4 solar masses. When this happens, the white dwarf begins to collapse, and the core ignites in a violent burst of fusion. The energies are sufficient to blow the star apart. These events are so luminous that we can see them billions of light-years away.

## Telescopes Mastery

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