Earth's Axial Tilt

The Earth rotates around its own axis, which is slightly tilted relative to the plane of its orbit around the Sun. This axial tilt of approximately 23.5 degrees is responsible for seasonal variations: it causes the hemispheres’ exposure to solar radiation to vary throughout the year.

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How to measure it in class

The tilt of the Earth’s axis cannot be measured directly, but it can be deduced from the height of the Sun at noon, which FizziQ’s theodolite measures using the smartphone’s accelerometer.

Steps:

Plant a perfectly vertical stick (a gnomon) in horizontal, open ground, and measure its height H to the nearest decimeter.
At solar noon, when the shadow is shortest, measure its length L. Deduce the height of the Sun: h = arctan(H/L). Never look at the Sun directly with your eyes.
Check this result with FizziQ’s Theodolite tool, by measuring the elevation angle of the Sun-gnomon direction indicated by the shadow.
Repeat the measurement at the June solstice and at the December solstice, at the same location.
Calculate the half-difference of the two measured heights: (h_June − h_December) / 2. You recover the obliquity, about 23.4°.

Scientific activities on this topic

Day length and seasons - comparison of sunrise and sunset times throughout the year, to relate the lengthening of the day to the tilt of the axis.
Sun height and seasons - measurement of the maximum height of the Sun at different dates with the inclinometer, and comparison with ephemeris data.

Learn more

The Earth is tilted relative to the plane of its orbit around the Sun due to forces that acted upon it during its formation. Collisions between particles and celestial bodies in the early solar system gave rise to this tilt. Earth’s axial tilt is approximately 23.5 degrees.

This tilt has a significant impact on our planet. Combined with the Earth’s revolution around the Sun, it creates the seasons. Throughout the year, the tilt causes the hemispheres’ exposure to solar radiation to vary. When a hemisphere is tilted toward the Sun, it receives more light and heat, causing warm seasons (spring and summer). Meanwhile, the other hemisphere is tilted away from the Sun, receiving less light and heat, resulting in cold seasons (autumn and winter).

The tilt creates two easily observable scientific phenomena:

the lengthening of days during summer
variations in the height of the Sun in the sky

The axis keeps a fixed direction: that is what produces the alternation

The essential point, and one that is often misunderstood, is that the rotation axis does not tip over during the year. It keeps a nearly fixed direction in space, pointed toward the pole star, while the Earth travels along its orbit. It is the Earth’s position on this orbit that changes: six months after having its northern hemisphere tilted toward the Sun, the Earth is on the other side and it is the southern hemisphere that is tilted toward it. If the axis pivoted to follow the Sun, there would be no seasons at all.

It is not the distance to the Sun

The tilt, not the distance, explains the seasons. The Earth’s orbit is nearly circular (eccentricity 0.0167) and the Earth-Sun distance varies by only 3.4 % over the year. The Earth is in fact closest to the Sun in early January, in the middle of the northern winter. The reversal of the seasons between the two hemispheres, which are nevertheless at the same distance from the Sun at the same instant, definitively rules out the explanation by distance.

Not to be confused with magnetic inclination

Two distinct notions carry the same word. The Earth’s tilt, or obliquity, is a 23.4° angle between the rotation axis and the perpendicular to the orbital plane: it is an astronomical quantity, identical at every point on the globe. Magnetic inclination is the angle that the Earth’s magnetic field makes with the horizontal at a given place: it is about 0° at the magnetic equator and 90° at the magnetic poles, and it is measured with the smartphone’s magnetometer. The two quantities have no physical relationship.

The obliquity is not strictly constant

The Earth’s axis slowly traces a cone around the perpendicular to the orbit: this is the precession of the equinoxes, with a period of about 26,000 years. The current pole star will therefore not remain so. The obliquity itself oscillates slightly, between about 22.1° and 24.5°, over a period of about 41,000 years. These slow variations, together with those of the eccentricity, are the Milankovitch parameters, invoked to explain the alternation of ice ages. On the scale of a school year, the obliquity can be considered constant.

Orders of magnitude

Current obliquity: 23.44°, that is 23°26′, and it decreases by about 0.013° per century. Latitude of the tropics: 23.4°. Latitude of the polar circles: 66.6°. Precession period: about 26,000 years. Obliquity of Mars: 25.2°, very close to Earth’s. Obliquity of Venus: 177°, the planet rotates practically upside down. Obliquity of Uranus: 98°, the axis lies almost in the plane of the orbit.

Formula

The obliquity ε is the angle between the Earth’s rotation axis and the normal to the plane of the ecliptic:

ε ≈ 23.44°

It sets the amplitude of the solar declination over the course of the year:

−ε ≤ δ ≤ +ε

where:

δ: declination of the Sun, angular position relative to the celestial equator (°)
ε: obliquity of the ecliptic (°)

The height of the Sun at solar noon links the obliquity to a measurement feasible in class:

h = 90° − φ + δ

where:

h: angular height of the Sun at solar noon (°)
φ: latitude of the location (°)

By measuring h at the two solstices, the obliquity is recovered:

ε = (h_June_solstice − h_December_solstice) / 2

The obliquity also sets the latitude of the tropics and of the polar circles:

φ_tropic = ε and φ_polar_circle = 90° − ε

Application examples

In Paris (48.9° N), the height of the Sun at noon goes from 64.5° in June to 17.7° in December. The half-difference is (64.5 − 17.7) / 2 = 23.4°: the obliquity is recovered by a student measurement.
The Tropic of Cancer is at latitude 23.4° N and the Arctic Circle at 90 − 23.4 = 66.6° N. These two lines are not conventions: they are directly fixed by the obliquity.
Eratosthenes, around 240 BC, measured the shadow of a gnomon in Alexandria and in Syene to estimate the circumference of the Earth. The same method, applied at the two solstices in a single location, gives the obliquity.
On Uranus, whose axis is tilted at 98°, each pole remains continuously lit for about 42 Earth years, then plunged into night for the same duration.
Sundials and the solstice alignments of ancient buildings exploit the extreme position of the Sun imposed by the obliquity.
The optimal orientation of a fixed solar panel is calculated from the latitude and the ±23.4° declination range.

FAQ

Q: Why is the Earth tilted? A: The dominant hypothesis attributes this tilt to the giant impacts suffered during the formation of the solar system, notably the collision believed to have given birth to the Moon. Nothing required an axis perpendicular to the orbit: the other planets show very varied obliquities.

Q: Does the Earth’s axis tip over during the year? A: No. It keeps a nearly fixed direction in space, pointed toward the pole star. It is precisely this fixity that produces the alternation of the seasons: the Earth changes its position on its orbit, not the orientation of its axis.

Q: Are the Earth’s tilt and magnetic inclination the same thing? A: No, they are two unrelated notions. The Earth’s tilt is the obliquity of its rotation axis, 23.4°, the same everywhere on the globe. Magnetic inclination is the angle between the local magnetic field and the horizontal; it depends on the location and is measured with the magnetometer.

Q: Why do we sometimes read 23.4° and sometimes 23.5°? A: The exact value is 23.44°, that is 23°26′. Depending on the rounding used, the literature gives 23.4° or 23.5°. The difference is of no consequence for school calculations.

Q: What would happen if the obliquity were zero? A: There would be no more seasons: the Sun would keep the same height at noon all year round at a given location, and the day would last 12 h everywhere. A much larger obliquity, conversely, would produce extreme summers and winters all the way to the equator.

Seasons - Theodolite - Inclinometer - Magnetic Inclination