Tides and Earth's rotation

Any evening on a beach to enjoy with the uninterrupted show of waves and the roaring noise makes for a mesmerising experience.

It also leads you to ponder on a very pertinent question concerning the amount of energy that is dissipated in the phenomenon. More intriguing is the semidiurnal variation in the high and low tides which are exploited by the fishermen in an excellent way. In fact, the small variation in the difference between successive full moons and ‘super moons’ also is expressed by these high tides and low tides.

It was believed that the Earth’s orbital (spin) motions are quite stable to the extent determinable by the best instruments. However, a systematic study of these tides and the development of physics associated with them has revealed some unknown properties of the rotation of Earth.

Now, we have methods and tools to detect the variations in both angular speed and direction of Earth spin. The geological pole records a slow drift in time scales of thousand years due. Very careful measurements reflect the influence of slow internal processes. The Reference Pole was determined as average position of the Earth’s (geographic) pole between 1900 and 1905 (formerly called the Conventional International Origin).

Before the advent of quartz clocks, rotation of Earth was regarded as the most reliable clock except for planetary motion. The observations of star transit across meridian achieved accuracy better than one millisecond in the 1950s which led to the detection of periodic variations in the length of day (LOD). There were annual, semi-annual, and fortnightly perturbations. The Universal Time (UT), which is based on the rotation of Earth, has been replaced by the International Atomic Time (TAI) based on atomic clocks.

Understanding the variations

Based on the understanding of the tidal friction in the oceans and solid Earth during tides, Immanuel Kant and George Darwin suspected a decrease in the speed of rotation of Earth although they did not have sensitive instruments to detect the variation. They also concluded that the lunar orbit should be modified accordingly. The key is the conservation of angular momentum.
It is easy to understand that the tides are clearly locked up with the moon although the sun also contributes significantly (about 20%). Thus, we have the variation in the height of tides during full moon and new moon as distinctly different compared to the quarters. The fact that oceans bulge on diametrically opposite sides had to be explained by the universal law of gravitation again, leading to an inverse cube law.

As we understand today, the two identical tidal bulges have a minute phase delay which can be attributed to tidal friction. It can be several degrees. The rise in the layer due to this can range from 20 cm on the land to over two metres on the oceans. The associated energy dissipation amounts to 3.0 terawatt. This results in a tidal torque, which can reduce spin angular momentum of the Earth.  Now, we have accurate measures of the Earth’s deceleration rate which have shown that the LOD is increasing with a rate of 1.8 millisecond per century. The land which was under the ice long ago during a previous ice age moves up and down – a phenomenon called glacial isostatic adjustment, adds to the effect increasing the rate to 2.3 millisecond per century. Glaciers are retreating leading to changes in the Earth’s moments of inertia. The contribution of this to the variation of LOD is not accurately known.

Satellites play a very important role in the measurement. Their orbits are continuously monitored for effects other than Earth’s gravitation for example from the moon, the sun and solar radiation pressure. The measurements have hinted a lunar orbital retardation. Lunar laser ranging started since Apollo 11 landing in 1969, and enabled direct estimate of the present lunar recession as 3.82 cm per year. Paleontological evidences like the tree rings have supported the tidal effects. The differential growth of shells of corals record high and low ocean tides.

Ring Laser Gyroscope measures very accurately the Earth’s spin rotational angular velocity. VLBI (Very Long Baseline Interferometry), Global Positioning System (GPS) and Satellite Laser Ranging (SLR) have been used to measure the offset of the pole to one milliarcsecond accuracy. Extrapolating the results, we can say moon was quite close to the Earth billions of years ago and the duration of the day was different at that time.

Going back in time

Historical eclipse records have contributed to the study of the variation of the rotation period. A stone tablet recorded a total solar eclipse in Babylon on April 15, 136 BCE. The computations based on the assumption of a uniform rotation speed put the shadow path about 500 km away from this place. Now the rotation speed can to be adjusted to match the observational record.

In India, there are hardly any observational records of celestial events. Fortunately, there is an unconventional record of eclipses in the form of stone inscriptions which are scattered all over the country. The grant of donations, gifts and even self immolations for attaining salvation were performed on important celestial events like eclipses. There are more than 30,000 inscriptions in Karnataka alone. Of them, five have recorded total solar eclipses in 11th – 12th century. These records have been used to determine the variation in the rate of rotation.

It is amazing that stone inscriptions from non-descriptive villages like Otturu in Soraba taluk (eclipse of February 3, CE 938), Pattadakallu in Badami (eclipse of June 25, 754 CE) and Soundatti in Belgaum (eclipse of 1087 CE August 1) have contributed to the understanding of the variation in the speed of rotation of Earth.

(The author is director, Jawaharlal Nehru Planetarium, Bengaluru)