## Chile’s Earthquake Changed Earth’s Mass Distribution & Shortened Days

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Large magnitude earthquakes, such as Chile’s 8.8 magnitude earthquake, can redistribute mass in Earth’s crust enough to change the day length. Why?

Dr. Richard Gross, at NASA’s Jet Propulsion Laboratory in Pasadena, calculated that the Richter magnitude 8.8 earthquake in Chile in 2010 speeded up Earth’s rotation. According to his calculations, the Chile earthquake shortened Earth’s days by about 1.26 microseconds. Gross also calculated that the undersea earthquake that caused the disastrous December 2004 tsunami shortened Earth’s day by 2.68 microseconds.

Amounting to only about 1 part in 100 billion, these shorter days hardly explain why it keeps getting harder to find time to do everything. They are, however, real if imperceptible.

### How do earthquakes affect Earth’s rotation?

During earthquakes, the ground shakes as tectonic plates shift along a fault line. Tectonic plates can move horizontally or vertically. Either way masses of rock in Earth’s crust change location. The mass distribution in Earth’s crust changes. While very significant to people living near the earthquake zone, the masses of rock that move are very small compared to Earth’s mass.

### Conservation of Angular Momentum

In physics, the law of conservation of angular momentum requires that the total angular momentum of a system with no external torques (rotational forces) remains constant. Angular momentum is how physicists measure the amount of spinning motion. Hence, angular momentum conservation requires an object with no external rotational forces to keep the same amount of spinning motion.

Physicists call the angular rotation rate angular velocity. The angular analog to mass is the moment of inertia. Analogous to linear momentum being mass multiplied by velocity, angular momentum is the moment of inertia multiplied by angular velocity.

In order to keep the angular momentum constant, if the moment of inertia increases, the angular velocity decreases. If however the moment of inertia decreases, the angular velocity increases.

### Moment of Inertia

The moment of inertia of a point mass is its mass multiplied by the square of its distance from the rotation axis. For an extended mass, the total moment of inertia is the total of the moments of inertia for each point in the mass distribution.

The key idea is that the moment of inertia involves the mass and the distance from the rotational axis. If the distribution of mass in an object changes so that its average distance from the rotational axis changes, then its moment of inertia changes.

### Earthquakes and Earth’s Moment of Inertia

As an earthquake shifts rock in Earth’s crust; it changes how Earth’s mass is distributed. Earthquakes that move tectonic plates vertically change the distance of the tectonic plate from Earth’s rotational axis. This small distance change affects Earth’s moment of inertia, which will in turn change, ever so slightly, Earth’s rotation rate.

If part of a tectonic plate moves downward, its distance from Earth’s rotational axis decreases. Earth’s moment of inertia decreases. Earth’s angular velocity increases to conserve angular momentum. As Earth spins faster, the day length shortens an imperceptible amount. If the tectonic plate moves upward, the opposite occurs and the day gets longer.

The day got shorter after the major earthquakes in 2010 and 2004 because tectonic movements shifted some mass closer to Earth’s rotation axis, decreased Earth’s moment of inertia, and increased Earth’s rotation rate. The detailed calculations are very complex, but the fundamental physics principle is less difficult to understand.

The fundamental physics involved is the same principle that causes **figure skaters to spin** more or less rapidly as they move their arms in or out.

The beauty of physics lies in the ability of simple principles, like conservation of angular momentum, to explain disparate phenomena such as Earth’s changing rotation rate, figure skaters spinning, **balancing bicycles**, spinning tops, and gyroscopic compasses.