IV. Translate at sight

The Realm of the Stars

Beyond the Solar System, tens of thousands and more miles from us, in our model, and hundreds of millions of millions of miles in the vastness of real space, lie the stars. Each of the stars that we see in our skies is a Sun, like ours. Most are smaller and fainter than our Sun, but almost all seen without optical aid are larger and brighter, and in some cases, much larger and brighter than the Sun. Polaris, for instance, appears as a very faint star to those who live in brightly-lit city skies (which is, of course, most of the people in the world). This is partly because it is relatively far away, compared to the closest stars, and partly because all stars are far away, in any normal conception of distance. The nearest star we know of, Proxima Centauri, is two hundred fifty thousand times further than the Sun, or in our scale model, fifty thousand miles. Other stars are scattered through the vastness of space at similar or larger distances from each other, so that each star's nearest neighbors are tens of thousands of miles away in our model, and hundreds of millions of millions of miles away, in space.

Because the stars are so far away, using AU's, or miles, or kilometers, is ridiculous. Instead, we invent new units. The first such unit was the Light Year (LY). Light goes 186,400 mi/sec, or 300,000 km/sec, or, since there are 31,000,000 sec/yr, about 6 trillion miles, or 10 trillion km, in one year. That makes it a good yard-stick for stars.

The nearest star, other than the Sun, is alpha Centauri, which is a little over 4 light years away. Polaris is about 1000 light years away. Rigel, in Orion, about 2000 light years away. Most of the stars in the night-time sky are a few tens or hundreds of light-years away, and a very few are just a few LY away, or thousands of LY away.

LIGHT YEARS are nice, because they are easy to understand. AND, because when you look out into space, you are looking back into time. We see the Sun as it was, 8 minutes and 20 seconds ago. We see Jupiter as it was, somewhere between 35 minutes and 50 minutes ago.

If you look at a star, you see it as it was, as many years ago, as its distance in LY. NORMALLY, this makes no difference. Stars don't change much, in times that are short compared to millions or billions of years. But occasionally, it can make a difference.

THIS IS PARTICULARLY TRUE, if we look at things that are VERY far away, such as GALAXIES. However, we also use a different unit, the PARSEC, to measure large distances, for reasons we'll discuss later in the book.

V. Retell the text.

Age of the Universe

There are at least 3 ways that the age of the Universe can be estimated.

• The age of the chemical elements.

• The age of the oldest star clusters.

• The age of the oldest white dwarf stars.

The age of the Universe can also be estimated from a cosmological model based on the Hubble constant and the densities of matter and dark energy. This model-based age is currently 13.7 +/- 0.2 billion years old. But this Web page will only deal with actual age measurements, not estimates from cosmological models. The actual age measurements are consistent with the model-based age which increases our confidence in the Big Bang model.

The Age of the Elements

The age of the chemical elements can be estimated using radioactive decay to determine how old a given mixture of atoms is. The most definite ages that can be determined this way are ages since the solidification of rock samples. When a rock solidifies, the chemical elements often get separated into different crystalline grains in the rock. For example, sodium and calcium are both common elements, but their chemical behaviours are quite different, so one usually finds sodium and calcium in different grains in a differentiated rock.

When applied to rocks on the surface of the Earth, the oldest rocks are about 3.8 billion years old. When applied to meteorites, the oldest are 4.56 billion years old. This very well determined age is the age of the Solar System.

When applied to a mixed together and evolving system like the gas in the Milky Way, no great precision is possible. One problem is that there is no chemical separation into grains of different crystals, so the absolute values of the isotope ratios have to be used instead of the slopes of a linear fit. This requires that we know precisely how much of each isotope was originally present, so an accurate model for element production is needed. One isotope pair that has been used is rhenium and osmium: in particular Re-187 which decays into Os-187 with a half-life of 40 billion years. It looks like 15% of the original Re-187 has decayed, which leads to an age of 8-11 billion years. But this is just the mean formation age of the stuff in the Solar System, and no rhenium or osmium has been made for the last 4.56 billion years. Thus to use this age to determine the age of the Universe, a model of when the elements were made is needed. If all the elements were made in a burst soon after the Big Bang, then the age of the Universe would be t_D = 8-11 billion years. But if the elements are made continuously at a constant rate, then the mean age of stuff in the Solar System is t₀ = 11.5-17.5 billion years.

Exercises: