Earth's
orbital plane is known as the
ecliptic plane, and
Earth's tilt is known to astronomers as the
obliquity of the ecliptic, being the angle between the ecliptic and the
celestial equator on the
celestial sphere. It is denoted by the
Greek letter ε. Earth currently has an axial tilt of about 23.44°. This value remains about the same relative to a stationary orbital plane throughout the cycles of
axial precession. But the ecliptic (i.e., Earth's orbit) moves due to planetary
perturbations, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about
46.8″ per
century (see details in Short term below).
History The ancient Greeks had good measurements of the obliquity since about 350 BCE, when
Pytheas of Marseilles measured the shadow of a
gnomon at the
summer solstice. About 830 CE, the Caliph
Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years. In 1437,
Ulugh Beg determined the Earth's axial tilt as 23°30′17″ (23.5047°). During the
Middle Ages, it was widely believed that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as
trepidation of the equinoxes. Perhaps the first to realize this was incorrect (during historic time) was
Ibn al-Shatir in the fourteenth century and the first to realize that the obliquity is decreasing at a relatively constant rate was
Fracastoro in 1538. The first accurate, modern, western observations of the obliquity were probably those of
Tycho Brahe from
Denmark, about 1584, although observations by several others, including
al-Ma'mun,
al-Tusi,
Purbach,
Regiomontanus, and
Walther, could have provided similar information.
Seasons . The axis of Earth remains oriented in the same direction with reference to the background stars regardless of where it is in its
orbit. Northern Hemisphere summer occurs at the right side of this diagram, where the North Pole (red) is directed toward the Sun, winter at the left.
Earth's axis remains tilted in the same direction with reference to the background stars throughout a year (regardless of where it is in its
orbit) – this is known as
axial parallelism. This means that one pole (and the associated
hemisphere of Earth) will be directed away from the Sun at one side of the orbit, and half an orbit later (half a year later) this pole will be directed towards the Sun. This is the cause of Earth's
seasons.
Summer occurs in the
Northern Hemisphere when the North Pole is directed toward and the South Pole away from the Sun. Variations in Earth's axial tilt can influence the seasons and is likely a factor in long-term
climatic change (also see Milankovitch cycles).
Oscillation Short term (1986). The red point represents the year 2000. The exact angular value of the obliquity is found by observation of the motions of Earth and
planets over many years. Astronomers produce new
fundamental ephemerides as the accuracy of
observation improves and as the understanding of the
dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived. Annual
almanacs are published listing the derived values and methods of use. Until 1983, the
Astronomical Almanac's angular value of the mean obliquity for any date was calculated based on the
work of Newcomb, who analyzed positions of the planets until about 1895: : where is the obliquity and is
tropical centuries from
B1900.0 to the date in question. From 1984, the
Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the
fundamental ephemeris of the
Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated: : where hereafter is
Julian centuries from
J2000.0. JPL's fundamental ephemerides have been continually updated. For instance, according to IAU resolution in 2006 in favor of the P03 astronomical model, the
Astronomical Almanac for 2010 specifies: : These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps several centuries.
Jacques Laskar computed an expression to order good to 0.02″ over 1000 years and several
arcseconds over 10,000 years. : where here is multiples of 10,000
Julian years from
J2000.0. These expressions are for the so-called
mean obliquity, that is, the obliquity free from short-term variations. Periodic motions of the Moon and of Earth in its orbit cause much smaller (9.2
arcseconds) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known as
nutation, which add a periodic component to Earth's obliquity.
Long term Using
numerical methods to simulate
Solar System behavior over a period of several million years, long-term changes in Earth's
orbit, and hence its obliquity, have been investigated. For the past 5 million years, Earth's obliquity has varied between and , with a mean period of 41,040 years. This cycle is a combination of precession and the largest
term in the motion of the
ecliptic. For the next 1 million years, the cycle will carry the obliquity between and . The
Moon has a stabilizing effect on Earth's obliquity. Frequency map analysis conducted in 1993 suggested that, in the absence of the Moon, the obliquity could change rapidly due to
orbital resonances and
chaotic behavior of the Solar System, reaching as high as 90° in as little as a few million years (
also see Orbit of the Moon). However, more recent numerical simulations made in 2011 indicated that even in the absence of the Moon, Earth's obliquity might not be quite so unstable; varying only by about 20–25°. To resolve this contradiction, diffusion rate of obliquity has been calculated, and it was found that it takes more than billions of years for Earth's obliquity to reach near 90°. The Moon's stabilizing effect will continue for less than two billion years. As the Moon continues to recede from Earth due to
tidal acceleration, resonances may occur which will cause large oscillations of the obliquity. == Solar System bodies ==