Radio astronomers have learned to overcome the limitations of diffraction with interferometry, the use of two or more telescopes viewing the same source at the same time. The instantaneous beam of two telescopes is an interference fringe pattern on the sky. As the earth rotates, the pattern sweeps across a postulated point source yielding a time varying interference signal when the signals from the two telescopes are summed or multiplied. Simple examples show that two telescopes on the rotating earth can, in most cases, locate the position of a point source. Each brief two-telescope observation with a given baseline (telescope separation and relative orientation) can be described as a point on a two-dimensional plot (Fourier plane) of the x and yspatial frequencies. For each such point, the detected oscillatory signal yields a value of the complex visibility function V(b) which is one spatial Fourier component of the sky brightness distribution. Large arrays of telescopes making repeated observations as the earth rotates provide additional points in the Fourier plane and thus additional Fourier components. With sufficient coverage of the Fourier plane, the Fourier transform of V(b) yields a reasonable approximation of the true sky brightness function. This process is called aperture synthesis.

Interferometry dominates radio astronomy, e.g., the US VLA and the Australian AT arrays. The greatest antenna spacings yield the highest angular resolution. […]

Celestial measurements reaching back 3000 years or more were carried out in many cultures worldwide. Early astronomers in Greece deduced important conclusions about the nature of the earth and the solar system. Modern astronomy began in the renaissance with the observations of Tycho Brahe and Galileo and the theoretical work of Kepler and Newton. The progress of our knowledge of the sky may be traced through a series of major discoveries which often follow the development of new technologies such as the telescope, computers, and space observatories. Astronomy is now carried out across the entire electromagnetic spectrum from the radio to the gamma ray (see cover illustrations) as well as with cosmic rays, neutrinos, and gravitational waves. The mutual dependence of theory and observation has led to major advances in the understanding of a wide diversity of celestial objects such as stars, supernova remnants, galaxies, and the universe itself. Current observations reveal important phenomena that are not understood. The promise of new fundamental discoveries remains high.

The detectors at the foci of telescopes may be position-insensitive such as the classic photomultiplier and the simple proportional counter. Position-sensitive detectors at the focus of a telescope provide an overall field of view that includes many beams (resolution elements). The charge-coupled device is widely used in optical and x-ray astronomy for this purpose. Its internal structure and operation reveal its strengths and weaknesses. Gamma-ray astronomers use plastic and crystal scintillators and spark chambers or their equivalent. Examples are the EGRET and BATSE instruments that were in orbit during the 1990s. The precision of a detected signal is limited by statistical and systematic errors. Knowledge of basic statistical theory enables one to assess the significance and meaning of one's data. Aspects of this are the character of statistical fluctuations (the Poisson and normal distributions), background subtraction with error propagation, and comparison of data to a model with a least squares fit and the chi square test.

The distribution with frequency of radiation from a source is called a spectrum. It can be plotted as an energy spectrum or as a number spectrum and as a function of either frequency or wavelength. Conversions from one to another are possible and useful. Continuum spectra are without spectral lines though spectral lines may be superposed upon them. They can arise from interactions of atoms and free electrons, for example in the solar atmosphere. Three kinds of such spectra encountered in astronomy are thermal bremsstrahlung from an optically thin gas, blackbody radiation from an optically thick gas in thermal equilibrium, and synchrotron radiation from a gas of extremely energetic electrons in the presence of magnetic fields. Antenna temperatures used by radio astronomers are a measure of specific intensity. The total power radiated by unit area of a blackbody, σT4, allows one to relate approximately the radius of a star to its luminosity and temperature.

Spectral lines arise from atomic transitions in emitting or absorbing gases. They provide powerful diagnostics of the regions that form the lines. Stars exhibit mostly absorption lines while gaseous nebulae exhibit emission lines. Some of the latter are forbidden lines which occur only at the extremely low gas densities found in space. The shapes of spectral lines reveal the presence of turbulent motions and the effects of collisions, the latter providing the local density. […]

Astronomers learn about the cosmos through the study of signals arriving at the earth in the form of electromagnetic radiation or as neutrinos, cosmic rays, meteorites, and, hopefully in the near future, gravitational waves. Electromagnetic radiation travels at speed c and can behave either as a wave or as a flux of photons each of energy E=hν. One can convert between wavelength, frequency and photon energy through algebraic or numerical relations. The bands of electromagnetic radiation extend from radio waves at the lowest frequencies to gamma rays at the highest. The average photon energy, or frequency, of radiation from an object is an indicator of the temperature of the emitting source if the radiation is thermal. Absorption of photons in the earth's atmosphere is frequency dependent so observations of some bands must be carried out from high altitude balloons or space vehicles. Similarly, absorption in the interstellar medium by dust and atoms renders the cosmos more or less transparent, depending upon the frequency band (see also Chapter 10).

Our knowledge of celestial objects must take into account absorption and scattering of photons as they travel to earth observers. These processes are highly frequency dependent and thus affect some bands more than others. Photon–electron interactions include Rayleigh, Thomson and Compton scattering which explain, respectively, the blue sky, light from the solar corona, and a distorted spectrum of 3-K background radiation in the direction of x-ray emitting clusters of galaxies (Sunyaev–Zeldovich effect). Photons of very high energy, ≳ 1015 eV, are absorbed through pair production interactions with photons of the cosmic microwave background. Photons with energies from 13.6 eV (ultraviolet) through ∼2 keV (“soft” x ray) are absorbed by atoms in interstellar space through the photoelectric effect. Optical light from stars in the plane of the Galaxy is absorbed (extinction), reddened (color excess), and polarized by interstellar grains (dust). The polarized starlight maps out interstellar magnetic fields. A useful correlation exists between the locations of dust and hydrogen in the Galaxy.

The beam intensity that survives passage through a uniform absorbing medium decreases exponentially with distance traveled. The rate of decrease depends upon the cross section (m2 per absorbing atom) or opacity (m2 per kg) of the absorbing medium. Photoelectric absorption in the interstellar medium (ISM) depends strongly on the composition of the interstellar gases (cosmic abundances) and is a strong function of photon energy. […]

Stars are located on the sky with two angular coordinates. Distances to them may be ignored by visualizing all of them as being on a celestial sphere at “infinite” distance. The angular coordinates define the star's location on the sphere. Any number of coordinate systems can be defined on this sphere. Astronomers use the equatorial, galactic, ecliptic, and horizon systems. The coordinates of a star differ from coordinate system to coordinate system so transformations between them are needed. In the equatorial system, the coordinates of a given star vary steadily and slowly due to precession of the earth, so one must define the epoch, e.g., J2000.0, of any quoted coordinates. “Areas” on the sky are defined as solid angles. Cataloging of stars is accomplished through photographic surveys, printed sky charts, and printed lists (“catalogs”). Unnamed stars can be specified unambiguously by marking the star on a finding chart, a sky photograph of the local region. The name of a star or galaxy may depend on its location and brightness within a constellation, its equatorial coordinates (“telephone number”), or simply its sequential number in a published catalog of objects together with the catalog name, e.g., Messier 42 is the Orion nebula.

The information content in the radiation recorded in observations allows astronomers to derive the properties of celestial objects. The ranges of the values of these properties are found to be “astronomically” large. Luminosities are derived from measured fluxes and distances. The solar luminosity, 3.8 × 1026 W, is a benchmark reference; that of a bright quasar is 1013 times larger. The mass of the moon, earth, or of a galaxy can be determined by tracking the motion of one or more orbiting objects. The sun's mass, 1.99 × 1030 kg, is also a standard reference; the (Milky Way) Galaxy is > 1011 times more massive. The virial theorem is used to obtain the masses of clusters of galaxies. Temperatures can be defined for thermal sources, wherein the matter and radiation are in, or approximately in, thermal equilibrium. The temperatures of a hot gas may be determined in a variety of ways that may yield different values. Thus astronomers refer to kinetic, color, effective, excitation, and ionization temperatures. The last is obtained from spectral observations with the aid of the Saha equation.

The distance to a celestial object is not an intrinsic property but it is required to find intrinsic quantities. Ancient astronomers used geometry to learn the earth size and distance to the moon. The mean earth–sun distance is defined as the astronomical unit (AU). 1.00 AU =1.496 × 1011 m. […]

Major new facilities that detect signals from the cosmos other than electromagnetic radiation are bringing new fields into the forefront of astronomy. Neutrino observatories study the energy-producing thermonuclear reactions at the center of the sun with detectors utilizing chlorine, gallium, and pure water, the latter making use of Cerenkov radiation from recoil electrons. The pioneering Homestake mine experiment and the huge Super-Kamiokande experiment are important examples. Neutrino astronomers detected a flash of neutrinos from the collapse of a star in the supernova SN 1987A and hope to see extragalactic flashes from gamma-ray bursts.

Cosmic ray observatories study highly energetic charged particles (mostly protons) entering the atmosphere from the Galaxy and probably extragalactic sources. The element abundances at energies ≳1 GeV provide a lifetime (∼107 yr) for their storage in the Galaxy. The highest energy particles initiate extensive air showers (EAS) of particles in the earth's atmosphere, facilitating their study with detector arrays covering 103 km2, such as the HiRes Fly's Eye and the Auger project. The most energetic such particles, ∼10 to 300 EeV (1019 to 3 × 1020 eV) are probably extragalactic in origin and may arrive from the approximate directions of their origin. Small EAS initiated by TeV gamma rays high in the atmosphere produce Cerenkov radiation observed with ground based mirror-PMT systems, i.e., TeV photon astronomy.

Gravitational waves (G waves) are predicted by Einstein's general theory of relativity and searches for them have so far not reached the needed sensitivities. […]

Gravity is the underlying reason for the spin of the earth, the motions of stars within galaxies, and the evolution of stars and the universe. The apparent motions of stars in the equatorial coordinate system arise from precession and nutation of the coordinate system, from parallax and stellar aberration due to the orbital motion of the earth about the sun, and from proper motion, the projection onto the celestial sphere of the peculiar motion of a star relative to the local standard of rest. Precession and nutation of the earth arise from gravitational torques on its equatorial bulge applied by the sun, moon and planets.

The calendar is tied to the seasons such that the first day of spring occurs when the sun moving north crosses the (precessing) vernal equinox. The non-integral number of days in the tropical year (equinox to equinox) was accommodated with the addition of a leap day every 4 yr in Caesar's Julian calendar (46 BCE). The Gregorian calendar (1542) of Pope Gregory XIII removes some of these leap years to obtain a more precise agreement.

Eclipses of the sun and moon are a consequence of the motions of the earth and moon in their respective orbits about the sun and earth. The 18-yr saros cycles of lunar eclipses allowed the ancients and early astronomers to predict when they would occur. Total solar eclipses are wonderful to behold. […]

In this chapter: mastering interplanetary navigation has opened up the planets to exploration in the last 50 years. The discoveries have been astonishing. The motion of spacecraft teach us much about mechanics: about energy and the way it changes, about momentum and angular momentum, and deepest of all about the role that invariance plays in modern physics.