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Unformatted text preview: AST 204 February 4 2008 LECTURE I: THE EXPANDING UNIVERSE, THE CRITICAL DENSITY, AND THE AGE OF THE UNIVERSE I. The Observations, Simplified We live in an expanding universe, a fact which we have known for about seventy years. What does this mean? We live in a galaxy which is much like billions of others, whose physics we understand fairly well. The earth is in orbit about the sun, an ordinary star much like billions of others in this galaxy. Though we have been observing for far too short a time to have followed the sun very far in its orbit about the center of the galaxy, we know that its velocity about the center is roughly what one would expect from what we understand about the mass of the galaxy and simple Newtonian dynamics. We know with some confidence that the galaxy is not expanding. Neither is the solar system, or the sun, or the earth. But the universe is . And what that means is that the other galaxies we observe are receding from our own, in a remarkably uniform pattern. We infer that they are receding from their redshift , which is normally (and indeed, very persuasively, as we shall see later) interpreted as an ordinary Doppler shift. The observed phenomenon is that features in the spectra of galaxies which belong to well-known atomic transitions in common chemical elements and molecules are observed to be at longer wavelengths than they are observed in those species in a laboratory. All features in the spectrum of a given galaxy are longer in wavelength by a constant factor, as one would expect from a Doppler shift, obs / lab 1 + z 1 + v/c. (1) The Doppler formula, obs / lab 1 + v/c is easily derived from a consideration of the spacing of spherical wavefronts emanating from a moving source. The remarkable pattern in the recession velocities of galaxies is embodied in the Hubble Law , which is named after its discoverer, Edwin Hubble (though there is some controversy, as there often is in science, over who actually has priority), which relates the recession velocity very simply to the distance of a galaxy: v = Hd (2) Here d is the distance and H a number called the Hubble constant . The best determinations of H at the present time (the uncertainties are all in the distances, which are poorly determined at best) yield a number of about 22 km/sec velocity per million light years distance, or in units which are in more common use, about 72 km/sec per megaparsec. (a parsec is 3 . 08 10 18 cm, about 3.26 light years, and is the unit of distance most commonly used in astronomy.) It is of some interest that quoting these numbers to this accuracy was not possible until 2003, with the announcements of the results from the 1 WMAP satellite, which we will discuss later. Since observing the spectra of galaxies and interpreting the redshift as a velocity gives us information about only the component of velocity along the line of sight to the object in question, we know nothing about the components perpendicular to the line of sight, but there is other information from the very...
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- Spring '08