## The Astronomical Unit

Astronomers studying the solar system use a unit of length, the astronomical unit (AU), that provides a convenient way to express and relate distances of objects in the solar system and to carry out various astronomical calculations. The astronomical unit is effectively equal to the average, or mean, distance between Earth and the Sun. Alternately, it can be considered the length of the semimajor axis—i.e., the length of half of the maximum diameter—of Earth's elliptical orbit around the Sun. An astronomical constant is defined in terms of a form of Kepler's third law of planetary motion and has a value of149,597,870 km (92,955,808 miles). Thus, stating that the planet Jupiter is 5.2 AU (5.2 Earth distances) from the Sun and that Pluto is nearly 40 AU gives ready comparisons of the distances of all three bodies.

In principle, the easiest way to determine the value of the astronomical unit would be to measure the Earth-Sun distance directly by means of the parallax method. In this approach, two observers stationed at the ends of a long, accurately known baseline—ideally, a baseline as long as Earth's diameter—would simultaneously record the position of the Sun against the essentially motionless background of the distant stars. Comparison of the observations would reveal an apparent shift, or angular (parallax) displacement, of the Sun against the remote stars. A simple trigonometric relationship incorporating this angular value and the baseline length then could be used to find the Earth-Sun distance. In practice, however, the method cannot be applied, because the Sun's intense glare blots out the background stars needed for the parallax measurement.

By the 17th century, astronomers understood the geometry of the solar system and the motion of the planets well enough to develop a proportional model of objects in orbit around the Sun, a model that was independent of a particular scale. To establish the scale for all orbits and to determine the astronomical unit, all that was needed was an accurate measurement of the distance between any two objects at a given instant. In 1672 the Italian-born French astronomer Gian Domenico Cassini made a reasonably close estimate of the astronomical unit based on a determination of the parallax displacement of the planet Mars—and thus its distance to Earth. Later efforts made use of widely separated observations of the transit of Venus across the Sun's disk to measure the distance between Venus and Earth. In 1932, determination of the parallax displacement of the asteroid Eros as it made a close approach to Earth yielded what was at the time a very precise value for the astronomical unit. Since the mid-20th century, astronomers have further refined their knowledge of the dimensions of the solar system and the value of the astronomical unit through a combination of radar ranging of Mercury, Venus, and Mars; laser ranging of the Moon (making use of light reflectors left on the lunar surface by Apollo astronauts); and timing of signals returned from spacecraft as they orbit or make close passes of objects in the solar system.

revolution—counterclockwise as viewed down from the north—is in the same sense, or direction, as the rotation of the Sun; Earth's spin, or rotation about its axis, is also in the same sense, which is called direct or prograde. The rotation period, or length of a sidereal day—23 hours, 56 minutes, and 4 sec—is similar to that of Mars. The 23.5° tilt, or inclination, of Earth's axis to its orbital plane, also typical, results in greater heating and more hours of daylight in one hemisphere or the other over the course of a year and so is responsible for the cyclic change of seasons.

With an equatorial radius of 6,378 km (3,963 miles), Earth is the largest of the four inner, terrestrial (rocky) planets, but it is considerably smaller than the gas giants of the outer solar system. Earth has a single satellite, the Moon, which orbits the planet at a mean distance of about 384,400 km (238,900 miles). The Moon is one of the bigger natural satellites in the solar system; only the giant planets have moons comparable or larger in size. Some planetary astronomers consider the Earth-Moon system a double planet, with some similarity in that regard to the dwarf planet Pluto and its largest moon, Charon.

Earth's gravitational field is manifested as the attractive force acting on a free body at rest, causing it to accelerate in the general direction of the centre of the planet. Departures from the spherical shape and the effect of Earth's rotation cause gravity to vary with latitude over the terrestrial surface. The average gravitational acceleration at sea level is about 980 cm/sec2 (32.2 feet/sec2).

Earth's gravity keeps the Moon in its orbit around the planet and also generates tides in the solid body of the Moon. Such deformations are manifested in the form of slight bulges at the lunar surface, detectable only by sensitive instruments. In turn, the Moon's mass—relatively large for a natural satellite—exerts a gravitational force that causes tides on Earth. The Sun, much more distant but vastly more massive, also raises tides on Earth. The tides are most apparent during the daily rise and fall of the ocean water, although tidal deformations occur in the solid Earth and in the atmosphere as well. The movement of the water throughout the ocean basins as a result of the tides (as well as, to a lesser extent, the tidal distortion of the solid Earth) dissipates orbital kinetic energy as heat, producing a gradual slowing of Earth's rotation and a spiraling outward of the Moon's orbit. Currently this slowing lengthens the day by a few thousandths of a second per century, but the rate of slowing varies with time as plate tectonics and sea-level changes alter the areas covered by inland bays and shallow seas. (For additional orbital and physical data, see the table.)

Blankets of volatile gases and liquids near and above the surface of Earth are, along with solar energy, of prime importance to the sustenance of life on Earth. They are distributed and recycled

 PLANETARY DATA FOR EARTH mean distance from Sun 149,600,000 km (1.0 AU) eccentricity of orbit 0.0167 inclination of orbit to ecliptic 0.000° Earth year (sidereal period 365.256 days of revolution) mean orbital velocity 29.79 km/sec equatorial radius 6,378.14 km polar radius 6,356.78 km surface area 510,066,000 km2 mass 5.976 x 1024 kg mean density 5.52 g/cm3 mean surface gravity 980 cm/sec2 escape velocity 11.2 km/sec rotation period (Earth sidereal day) 23.9345 hr (23 hr 56 min 4 sec) of mean solar time Earth mean solar day 24.0657 hr (24 hr 3 min 57 sec) of mean sidereal time inclination of Equator to orbit 23.45° magnetic field strength at Equator 0.3 gauss (but weakening) dipole moment 7.9 * 1025 gauss/cm3 tilt angle of magnetic axis 11.5° atmospheric composition (by volume) molecular nitrogen, 78%; molecular oxygen, 21%; argon, 0.93%; carbon dioxide, 0.037% (presently rising); water, about 1% (variable) mean surface pressure 1 bar mean surface temperature 288 K (59 °F, 15 °C) number of known moons 1 (the Moon)

throughout the atmosphere and hydrosphere of the planet.