We are now ready to make another step outwards in our exploration of the Universe: we change from looking at stars to looking at galaxies. As we saw in Chapter 9, galaxies are vast collections of stars. Our own Galaxy, the familiar Milky Way, contains about 1011 stars. Figure 14.1 on the following page shows photographs of two typical galaxies. Galaxies are held together by the mutual gravitational attraction of all the stars. It is remarkable indeed that Newton's force of gravity, which he devised in order to explain what held the planets in their orbits, turns out to explain just as well what holds the whole Milky Way together.

Galaxies are more than just collections of stars. The collective gravity of all the stars makes the centers of galaxies very unusual places. Stars and gas crowd together so densely that in some cases they can form immense black holes, with masses of millions or even billions of stars.

We have now pushed our model of the history of our Universe back just about as far as we could hope to go: the Universe had a beginning, and that beginning was the source of all that happened afterwards – all matter, all stars, all galaxies, even life itself. Big Bang cosmology has placed modern physics in the remarkable position of being able in principle to trace back to the beginning every aspect of the world we live in, to say “This is where X came from, and this is how Y started”.

1. ▷ The background image on this page is a plot of the spatial distribution of galaxies in a thin wedge of space centered on our position, from the CfA Redshift Survey. Measured in 1985, this distribution gave astronomers their first indication that galaxies were grouped into chains as well as clumps. The human-like pattern (horizontal in this view, with the legs to the left) became a celebrity in its own right. Data from M Geller and J Huchra, image copyright South African Observatory (sao).

The tides wash the margins of all the great oceans, regulate the lives of sea urchins and fishermen, power the great bore waves on rivers like the St. John, the Amazon, and the Severn. For most of us the tides are romantic, primeval, poetic. Standing on an ocean beach, we might be impressed by this tangible manifestation of the gravity of the distant rock we call the Moon, but few of us would be led to reflect on how fundamental the tides are to an understanding of gravity itself. But fundamental is the right word. In the modern view, the real signature of gravity, the part of gravity that can't be removed by going into free fall, is the tidal force, whose most spectacular effect on Earth is to raise the ocean tides. In this chapter we will examine this aspect of gravity, starting with the simplest effects first and working our way up to ocean tides and then to tides elsewhere in the Solar System and beyond. We will return again and again in later chapters to the fundamental role of tides. Indeed, many astronomical systems transmit tidal forces as signals right across the Universe, signals that we call gravitational waves.

When Einstein began to develop his theory of gravity, he knew he had to build on special relativity, but he felt strongly that he also had to preserve Galileo's other great contribution to physics, the principle of equivalence (Chapter 1). As with special relativity, Einstein worked by blending the old and the new in equal proportions: special relativity combined the old principle of relativity with the new principle of the universality of the speed of light; in his new theory of gravity Einstein combined the old principle of equivalence with his new theory of special relativity.

1. ▷ Underneath the text on this page is the familiar Mercator projection map of the entire Earth. This map illustrates strikingly the fact that the surface of the Earth cannot be represented faithfully on flat paper.

Observational astronomy is based on the detection of radiation emitted by astrophysical objects. All morphological and physical information about astrophysical sources is derived from observation and analysis of the emitted radiation. Continuum radiation is a natural consequence of the principle that accelerating charges radiate. In this part of the book I will review and apply principles of electromagnetism to further our understanding of important astrophysical phenomena, demonstrating in the process that important radiation processes can be derived from the basic principle that accelerating charges radiate. To that end, I will develop the theory that describes bremsstrahlung and synchrotron radiation. A theoretical understanding of these two radiation mechanisms allows us to interpret the emission of a wide range of objects, ranging from distant radio galaxies to nearby HII regions. The specific astrophysical topics covered in this part of the book include: the radiative properties of pulsars, dispersion and Faraday rotation of electromagnetic radiation, active binary star systems, accretion disks, supernova remnants, particle acceleration, cosmic rays and active galaxies.

Many people assume that satellites orbit the Earth far above its surface, but the numbers tell a different story. Most satellites orbit at less than 300km above the ground. Compared with the radius of the Earth, 6400km, this is very small. Their orbits just skim the top of the atmosphere. We can expect, therefore, that the acceleration of gravity on such a satellite will not be very different from what it is near the ground. How then can it happen that the satellite doesn't fall to the ground like our cannonballs in the first chapter?

1. ▷ Communications and many weather satellites, which must be in “geostationary” orbits, are an important exception, being in distant orbits. We will return to these orbits in Chapter 4.

The answer is that it tries to, but the ground falls away as well. Imagine firing a cannon over a cliff. Eventually the ball will fall back to the height from which it was fired, but the ground is no longer there. The Earth has been cut away at the cliff, so the ball must fall further in order to reach the ground.

1. ▷ The picture behind the words on this page is the Hubble Space Telescope (HST), a satellite launched by the National Aeronautics and Space Administration (NASA), with participation from the European Space Agency (ESA) as well. […]

Binary stars are stars bound in orbit about one another by their gravitational attraction. Most stars seem to form in binary systems or in systems containing more than two stars. This is not really surprising: stars form from condensations in giant clouds of gas, so where one star forms, others are likely, and they may form close enough to each other to be bound together forever. We saw this in the numerical simulation reproduced in Figure 12.2 on page 138.

We have already studied special cases of binaries: planets in motion around the Sun, and the Moon around the Earth. These orbits allow us to measure masses in the Solar System. We learn the Sun's mass once we know the radius and period of the Earth's orbit. Similarly, we measure the mass of the Earth by studying the motion of the Moon (and of artificial Earth satellites). In the same way, binary star orbits are used to measure the stars' masses. Binaries are often our best, indeed our only, way of measuring the masses of stars.

Born in the same year, 1642, as Galileo died, Isaac Newton revolutionized the study of what we now call physics. Part of his importance comes from the wide range of subjects in which he made fundamental advances – mechanics (the study of motion), optics, astronomy, mathematics (he invented calculus), … – and part from his ability to put physical laws into mathematical form and, if necessary, to invent the mathematics he required. Although other brilliant thinkers made key contributions in his day – most notably the German scientist Gottfried Leibniz (1646–1716), who independently invented calculus – no physicist living between Galileo and Einstein rivals Newton's impact on the study of the natural world.

Nevertheless, it is hard to imagine that Newton could have made such progress in the study of motion and gravity if he had not had Galileo before him. Newton proposed three fundamental laws of motion. The first two are developed from ideas of Galileo that we have already looked at: