The speed of rotation of Earth is decreasing due to revolution

of moon around the Earth. (Credit: NASA)



The days are getting longer due to motion of moon around the Earth. Although this is happening at extremely slow rate but the day length is getting longer. The day length has increased by 1.7 milliseconds during the last 100 years. This seems unusual because we have never felt the elongation of day length. The day length is increasing because of the decrease in speed of rotation of Earth. The revolution of moon around the Earth is applying a pull which is trying to slow down the rotation of Earth. Let’s understand it in detail.

Revolution of Moon around the Earth





revolution of moon. The moon revolves around the Earth at an average distance of 384000 km and completes on revolution in 27 days 7 hours and 43 minutes. The moon keeps the same face towards the Earth throughout its motion because the rotation period is exactly same as the period

The moon revolves around the Earth because of the force of gravitation between the Earth and the moon. The moon also applies force on the Earth and both revolve around their common Center of mass. As the mass of moon is 81 times smaller than the mass of Earth so the Earth does not move much but it is only the moon which appears to revolve around the Earth.



Effect of gravity of moon The effect of gravity of moon can be seen in the phenomena of tides. The moon exerts gravitation pull on the surface of Earth but due to rigidity of the solid surface its effect is very less. The oceans are not rigid so they easily deform under the effect of gravitational pull. The level of water of the ocean increases on the surface of Earth which is facing moon. The water level on the back side of Earth also increases. This results in a bulge on the front and back surface of Earth.

Drag between the Earth and moon

The bulge is not localised to a particular place because the speed of rotation of Earth is larger than the speed of revolution of moon around the Earth. The surface below the water bulge moves with the rotation of Earth but bulge is pulled by the moon. The Earth tries to drag the bulge along the direction of rotation. Thus the bulge is not exactly along the direction of line joining the Earth and moon but bulge lies slight towards the direction of rotation of Earth.





Formation of bulge due to gravity of moon which exerts drag on the Earth. (Credit: astrointerest)





This situation results in a torque on the bulge due to moon. Since a friction force exists between the surface of Earth and the bulge in the ocean water, the torque also acts on the surface of Earth which is in the opposite direction of the motion of Earth. So this torque tries to slow down the rotation of Earth. The torque also acts on the bulge on the back surface of Earth and this torque is in the same direction of rotation of Earth. This torque on the back surface tries to increase the speed of rotation of Earth but the magnitude of torque on the back surface is less than the torque on the front surface. The net result is the torque in the opposite direction of rotation of Earth which tries to decrease the speed of rotation of Earth.





Result of decrease in speed of rotation of Earth





speed of rotation of Earth also results in the increase in speed of revolution of moon around the Earth. Due to decrease in speed of Earth the angular momentum of Earth decreases and the angular momentum of moon increases. So we can say that the angular momentum is transferring from the Earth to moon. The net angular momentum of Earth moon system remains constant and follows the law of conservation of angular momentum. The slowing of theof Earth also results in the increase in speed of revolution of moon around the Earth. Due to decrease in speed of Earth the angular momentum of Earth decreases and the angular momentum of moon increases. So we can say that the angular momentum is transferring from the Earth to moon. The net angular momentum of Earth moon system remains constant and follows the law of conservation of angular momentum.





The increase in speed of revolution of moon around the Earth also results in the increase in radius of orbit of moon. The moon is moving away from us at the rate of 3.78 cm per year.





The Earth will keep on slowing down and moon will keep on speeding up until they reach at the common speed. Then the period of rotation of Earth and period of revolution of moon will be same. But it will take billions of years.



