{Geography} Earth’s Rotation and Solar Day

Earth rotates around its own axis from west to east. When seen from the North Star Polaris {Alpha Ursae Minoris}, Earth turns counter-clockwise. Rotation of Earth results in days and nights. Earth’s rotation is mostly the result of angular momentum left over during the formation process of Earth. There are three distinct motions, the most noticeable being Earth’s rotation. Earth rotates once every 23 hours, 56 minutes, causing our cycles of day and night. Earth also has precession (a wobble of the rotational axis) and nutation (a back-and-forth wiggle of Earth’s axis), caused primarily by the gravitational pull of the Moon as it orbits Earth. Precession and nutation, over long periods of time, cause Earth’s north and south poles to point toward different stars.

Solar Day

A Solar day refers to one complete rotation of Earth on its own axis relative to Sun. However, since Earth also revolves around the sun, there are three kinds of days recognized by astronomers viz. Apparent  or True solar day; Mean solar day and sidereal day. These are discussed as follows:

Apparent {True} Solar Day

Apparent solar day is the interval between two successive returns of the Sun to the local meridian. A sundial can measure the apparent solar day with limited precision. The length of true solar day keeps changing throughout the year. There are two reasons for this. Firstly, Earth’s orbit around sun is an ellipse. The second law of Kepler says that in elliptical orbits, the line joining the planet  and sun sweeps out equal areas during equal intervals of time.  Thus, earth moves faster when its is nearest to Sun (perihelion) and moves slower when it is farthest from Sun (Aphelion).  Secondly, Earth currently has an axial tilt of about 23.5° and remains tilted in the same direction towards the stars throughout a year. This implies that when a hemisphere is pointing away from the Sun at one point in the orbit then half an orbit later (half a year later) this hemisphere will be pointing towards the Sun. This effect is the main cause of the seasons.

What is obliquity of the ecliptic?

Earth’s orbital plane is known as the ecliptic plane, and so the Earth’s axial tilt is called the obliquity of the ecliptic.

Due to Earth’s tilt, Sun moves along a great circle (the ecliptic) that is tilted to Earth’s celestial equator. When the Sun crosses the equator at both equinoxes, the Sun is moving at an angle to the equator, so the projection of this tilted motion onto the equator is slower than its mean motion; when the Sun is farthest from the equator at both solstices, the Sun moves parallel to the equator, so the projection of this parallel motion onto the equator is faster than its mean motion. The result is that apparent solar days are shorter in March (26–27) and September (12–13) than they are in June (18–19) or December (20–21).

The true solar day tends to be longer near perihelion taking about 10 seconds longer and is about 10 seconds shorter near aphelion. It is about 20 seconds longer near a solstice and shorter by 20 seconds near equinox.

Mean Solar Day

The average of the true or apparent solar day over an entire year is called the mean solar day. It has 86400 seconds. Albeit, the amount of daylight varies significantly, the length of a mean solar day does not change on a seasonal basis. However, the length of the Mean Solar Day increases by 1.4 milliseconds per century. The astronomers have calculated that Mean Solar Day was exactly 86,400 (24 hours × 60 minutes × 60 seconds) SI seconds in approximately 1820 AD and now it is 86400.002 SI seconds. The reason behind this slow down is the net effect of tidal acceleration and global glacial rebound.

Tidal Acceleration

Tidal acceleration refers to the effect of the tidal forces between an orbiting natural satellite and the primary planet that it orbits.

We know that Moon’s mass is a considerable fraction of that of the Earth. The Ratio of masses of moon and Earth is about 1:81. So these two bodies can be regarded as a double planet system, rather than as a planet with a satellite. The large mass of moon is sufficient to raise tides in the matter of earth. The water of the oceans bulges out along both ends of the axis, passing through the centers of Moon as well as Earth. This tidal bulge is shown below.

The average tidal bulge shown in above figure closely follows the Moon in its orbit. However, since earth also rotates, the rotation drags this bulge ahead of the position directly under the Moon. The arrow shown in the earth shows the direction of this drag. Due to the simultaneously forces of moon’s gravitational force giving rise to the bulges in ocean water and substantial amount of mass in these bulges of water dragged by earth’s rotation, this bulge is deviated from the line through the centers of Earth and Moon. This gives rise to a Torque which is perpendicular to the earth moon line. This torque boosts moon in its orbit and decelerates earth’s rotation. The above phenomenon is responsible for the slowing Earth’s rotation. Due to the tidal acceleration, Earth’s mean solar day extends by 2.3 milliseconds every century. However, due to glacial rebound, this extension gets reduced by 0.6 seconds per century. So the net effect on mean solar day every century is 1.7 milliseconds.

Global Glacial Rebound

The average position of water is always nearer the equator. During glaciations water is taken from the oceans and deposited as ice over the higher latitudes closer to the poles. These poles are close to the polar axis or rotational axis of the Earth. The moment of inertia of Earth-water-ice system gets reduced which is very much similar to a rotating figure skater bringing her arms closer to her body, the earth should spin faster. This process leads to an increase in the rotation speed of the Earth and therefore to a decrease of the length of day.

Sidereal Day

The spinning of the earth on its polar axis is in fact takes 23 hours, 56 minutes and 4.09 seconds for rotation through the 360 degree. This is called sidereal day. During the time needed by the Earth to complete a rotation around its axis (a sidereal day), the Earth moves a short distance (approximately 1°) along its orbit around the sun. So, after a sidereal day, the Earth still needs to rotate a small additional angular distance before the sun reaches its highest point. A solar day is, therefore, nearly 4 minutes longer than a sidereal day.

Precession Movement of earth

The Precession movement of Earth is very slow and proceeds in the direction of the opposite of Earth’s Rotation. The one cycle completes in 28000 years.  The reason of precession movement is gravitational attraction of Moon as well as Sun.  The slightly irregular movement of earth’s axis due to precession is called Nutation.