How These Motions Are Changing
These terrestrial motions are not stable, but changing. The changes are important to us, since they affect our time reckoning, our climate, and our understanding of the Earth's past.
The Earth's rate of rotation is decreasing, so that the length of the day is increasing. Tides raised on the Earth, primarily by the Moon, cause the Earth's rotation to decelerate. In accordance with the principle of conservation of angular momentum, the Moon's orbit is correspondingly receding from the Earth (see Figure 5).
Figure 5. The Moon recedes and the Earth's rotation slows. Illustration courtesy of author.
Records of solar and lunar eclipses over the past 2500 years indicate that the tidal effect, about 2.3 milliseconds per century, is partially opposed by a factor which reduces the increase in the length of the day to about 1.7 milliseconds per century. This countereffect is probably caused by the recovery of the Earth's shape from the distortion of the last ice age, when the polar latitudes were depressed by the weight of the ice caps. In the long run, the effect should vary with the growth and shrinking of the ice caps. It has been suggested that today the tidal effect is also being slightly reduced by the growing number of huge water reservoirs on Earth, particularly in the northern hemisphere.
Sediments preserved in rock record daily tidal changes, and also changes in step with the phases of the Moon, during earlier geological periods. These records have enabled scientists to determine that some 900 million years ago, assuming the length of the year has not changed significantly, the day was only about 18 modern hours long, and there were about 480 days in the year.
Currently, the sidereal year -- the time it takes the Sun to return to the ecliptic longitude of a given fixed star-is about 365.2564 solar days. The sidereal year appears to be increasing slightly, about 0.01 second per century. This increase may not mean that the Earth's orbital motion is slowing down. Instead, the orbit may be increasing in size, which increases the period of revolution. The change is very small. If constant, it would amount to an increase of less than one day in one billion years.
The Orientation of the Earth in Space
The orientation in space of the Earth and its orbit is gradually changing, in several ways.
The Invariable Plane
Figure 6. The current location of the celestial north pole, the ecliptic north pole, and the north pole of the invariable plane in the northern sky. Illustration courtesy of author.
To consider how this is happening, we need a reasonably stable frame of reference. For this, we can use the so-called invariable plane of the Solar System. The invariable plane is formally defined as "the plane through the center of mass of the solar system perpendicular to the angular momentum vector of the solar system." It represents the total angular momentum of all Solar System objects, insofar as their elements are known. It is not absolutely invariable but for most practical purposes can be considered so. The north pole of the invariable plane lies in Draco, its south pole in Mensa. The ecliptic is currently only about 1.58° from the invariable plane (Figure 6).
Precession of the Earth's Axis
The rotation of the Earth on its axis causes it to bulge at the equator and flatten at the poles. The gravitational force exerted on the equatorial bulge, almost entirely by the Moon and Sun, attempts to align the Earth's equator more closely with the ecliptic, but the rate of the Earth's rotation tends to maintain its obliquity. Instead, this gravitational force causes the Earth's axis of rotation to precess slowly. The poles describe an arc clockwise (opposite the direction of the Earth's rotation and revolution) as viewed from above the Earth's North Pole, looking down, but counterclockwise as viewed from the Earth's surface, looking up at the northern stars (Figure 7). The Earth behaves like a top spinning too slowly to remain stationary against the forces acting on it. The celestial equator rotates like a plate wobbling on top of a pole in a juggler's act.
This motion is called lunisolar precession. It tends to shift the intersection of the celestial equator and the ecliptic westward along the ecliptic, through the zodiacal constellations. The celestial poles take about 26,000 years to complete one cycle of precession. In the Pyramid Age, about 2500 BC, the North Celestial Pole (NCP) was in Draco, near the star Thuban. About 2000 years from now the NCP will enter the constellation Cepheus.
Figure 7. The precession of the celestial north pole, viewed from above the north pole and against the background of northern stars. Illustration courtesy of author.
The path of the poles is not a circle, but a loop or spiral. This time around, the NCP has come very close to Polaris, but the next time it is expected to pass about 3° from that star. This changes the angle between the celestial and ecliptic poles slightly, contributing to changes in the obliquity of the ecliptic.
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