# Dictionary Definition

obliquity

### Noun

1 the presentation during labor of the head of
the fetus at an abnormal angle [syn: asynclitism]

2 the quality of being deceptive [syn: deceptiveness]

# User Contributed Dictionary

### Pronunciation

- (UK) /əˈblɪkwɪti/
- (US) /əˈblɪkwɪdi/, /oʊˈblɪkwɪdi/

### Noun

- The quality of being oblique in direction; deviating
from the horizontal
or vertical, or the
angle created by such a deviation.
- 1667, John Milton, Paradise Lost, lines 766-769:
- The Planet Earth, so stedfast though she seem, / Insensibly three different Motions move? / Which else to several Sphears thou must ascribe, / Mov'd contrarie with thwart obliquities

- 1667, John Milton, Paradise Lost, lines 766-769:
- Mental or moral deviation or perversity; immorality.
- 1924, Herman Melville, Billy Budd,
Chapter 2:
- Habitually living with the elements and knowing little more of the land than as a beach, or, rather, that portion of the terraqueous globe providentially set apart for dance-houses, doxies and tapsters, in short what sailors call a "fiddlers'-green," his simple nature remained unsophisticated by those moral obliquities which are not in every case incompatible with that manufacturable thing known as respectability.

- 2006, Thomas Pynchon, Against the Day, Vintage 2007, p. 404:
- Stray's [friends], apt to keep more to the shadows, tended to be practitioners of obliquity—as it quite often came down to, varieties of pimp.

- 1924, Herman Melville, Billy Budd,
Chapter 2:
- The quality of being obscure, oftentimes willfully,
sometimes as an exercise in euphemism.
- 1879, Mark Twain, A Tramp Abroad,
Chapter 25:
- That spiked my gun. I could not say anything. I was entirely out of verbal obliquities; to go further would be to lie, and that I would not do; so I simply sat still and suffered , -- sat mutely and resignedly there, and sizzled, -- for I was being slowly fried to death in my own blushes.

- 1879, Mark Twain, A Tramp Abroad,
Chapter 25:

# Extensive Definition

In astronomy, axial tilt is the
inclination angle of
a planet's rotational
axis in relation to a perpendicular to its orbital
plane. It is also called axial inclination or obliquity. The
axial tilt is expressed as the angle made by the planet's axis
and a line drawn through the planet's center perpendicular to the
orbital plane.

## Obliquity

The axial tilt may equivalently be expressed in terms of the planet's orbital plane and a plane perpendicular to its axis. In our solar system, the Earth's orbital plane is known as the ecliptic, and so the Earth's axial tilt is officially called the obliquity of the ecliptic. In formulae it is abbreviated with the Greek letter ε (Epsilon).The Earth has an axial tilt of about 23.44° (23°
26’). The axis is tilted in the same direction throughout a year;
however, as the Earth orbits the Sun, the hemisphere
(half part of earth) tilted away from the Sun will gradually become
tilted towards the Sun, and vice versa. This effect is the main
cause of the seasons (see
effect of sun angle on climate). Whichever hemisphere is
currently tilted toward the Sun experiences more hours of sunlight each day, and the
sunlight at midday also strikes the ground at an angle nearer the
vertical
and thus delivers more energy per unit surface area.

Lower obliquity causes polar regions to receive
less solar radiation,
producing conditions more favorable to glaciation. Like
changes in precession
and eccentricity,
changes in tilt influence the relative strength of the seasons, but
the effects of the tilt cycle are particularly pronounced in the
high latitudes where the great ice ages began . Obliquity is a
major factor in glacial/interglacial fluctuations (see Milankovitch
cycles).

The obliquity of the ecliptic is not a fixed
quantity but changing over time. It is a very slow effect known as
nutation, and at the
level of accuracy at which astronomers work, does need to be taken
into account on a daily basis. Note that the obliquity and the
precession of the equinoxes are calculated from the same theory and
are thus related to each other. A smaller ε means a larger p
(precession in longitude) and vice versa. Yet the two movements act
independent from each other, going in mutually perpendicular
directions.

## Measurement

Knowledge of the obliquity of the ecliptic (ε) is critical for astronomical calculations and observations from the surface of the earth (earth-based, positional astronomy).To quickly grasp an idea of its numerical value
one can look at how the sun's angle above the horizon varies with
the seasons; this was
the way the Chinese astronomers determined it in 1000 BC. They
measured the difference between the angles of the Sun above the
horizon at noon on the longest and shortest days of the year. That
difference in the angles is twice the obliquity.

The extreme northern and southern declination of the Sun
during the year are equal to the obliquity. On the longest day of
the year the earth is tilted toward the sun and we say that the
sun's declination is
+ 23° 26’. To an observer on the equator standing all year long
looking above, the sun will be directly overhead at noon in March
(Vernal
Equinox), then swing north until it is ε degrees away from the
zenith in June (Summer
Solstice). In September (Autumnal
Equinox) it will be back overhead, then at the Winter
Solstice in December it will be ε degrees away from the
vertical again.

Example: an observer at 50° latitude (either north or
south) will see the Sun 63° 26’ above the horizon at noon on the
longest day of the year, but only 16° 34’ the shortest day. The
difference is 2ε = 46° 52’, and so ε = 23° 26’.

(90° - 50°) + 23.4394° = 63.4394° when measuring
angles from the horizon (90° - 50°) - 23.4394° = 16.5606°

At the equator, this would be 90° + 23.4394° =
113.4394° and 90° - 23.4394° = 66.5606° (measuring always from the
southern horizon).

## Values

The Earth's axial tilt varies between 22.1° and 24.5° (but see below), with a 41,000-year period, and at present, the tilt is decreasing. In addition to this steady decrease, there are also much smaller short term (18.6 years) variations, known as nutation.Simon
Newcomb's calculation at the end of the nineteenth century for
the obliquity of the ecliptic gave a value of 23° 27’ 8.26” (epoch
of 1900), and this was generally accepted until improved telescopes
allowed more accurate observations, and electronic computers
permitted more elaborate models to be calculated. Lieske came with an
updated model in 1976 with ε equal to 23° 26’ 21.448” (epoch of
2000), which is part of the approximation formula recommended by
the
International Astronomical Union in 2000:

ε = 84,381.448 − 46.84024T − (59 × 10−5)T² +
(1,813 × 10−6)T³, measured in seconds of arc, with T being the time
in Julian centuries (that is, 36,525 days) since the ephemeris epoch of 2000 (which occurred on
Julian day 2,451,545.0). A straight application of this formula to
1900 (T=-1) returns Newcomb's value.

With the linear term in T being negative, at
present the obliquity is slowly decreasing. It is implicit that
this expression gives only an approximate value for ε and is only
valid for a certain range of values of T. If not, ε would approach
infinity as T approaches infinity. Computations based on a
numerical model of solar system show that ε has a period of
about 41,000 years, the same as the constants of the precession of
the equinoxes (although not of the precession itself).

Other theoretical models may come with values for
ε expressed with higher powers of T, but since no (finite)
polynomial can ever represent a periodic function, they all go to
either positive or negative infinity for large enough T. In that
respect one can understand the decision of the International
Astronomical Union to choose the simplest equation which agrees
with most models. For up to 5,000 years in the past and the future
all formulas agree, and up to 9,000 years in the past and the
future, most agree to reasonable accuracy. For eras farther out
discrepanies get too large.

## Long period variations

Nevertheless extrapolation of the average polynomials gives a fit to a sine curve with a period of 41,013 years, which, according to Wittmann, is equal to:ε = A + B sin (C(T + D)), with A = 23.496932° ±
0.001200°, B = − 0.860° ± 0.005°, C = 0.01532 ± 0.0009
radians/Julian century, D = 4.40 ± 0.10 Julian centuries, and T,
the time in centuries from the epoch of 2000 as above.

This means a range of the obliquity from 22° 38’
to 24° 21’, the last maximum was reached in 8700 BC, the mean value
occurred around 1550 and the next minimum will be in 11800. This
formula should give a reasonable approximation for the previous and
next million years or so. Yet it remains an approximation in which
the amplitude of the wave remains the same, while in reality, as
seen from the results of the Milankovitch
cycles, irregular variations occur. The quoted range for the
obliquity is from 21° 30’ to 24° 30’, but the low value may have
been a one-time overshot of the normal 22° 30’.

If we go back over the last 5 million years, the
obliquity of the ecliptic (or more accurately, the obliquity of the
equator on the moving ecliptic of date) has varied from 22.0425° to
24.5044°. But for the next one million years the range will be only
from 22.2289° to 24.3472°.

Other planets may have a variable obliquity too,
for example on Mars
the range is believed to be between 15° and 35°, as a result of
gravitational perturbations from other planets
http://query.nytimes.com/gst/fullpage.html?res=9F0CE4DD163CF931A35750C0A965958260&sec=&spon=&pagewanted=all.
The relatively small range for the Earth is due to the stabilizing
influence of the Moon, but it will not remain so. According to
Ward, the orbit of the Moon (which is continuously increasing due
to tidal effects) will have gone from the current 60 to
approximately 66.5 Earth radii in about 1.5 billion years. Once
this occurs, a resonance from planetary effects will follow,
causing swings of the obliquity between 22° and 38°. Further, in
approximately 2 billion years, when the Moon reaches a distance of
68 Earth radii, another resonance will cause even greater
oscillations, between 27° and 60°. This would have extreme effects
on climate.

Tentative evidence has recently emerged for
extreme (> 50°) variations in terrestrial axial tilthttp://www.princeton.edu/main/news/archive/S15/64/72A37/index.xml?section=newsreleases

## Axial tilt of major celestial bodies

## References

- Explanatory supplement to 'the Astronomical ephemeris' and 'the American Ephemeris and Nautical Almanac'
- http://www.tenspheres.com/researches/precession.htm for a comparison of values predicted by different theories
- A.L. Berger; Obliquity & precession for the last 5 million years; Astronomy & astrophysics 1976, 51, 127
- A. Wittmann; The obliquity of the ecliptic; Astronomy & astrophysics 73, 129-131 (1979)
- W.R. Ward; Comments on the long-term stability of the earth's obliquity; Icarus 1982, 50, 444
- National Space Science Data Center; http://nssdc.gsfc.nasa.gov/planetary/

## External links

- Axial Tilts of Planets by Jeff Bryant, The Wolfram Demonstrations Project.

obliquity in Tosk Albanian: Bahnneigung

obliquity in Asturian: Enclín axal

obliquity in Bulgarian: Наклон на оста
(астрономия)

obliquity in Catalan: Obliqüitat

obliquity in Spanish: Oblicuidad de la
eclíptica

obliquity in Esperanto: Aksa dekliniĝo

obliquity in French: Inclinaison de l'axe

obliquity in Galician: Oblicuidade da
eclíptica

obliquity in Croatian: Nagib osi

obliquity in Italian: Inclinazione assiale

obliquity in Hebrew: נטיית ציר הסיבוב

obliquity in Lithuanian: Ašies posvyris

obliquity in Dutch: Obliquiteit

obliquity in Japanese: 赤道傾斜角

obliquity in Norwegian Nynorsk:
Aksehelling

obliquity in Portuguese: Inclinação axial

obliquity in Russian: Наклон оси вращения
планеты

obliquity in Slovenian: Nagib vrtilne osi

obliquity in Finnish: Akselikallistuma

obliquity in Swedish: Axellutning

obliquity in Chinese: 轉軸傾角