In astronomy, axial tilt is the inclination angle of a planet's rotational axis in relation to a perpendicular to its orbital plane. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Inclination in general is the Angle between a Reference plane and another plane or axis of direction A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation The orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded. 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. In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent
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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. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. The ecliptic is the apparent path that the Sun traces out in the sky during the year In formulae it is abbreviated with the Greek letter ε (Epsilon). The Greek alphabet (Ελληνικό αλφάβητο is a set of twenty-four letters that has been used to write the Greek language since the late 9th or early Epsilon (uppercase Ε, lowercase ε; Έψιλον is the fifth letter of the Greek alphabet, corresponding phonetically to a Close-mid front unrounded
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. The Sun (Sol is the Star at the center of the Solar System. This effect is the main cause of the seasons (see effect of sun angle on climate). A season is one of the major divisions of the Year, generally based on yearly periodic changes in Weather. The amount of heat energy received at any location on the globe is a direct effect of sun angle of climate, as the angle at which Sunlight strikes the earth 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. Sunlight, in the broad sense is the total spectrum of the Electromagnetic radiation given off by the Sun. In Astronomy, Geography, Geometry and related sciences and contexts a direction passing by a given point is said to be vertical if
Lower obliquity causes polar regions to receive less solar radiation, producing conditions more favorable to glaciation. Insolation is a measure of Solar radiation energy received on a given surface area in a given time An ice age is a period of long-term reduction in the Temperature of the Earth 's surface and atmosphere resulting in an expansion of continental Ice sheets 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]. Precession refers to a change in the direction of the axis of a rotating object In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape Obliquity is a major factor in glacial/interglacial fluctuations (see Milankovitch cycles). Milankovitch cycles are the collective effect of changes in the Earth 's movements upon its climate named after Serbian civil engineer and Mathematician
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. Nutation is a slight irregular motion (etymologically a "nodding" in the Axis of rotation of a largely axially symmetric object such as a Gyroscope 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. A season is one of the major divisions of the Year, generally based on yearly periodic changes in Weather. 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. In Astronomy, declination (abbrev dec or δ) is one of the two coordinates of the Equatorial coordinate system, the other being either 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’. In Astronomy, declination (abbrev dec or δ) is one of the two coordinates of the Equatorial coordinate system, the other being either 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). The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the An equinox is the event of the Sun passing over the Earth's equator in its annual cycle In broad terms the zenith is the direction pointing directly above a particular location ( Perpendicular, Orthogonal) Solstices occur twice a year when the tilt of the Earth's axis is most oriented toward or away from the Sun, causing the Sun to reach its northernmost and southernmost extremes 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. An equinox is the event of the Sun passing over the Earth's equator in its annual cycle The winter solstice occurs at the instant when the Sun 's position in the sky is at its greatest angular distance on the other side of the equatorial plane from the
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. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the 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). The horizon ( Ancient Greek ὁ ὁρίζων, /ho horídzôn/ from ὁρίζειν, "to limit" is the apparent line that separates
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. Nutation is a slight irregular motion (etymologically a "nodding" in the Axis of rotation of a largely axially symmetric object such as a Gyroscope
Simon Newcomb's calculation at the end of the nineteenth century for the obliquity of the ecliptic gave a value of 23° 27’ 8. Simon Newcomb ( March 12 1835 &ndash July 11 1909) was a Canadian American Astronomer and Mathematician 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. An ephemeris (plural ephemerides; from the Greek word ἐφήμερος ephemeros "daily" is a table of values that gives the positions of 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). A numerical model of the Solar system is a set of mathematical equations which when solved give the approximate positions of the planets as a function of time
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. The orbit of the Moon around the Earth is completed in approximately 27 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. Milankovitch cycles are the collective effect of changes in the Earth 's movements upon its climate named after Serbian civil engineer and Mathematician 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 [1]. This article presents information and images about viewing astronomical phenomena from the planet Mars. 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 tilt[2]
Axial tilt of major celestial bodies
| Object | Axial tilt (°) |
|---|---|
| Mercury | ~0. 01 |
| Venus | 177. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University 36 |
| Earth | 23. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 439 281 |
| Moon | 1. 5424 |
| Mars | 25. 19 |
| Ceres | ~4 |
| Pallas | ~60 |
| Jupiter | 3. Ceres (ˈsɪəriːz TemplateInfobox Planet. --> 2 Pallas (ˈpæləs, or as Παλλάς) is one of the largest 13 |
| Saturn | 26. 73 |
| Uranus | 97. 77 |
| Neptune | 28. Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. 32 |
| Pluto | 119. 61 |
| Eris | unknown |
See also
References
- Explanatory supplement to 'the Astronomical ephemeris' and 'the American Ephemeris and Nautical Almanac'
- [3] for a comparison of values predicted by different theories
- A. The celestial equator is a Great circle on the imaginary Celestial sphere, in the same plane as the Earth 's Equator. The north and south celestial poles are the two imaginary points in the sky where the Earth's Axis of rotation, "infinitely extended" intersects the The ecliptic is the apparent path that the Sun traces out in the sky during the year Nutation is a slight irregular motion (etymologically a "nodding" in the Axis of rotation of a largely axially symmetric object such as a Gyroscope The orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded. A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation The American Ephemeris and Nautical Almanac was published for the years 1855 to 1980 containing information necessary for astronomers surveyors and navigators 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.
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