Earth's Rotation

The rotation of the Earth results in the days and nights that provide the daily rhythm of life. Rotation causes the Earth to be flattened at the poles and to bulge at the equator. It also produces the Coriolis force, which influences the circulation of the atmosphere and oceans.

Overview

The spinning of the Earth on its polar axis is called rotation. The ancient Greeks considered the Earth to be a motionless body in the center of a geocentric (Earth-centered) universe. An exception was Heracleides (fourth century BCE), who thought that the Earth did rotate. In general, the Greeks reasoned that, in their experience, if the Earth moved, they would feel some effects of it. Later, the work of Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Sir Isaac Newton resulted in the paradigm shift to a heliocentric (sun-centered) system in which the Earth was a planet simultaneously rotating on an axis while revolving around the sun. The Earth rotates from west to east, thus making the sun, moon, planets, and stars appear to move from east to west across the sky. We commonly refer to the sun, moon, planets, and stars as rising and setting because it appears that they all are moving around the Earth, when in fact the Earth is rotating on its axis while revolving around the sun.

The Earth’s axis of rotation is inclined 23.5° from the perpendicular to the ecliptic (the plane of the Earth’s orbit around the sun); thus the axis of the Earth makes an angle of 66.5° to the plane of the ecliptic. The inclination causes the seasons (and the seasonal variation in the length of day and night) as the Earth orbits the Sun during the course of a year. When either the Northern or Southern Hemisphere of Earth is tilted toward the sun, the period of daylight is longer and night is shorter in that hemisphere. The longer duration of daylight, coupled with the Sun’s rays striking that hemisphere more nearly head-on, results in summer in that hemisphere. Conversely, when either hemisphere is tilted away from the sun, the duration of daylight is shorter and night is longer, the sun’s rays strike that hemisphere more obliquely, and that hemisphere experiences winter.

Because of rotation, a point on the Earth’s equator moves 1,674 kilometers per hour; the speed decreases to 1,450 kilometers per hour at 30° north or south latitude, and to 837 kilometers per hour at 60° north or south latitude. The Earth’s rotation defines the unit of time called the day. A day is defined as the interval of time between successive passages of a meridian, or line of Longitude from the North to South Pole, under a reference object (for example, the sun or a star). A day with reference to the Sun is called a solar day, and a day with reference to the stars is called a sidereal day. Because of the Earth’s orbital motion around the sun in one year, the sun appears to move eastward relative to the stars approximately one degree per day. This makes the solar day approximately four minutes longer than the sidereal day, since the Earth must rotate a little bit farther to complete one rotation relative to the sun as compared to the stars.

The Earth’s orbit around the sun is slightly elliptical, and the Earth’s orbital speed varies with its distance from the Sun, being fastest when Earth is closest to the sun (perihelion), around January 3, and slowest when Earth is farthest from the sun (aphelion), around July 4. This means the sun’s apparent motion relative to the stars varies during the year, being greatest when the Earth’s orbital speed is fastest at perihelion and smallest when the Earth’s orbital speed is slowest at aphelion. Thus the length of the solar day as measured by a sundial (called the apparent solar day) varies slightly during the year. The length of the apparent solar day averaged over a year is called the mean solar day, and mean solar time is the basis for the 24-hour day (of 86,400 seconds) kept by clocks. (The sidereal day is 23 hours, 56 minutes, and 4.091 seconds long.)

Because of rotation, the Earth is flattened in the polar regions and bulges at the equator, thus making it slightly ellipsoidal, an oblate spheroid. The equatorial radius is 6,378 kilometers, while the polar radius is 6,357 kilometers. Thus a point on the equator is 21 kilometers farther from the center of the Earth than either pole is. Because the Earth is slightly flattened, the length of a degree of latitude changes from 109.92 kilometers at the equator to 111.04 kilometers at the poles. Also, because a point on the equator is farther from the center of the Earth and its rotational speed is faster, the effect of gravity is reduced there compared to other points on Earth. Thus an object at the equator weighs less, about 1 pound in 200, compared to the same object at either pole.

The Coriolis force or effect, named after a nineteenth century French engineer who studied this phenomenon, is caused by the Earth’s rotation. It is an apparent force that affects free-moving bodies (such as wind, water, or missiles). For example, a fired projectile will veer to the right relative to the Earth’s surface in the Northern Hemisphere, and to the left in the Southern Hemisphere. Precisely on the equator itself, free-moving objects are not deflected, but as they move north or south of the equator, the deflection becomes more pronounced.

The Coriolis effect is responsible for the global prevailing wind belts. Warm air near the equator rises and flows toward the poles. Cooled at higher altitude, the air descends around 30° north and south latitudes and spreads out both toward the equator and the poles. Air flowing toward the equator is deflected westward in both hemispheres, producing the easterly trade winds of the tropics. Air flowing toward the poles is deflected eastward in both hemispheres, producing the westerly winds of temperate latitudes. The Coriolis effect determines the direction wind blows around local high and low pressure systems in the atmosphere. Air moves outward from high pressure systems and inward toward low pressure systems. In the northern hemisphere, the moving air veers toward the right, setting up clockwise rotation around atmospheric highs and counterclockwise rotation around atmospheric lows. In the southern hemisphere, the moving air veers left, setting up counterclockwise rotation around highs and clockwise rotation around lows. This effect is especially noticeable in hurricanes (also called typhoons), which are regions of extremely low atmospheric pressure. The Coriolis force also influences ocean currents, which in turn affect the climate of coasts they flow along. The ocean currents of the Northern Hemisphere tend to flow clockwise, while those of the Southern Hemisphere flow counterclockwise. Witness the Gulf Stream of the north Atlantic and the Japanese (Alaskan) current of the north Pacific, always turning to the right, while the south Atlantic flow is to the left.

Overall, the rotation of the Earth is slowing down, and the length of the day is increasing by milliseconds per century. The decrease in rotational speed is primarily a result of the tidal friction caused by the gravitational pull of the moon and to a lesser extent the sun. Evidence for a lengthening day during geologic history comes from the study of fossils. Clams, corals, and some other marine invertebrates add a microscopically thin layer of new shell material each day, and the thickness varies seasonally throughout the year. Counting the daily growth lines in an annual set in well-preserved fossils yields the number of days in a year. Since the length of a year (the period of the Earth’s orbit around the Sun) presumably has not changed, the length of a day in past geologic times can be determined. During the early Cambrian period (540 million years ago), there were 424 days in a year, and thus each day was about 20 hours, 40 minutes long. In the late Devonian period (365 million years ago), a year consisted of 410 days, each about 21 hours, 23 minutes long. At the beginning of the Permian period (290 million years ago), a year was down to 390 days, each about 22 hours, 29 minutes long.

As Earth’s rotation slows in response to the moon’s tidal drag, the Earth’s rotational angular momentum is transferred to the moon, which increases the moon’s orbital angular momentum around the Earth, causing the Moon to move outward, away from Earth. This in turn increases the moon’s orbital period around Earth. This will continue until Earth’s rotation on its axis is tidally synchronized with the moon’s revolution around Earth, both Earth and moon keeping the same side facing each other. To conserve angular momentum, the moon’s distance and orbital period will increase to 549,000 kilometers (341,000 miles) and 46.7 of Earth’s present days. Thus Earth’s sidereal rotation period will be 46.7 days, and the mean solar day (time from noon to noon) will be 53.5 of Earth’s present days. Since the length of the year will be unaffected, there will be only 6.8 solar days in a year.

Currently Earth’s day is lengthening by an average of about 2 10^-5 seconds each year, but the rate is quite erratic and sometimes even speeds up a bit. If this current average slowdown rate is extrapolated into the future, it will take 2 10¹¹ years for Earth and Moon to become tidally locked. Alternatively, laser ranging (using retroreflectors left on the moon’s surface by the Apollo moon landings) shows that the moon currently is moving away from Earth at 3.8 centimeters per year. Extrapolating this rate into the future, it will take 4 10⁹ years for the Moon to reach its final distance. The disagreement of these two time estimates indicates that the rates of slowdown of Earth’s rotation and the increase in the Moon’s distance probably will not remain constant, and the time to achieve Earth-moon tidal lock is probably at least billions of years. However, before this can occur, the sun probably will expand and become a red giant first.

Numerous detailed studies show that, superimposed on the systematic long-term slowdown, Earth’s rotation has numerous small random changes. The reasons for these variations include transfer of angular momentum between different parts of the Earth’s interior; transfer of angular momentum between the atmosphere, the oceans, and the Earth’s surface; movement of air masses and changes in wind patterns; growth or shrinkage of polar ice caps; volcanic activity; earthquakes; and plate tectonic movements. The timescales for the various effects on the Earth’s rotation vary, from short-term to long-term, and from systematic seasonal to erratic. It is evident from many studies that the Earth’s rotational speed has varied throughout geologic time and continues to change on a daily, weekly, monthly, seasonal, yearly, and even longer-term basis.

Currently the Earth’s axis of rotation points toward Polaris, Earth’s present North Star. However, the Earth’s axis slowly changes direction in space in a process called precession. Recall the Earth has an equatorial bulge, and it is tilted about 23.5° from the ecliptic, the plane of the Earth’s orbit around the sun. The torque exerted by the gravitational pull of the Moon and the Sun on the Earth’s equatorial bulge trying to make it line up with the ecliptic plane causes the Earth’s axis to slowly precess, like the axis of a tilted spinning toy top. This precession causes the Earth’s axis to trace out in space a double cone (two cones joined at their vertices) with a vertex angle of 47° (twice the 23.5° axial tilt). The Earth’s axis slowly shifts direction about 50 arc seconds per year, and it takes about 26,000 years for a complete precession cycle. As the axis points to different parts of the sky in response to precession, stars other than Polaris have served and will serve as north stars. Also, in about 13,000 years (half the precessional cycle), the constellations seen during specific months on Earth will be “shifted” by six months, so that those constellations now seen during June (for example) will be seen during December, and so on. Consequently, the astronomical coordinate system of right ascension and declination slowly and systematically changes during the precessional cycle. Catalogs listing those coordinates for stars, nebulae, galaxies, and other celestial bodies must specify the epoch (year) for which the listed coordinates are rigorously correct. To point a telescope at some desired object some other year requires calculating precessional corrections to the listed coordinates.

Superimposed upon the precessional motion are two other motions. One of these is a small oscillating motion called nutation, which has a semiamplitude of 9.2 seconds of arc and a period of 18.6 years. This motion is associated with the periodic variation in the orientation of the Moon’s orbital plane around the Earth with the Earth’s orbital plane around the sun. The other motion, called Chandler’s wobble, has two oscillations. One of the oscillations, the Chandler component, with a period of twelve months, is a result of meteorological effects associated with seasonal changes in air masses. The second oscillation of the Chandler wobble, the 14.2-month component, is caused by shifts in the Earth’s interior mass. Thus the changing direction of the Earth’s rotational axis is not smooth but “wiggly” or “wobbly.”

Methods of Study

Sundials were first used to mark the passage of the apparent solar day, as the shadow of the gnomon (stick) moved across the face of the dial. In 1671, the French astronomer Jean Richer made time measurements with a pendulum clock both in Paris (49° north) and in Cayenne, French Guiana (5° north) and compared the two. In French Guiana, the clock “lost” 2.5 minutes per day compared to Paris. He attributed this loss to a decrease in effective gravitational pull toward the equator due to the Earth’s rotation; the practical consequence was that pendulum clocks needed to have the length of their pendula adjusted according to latitude to be able to keep accurate time.

In 1851, the French physicist Jean-Bernard-Léon Foucault hung a 25-kilogram iron ball with a 60-meter-long wire from the dome of the Panthéon in Paris, with a pin at the bottom of the ball to make marks in a smooth layer of sand underneath. After only a few minutes, the tracings in the sand showed that the plane of the ball’s swing slowly rotated clockwise as seen from above. Foucault explained this as a demonstration of the Earth’s rotation, which moved the attachment point on the dome and the sand on the floor, while the pendulum tried to maintain the plane of its swing in the same direction. In the 1950s, atomic clocks began to be used to measure time accurately over long periods. When time kept by these clocks was compared to time determined by the rotation of the Earth, small variations in the Earth’s rotation were found.

Newer techniques used to determine length of day and polar motion involve the use of satellites and lasers. One method, called lunar laser ranging (LLR), involves the emission of light pulses from a laser on Earth to reflectors left on the moon by Apollo and Soviet spacecraft. The returning pulses of light are received by a telescope. The total travel time is calculated to determine the Earth-to-moon distance. By observing the time the Moon takes to cross a meridian during successive passages, this method has provided very good length-of-day measurements. Another technique involves the use of the Laser Geodynamics Satellite (Lageos). This satellite is covered by prisms that reflect light from pulsed lasers on Earth. Again, the returned beam is received by a telescope and the round-trip travel time is used to infer the one-way distance from the Earth to the satellite. This method, which includes a network of stations on Earth, can provide insight into yearly movement of crustal plates, which is believed to cause variations in the Earth’s rotation. A very accurate technique known as very-long baseline interferometry (VLBI) is also being used to plot continental drift as well as variations in Earth’s rotation and the position of the poles. In this method, radio signals from space (typically from quasars) are received by two radio antennas and are tape-recorded. The tapes are compared, and the difference between the arrival times of the signals at the two radio antennas is used to calculate the distance between the two. If the distance between the two antennas has changed, the crustal plates have moved.

Context

The spinning of the Earth on its polar axis once every twenty-four hours is very much a part of the daily rhythm of life. Among the primary ways Earth’s rotation is felt by and governs life are its impact on our day, on gravitational pull, and on the atmosphere. Earth’s rotation gives us a daily time reference by the passage of days and nights. The spinning of the Earth on its polar axis causes the Earth to bulge at the equator and to be flattened in the polar areas. Because of this phenomenon, the distance to the center of the Earth varies with latitude, and as a result the effective gravitational pull on objects on the Earth’s surface also varies—objects weigh slightly less at the equator than in the polar regions of the world. The Coriolis effect, an apparent force caused by the rotation of the Earth, causes free-moving bodies to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. It governs the direction of winds as they flow in or out of pressure systems, establishing the wind belts of the world. The Coriolis force also affects the flow of ocean currents, and these patterns help to alter climates along the coasts of continents.

One of the many feared effects of global warming is the shifting of the Earth's axis and the slowing of its rotation. Several studies have proven in the early 2010s that this is the case; the melting of glaciers due to global warming has changed the planet's mass and continues to slow its rotational speed by 1 millisecond per day. The shift in mass distribution due to the rise in sea levels has also caused the Earth's axis to move.

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