Earth's Obliquity

Image description: Earth's obliquity is the angle between the Earth's axis of rotation and its orbital plane (ecliptic plane).

What is Earth's Obliquity?

Earth's Obliquity or Axial Tilt is the Angle between the Earth's rotational axis and the perpendicular to the plane of its orbit around the Sun (ecliptic). Equivalently, it is the angle between its equatorial plane and its orbital plane. Currently, this angle is approximately ≈23.4 degrees. In the solar system, the planets have orbits around the Sun that are all roughly in the same plane, the ecliptic.

Earth's obliquity is responsible for the seasons. The wider the angle, the more pronounced the contrast between the seasons. If the axial tilt were zero (0°), there would be no seasons, and the temperature would be evenly distributed across the planet. Because the Earth's axis is tilted, different parts of the planet receive varying amounts of solar radiation throughout the year. This results in temperature and daylength variations, thus creating the seasons.

What is Earth's Axis of Rotation?

The Axis of Rotation is the Line around which the Earth rotates on itself in 24 hours. This axis approximately passes through the North Pole and the South Pole on the Earth's surface. The plane of the equator is perpendicular to the Earth's axis of rotation. The Celestial Poles (north and south) are imaginary points in the sky that mark the extensions of the Earth's axis of rotation into space. The Celestial Equatorial Plane is the imaginary extension of the Earth's equatorial plane into space. Although the movements of the Earth's axis of rotation result in slight differences between the two planes over time, these deviations are minimal.

Variations in Earth's Obliquity

Earth's obliquity or axial tilt is not a constant angle but varies slightly over time. This movement is caused by the gravitational perturbations exerted by the other planets in the solar system, particularly Jupiter and Saturn. However, the obliquity remains confined between 22.1° and 24.5°. Over the past 5 million years, Earth's obliquity has varied between 22°2'33" and 24°30'16", with an average period of 41,040 years. Currently, it is 23.4361706743° but is slowly decreasing at a rate of approximately 0.00013 degrees per year, or ≈46.8 arcseconds per century. In other words, the axis is straightening towards the perpendicular at a rate of approximately 1° over a period of ≈7692 years.

In summary, Earth's obliquity ranges from 22.1° to 24.5°, then returns to 22.1° over 41,000 years.

Variations in Earth's Axis of Rotation

The Earth's axis of rotation describes a cone around the perpendicular to the ecliptic plane. This precession movement is caused by the gravitational forces exerted by the Sun and the Moon on the Earth's equatorial bulge. The 26,000-year period corresponds to the time required for the Earth's axis of rotation to complete one full cycle around this cone. This means that the axis of rotation returns to its initial position relative to the fixed stars after approximately 26,000 years.

Superimposed on the 26,000-year precession, another oscillation, known as Nutation, which is faster and of smaller amplitude, manifests as periodic variations in the inclination of the Earth's axis of rotation. Nutation has a principal period of approximately 18.6 years.

Factors Influencing Variations in Earth's Obliquity

Earth's obliquity varies due to several complex mechanisms. These variations result from gravitational interactions, internal processes within the Earth, and astronomical phenomena at different timescales.

1. Gravitational Interaction of the Moon

The Moon plays a central role as it exerts a stabilizing influence on the Earth's axis of rotation, limiting the oscillations of the obliquity. It contains the Earth's obliquity within a relatively narrow range between 22.1° and 24.5°. Without the Moon, simulations indicate that the Earth's obliquity could vary chaotically, oscillating between 0° and 85° over a few million years.

The Earth is not a perfect sphere; it is slightly flattened at the poles and has an equatorial bulge. This bulge means that the Earth's mass distribution is not isotropic (uniform in all directions). Since the equatorial bulge is not aligned with the Earth-Moon direction, this interaction creates a gravitational torque that tends to realign the Earth's axis of rotation towards a position perpendicular to the orbital plane. This torque partially compensates for the gravitational perturbations of other planets, notably Jupiter and Saturn, which would otherwise tend to destabilize the Earth's axis.

The Moon exerts a gravitational force on the Earth's bulge because it orbits with a different inclination to the Earth's equatorial plane, passing above and below this plane during its monthly orbital cycle. This means that the Moon does not remain aligned with the Earth's equatorial bulge. This asymmetry creates a gravitational torque responsible for the precessional movements of the Earth's axis (circular movement around an average direction).

2. Gravitational Interaction of Giant Planets

The giant planets (Jupiter and Saturn), due to their large mass, alter the shape and inclination of the Earth's orbit. This affects the angle between the Earth's axis of rotation and its orbital plane. These perturbations cause cyclical oscillations of the obliquity over a period of approximately 41,000 years.

3. Gravitational Interaction of the Sun

The Sun also exerts a gravitational force on the equatorial bulge, but this is less stabilizing than that of the Moon due to the Earth-Sun distance.

4. Redistribution of Earth's Masses

Ice melting, tectonic movements, and Earth tides also influence the Earth's axis of rotation. This mass transfer changes the Earth's moment of inertia (analogous to the change in speed of a skater who brings their arms closer or farther apart). However, these variations are minimal and oscillatory because the redistribution of masses can either "straighten" the axis (decrease the obliquity) or "tilt" it (increase the obliquity) depending on the direction of the displaced masses.

Satellite measurements, such as the GRACE (Gravity Recovery and Climate Experiment) missions, allow for the detection of minute but precise variations in the Earth's axis of rotation, the drift of the geographic poles (~10 cm/year), and fluctuations in the length of the day (a few milliseconds).

Main Causes of the Abnormal Geographic Deviation of 2023

The geographic deviation of the Earth's poles, often referred to as "polar motion" or "pole drift," is a complex phenomenon involving several geophysical factors. In 2023, a deviation of 31.5 inches (approximately 80 cm) can be explained by a combination of these factors.

The Chandler Wobble is a major component of polar motion. This wobble has a period of approximately 433 days and an amplitude of a few meters. It is caused by internal and external perturbations of the Earth, such as earthquakes, magma movements, and variations in atmospheric pressure and ocean tides. A deviation of 80 cm could be partially attributed to this wobble.

Seasonal variations in the distribution of mass in the atmosphere and oceans cause annual polar motion. This motion has a period of one year and can contribute to polar deviations on the order of a few tens of centimeters.

Variations in the internal mass distribution of the Earth, including major geological events such as earthquakes, tectonic plate movements, and magma displacements, can also influence polar motion.

Climatic variations, such as the melting of glaciers and ice caps, can alter the Earth's mass distribution and contribute to polar motion and the orientation of the axis of rotation.

Cumulative Effects

When all these factors are combined, they can result in a drift of the geographic poles on the order of 80 cm.
- The Chandler Wobble could contribute to a deviation of 30 to 40 cm.
- The annual polar motion could add 10 to 20 cm.
- Variations in the Earth's mass distribution could contribute an additional 10 to 20 cm.
- External forces and climatic effects could add a few more centimeters.