FACTOID # 5: Minnesota and Connecticut are both in the top 5 in saving money and total tax burden per capita.

 Home Encyclopedia Statistics States A-Z Flags Maps FAQ About

 WHAT'S NEW

SEARCH ALL

Search encyclopedia, statistics and forums:

(* = Graphable)

Encyclopedia > Axial tilt

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. For other uses, see Astronomy (disambiguation). ... For the science fiction novella by William Shunn, see Inclination (novella). ... The eight planets and three dwarf planets of the Solar System. ... The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ... The orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded. ... âˆ , the angle symbol. ...

## Contents

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 formulas it is abbreviated with the Greek letter ε (Epsilon). Image File history File links Axialtilt. ... This article is about the Solar System. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... Technical note: Due to technical limitations, some web browsers may not display some special characters in this article. ... Epsilon (upper case Î•, lower case Îµ) is the fifth letter of the Greek alphabet. ... Look up Î•, Îµ in Wiktionary, the free dictionary. ...

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 [1]. Obliquity is a major factor in glacial/interglacial fluctuations (see Milankovitch cycles). TOA and surface insolation, annual mean Insolation is the incoming solar radiation that reaches a planet and its atmosphere or, by extension, any object exposed to solar rays, such as watts per square meter of Sun-facing cross section, across the entire electromagnetic spectrum; most of that power is in... Variations in CO2, temperature and dust from the Vostok ice core over the last 400 000 years For the animated movie, see Ice Age (movie). ... Precession of a gyroscope Precession refers to a change in the direction of the axis of a rotating object. ... Look up Eccentricity in Wiktionary, the free dictionary. ... Milankovitch cycles are the collective effect of changes in the Earths movements upon its climate, named after Serbian civil engineer and mathematician Milutin MilankoviÄ‡. The eccentricity, axial tilt, and precession of the Earths orbit vary in several patterns, resulting in 100,000 year ice age cycles of the...

The obliquity of the ecliptic is not a fixed quantity but changing over time. It is a very slow effect, 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

The obliquity of the ecliptic is such a pervasive element in positional astronomy that it must be used in the calculations and observations of all planetary positions, including Sun and Moon. However to quickly grasp an idea of its value one can look at the seasons. It suffices to consider that the extreme northern and southern declination of the Sun are per definition equal to the obliquity. Therefore the difference of the heights of the Sun above the horizon at noon on the longest and shortest day of the year is twice the obliquity. This was the way the Chinese astronomers determined it in 1000 BCE. This article is about divisions of a year. ... In astronomy, declination (abbrev. ...

Example: an observer on 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’. Latitude,usually denoted symbolically by the Greek letter phi, , gives the location of a place on Earth north or south of the equator. ...

## 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. 22. ... Rotation (green), Precession (blue) and Nutation (red) of the Earth Nutation is a slight irregular motion (etymologically a nodding) in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet. ...

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 theory in 1976 with ε equal to 23° 26’ 21.448” (epoch of 2000), which became the officially approved theory by the International Astronomical Union in 2000: Simon Newcomb. ... Logo of the IAU The International Astronomical Union (French: Union astronomique internationale) unites national astronomical societies from around the world. ...

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). An ephemeris (plural: ephemerides) (from the Greek word ephemeros = daily) is a device giving the positions of astronomical objects in the sky. ... Look up epoch in Wiktionary, the free dictionary. ...

With the linear term in T being negative, at present the obliquity is slowly decreasing. It is implicit that this expression only gives 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. More elaborate calculations on the numerical model of solar system shows 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). A Solar System Numerical Model A Law of Motion for Entities in a Solar System Numerical Model The solar system may be modeled numerically using both Newtons Law of Gravitation and Newtons Second Law of Motion. ...

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: The orbit of the Moon around the Earth is completed in approximately 27. ...

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 BCE, 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’. Milankovitch cycles are the collective effect of changes in the Earths movements upon its climate, named after Serbian civil engineer and mathematician Milutin MilankoviÄ‡. The eccentricity, axial tilt, and precession of the Earths orbit vary in several patterns, resulting in 100,000 year ice age cycles of the...

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°. 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 less than 2,000,000,000 years. Once this occurs, a resonance from planetary effects will follow, causing swings of up to 65° in the obliquity. Under these conditions, places just outside the current locations of the arctic and antarctic circle would experience the sun directly overhead on the respective solstice, for example. More swings will occur again when the Moon reaches a distance of 68 Earth radii. This will have significant effects on climate. This article presents information and images about viewing astronomical phenomena from the planet Mars. ... World map showing the Arctic Circle in red A sign along the Dalton Highway marking the location of the Arctic Circle The Arctic Circle is one of the five major circles of latitude that mark maps of the Earth. ... Zoomable PDF of the map this is based on The Antarctic Circle is one of the five major circles of latitude that mark maps of the Earth. ... â€œSummer solsticeâ€ redirects here. ...

## Axial tilt of major celestial bodies

Object Axial tilt (°)
Mercury ~0.01
Venus 177.36
Earth 23.439 281
Moon 1.5424
Mars 25.19
Ceres ~4
Pallas ~60
Jupiter 3.13
Saturn 26.73
Uranus 97.77
Neptune 28.32
Pluto 119.61
Eris unknown

## References

• Explanatory supplement to 'the Astronomical ephemeris' and 'the American Ephemeris and Nautical Almanac'
• [1] 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

Results from FactBites:

 Axial tilt - Wikipedia, the free encyclopedia (349 words) Axial tilt is an astronomical term regarding the inclination angle of a planet's rotational axis in relation to its orbital plane. The axial tilt may equivalently be expressed in terms of the planet's orbital plane and a plane perpendicular to its axis. The Earth's axial tilt varies between 21.5° and 24.5° with a 41,000 year periodicity (currently decreasing: 24.049 in 3300 BC, 23.443 in 1973, 23.439 in 2000), while the direction of the tilt gradually undergoes precession, moving in a slow circle over a period of about 25,800 years.
More results at FactBites »

Share your thoughts, questions and commentary here