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Inclination

Inclination

Inclination in general is the angle between an axis of direction or a plane, and a reference plane.

Orbits

In particular, the inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit. It is the angular distance of the orbital plane from the plane of reference (usually the primary's equator or the ecliptic), normally stated in degrees. In the solar system, the inclination (i in figure 1, below) of the orbit of a planet is defined as the angle between the plane of the orbit of the planet, and the ecliptic, which is the orbit of Earth. It could be measured with respect to another plane, such as the Sun's equator, Jupiter's orbital plane, or some such, but the ecliptic is more practical for Earth-bound observers. The inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit (the equatorial plane is the plane perpendicular to the axis of rotation of the central body):
- an inclination of 0 degrees means the orbiting body orbits the planet in its equatorial plane, in the same direction as the planet rotates;
- an inclination of 90 degrees indicates a polar orbit, in which the spacecraft passes over the north and south poles of the planet; and
- an inclination of 180 degrees indicates a retrograde equatorial orbit. For the Moon however, this leads to a rapidly varying quantity and it makes more sense to measure it with respect to the ecliptic (i.e. the plane of the orbit that Earth and Moon track together around the Sun), a fairly constant quantity. Moon]

Other meanings

- For planets and other rotating celestial bodies, the angle of the axis of rotation on the plane of the orbit is also called inclination, or axial tilt.
- And in particular, for the Earth, the inclination or obliquity of the ecliptic is the angle between the plane of the ecliptic and the equator.
- The inclination of distant objects, such as a binary star, is defined as the angle between the normal to the orbital plane and the direction to the observer, since no other reference is available. Binary stars with inclination close to 90 degrees (edge-on) are often eclipsing.

Calculation

In astrodynamics, the inclination

i\,

can be computed as follows:

i=\arccos\,

where:
-

h_\mathrm\,

is z-component of

\mathbf\,

,
-

\mathbf\,

is orbital momentum vector perpendicular to the orbital plane.

Angle

This article is about angles in geometry. For other articles, see Angle (disambiguation) ---- An Angle (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Greek (angulοs) crooked, curved; both connected with the Aryan or Indo-European root ank-, to bend) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. Angles provide a means of expressing the difference in slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays. Angles are studied in geometry and trigonometry. Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.

Units of measure for angles

In order to measure an angle, a circle centered at the vertex is drawn. Since the circumference of a circle is always directly proportional to the length of its radius, the measure of the angle is independent of the size of the circle. Note that angles are dimensionless, since they are defined as the ratio of lengths.
- The radian measure of the angle is the length of the arc cut out by the angle, divided by the circle's radius. The SI system of units uses radians as the (derived) unit for angles. Because of the relationship to arc length, radians are a special unit. Sines and cosines whose argument is in radians have particular analytic properties, just as do exponential functions in the base e. (As we've discovered, this is no coincidence).
- The degree measure of the angle is the length of the arc, divided by the circumference of the circle, and multiplied by 360. The symbol for degrees is a small superscript circle, as in 360°. 2π radians is equal to 360° (a full circle), so one radian is about 57° and one degree is π/180 radians. Degrees are further broken down into minutes of arc and seconds of arc, which are 1/60th and 1/3600th of a degree, respectively. Minutes of arc are commonly encountered in discussions of external ballistics, as a minute of arc covers almost exactly 1 inch at 100 yards (1 m at 1200 m). A rifle capable of shooting "1 MOA", one minute of arc, can place all shots within 1 inch at 100 yards, 2 inches at 200 yards, etc. Minutes of arc were also used in navigation, and a nautical mile is roughly defined as one minute of arc of the earth's surface.
- The grad, also called grade, gradian or gon, is an angular measure where the arc is divided by the circumference, and multiplied by 400. It is used mostly in triangulation.
- The point is used in navigation, and is defined as 1/32 of a circle, or exactly 11.25°.
- The full circle or full turns represents the number or fraction of complete full turns. For example, π/2 radians = 90° = 1/4 full circle

Conventions on measurement

A convention universally adopted in mathematical writing is that angles given a sign are positive angles if measured counterclockwise, and negative angles if measured clockwise, from a given line. If no line is specified, it can be assumed to be the x-axis in the Cartesian plane. In navigation, bearings are measured from north, increasing clockwise, so a bearing of 45 is north-east. Negative bearings are not used in navigation, so north-west is 315. In mathematics radians are assumed unless specified otherwise because this removes the arbitrariness of the number 360 in the degree system and because the trigonometric functions can be developed into particularly simple Taylor series if their arguments are specified in radians.

Types of angles

An angle of π/2 radians or 90°, one-quarter of the full circle is called a right angle. Two line segments, rays, or lines (or any combination) which form a right angle are said to be either perpendicular or orthogonal:
- Angles smaller than a right angle are called acute angles
- Angles larger than a right angle are called obtuse angles.
- Angles equal to two right angles are called straight angles.
- Angles larger than two right angles are called reflex angles.
- The difference between an acute angle and a right angle is termed the complement of the angle
- The difference between an angle and two right angles is termed the supplement of the angle.

Some facts

In Euclidean geometry, the inner angles of a triangle add up to π radians or 180°; the inner angles of a quadrilateral add up to 2π radians or 360°. In general, the inner angles of a simple polygon with n sides add up to (n − 2) × π radians or (n − 2) × 180°. If two straight lines intersect, four angles are formed. Each one has an equal measure to the angle across from it; these congruent angles are called vertical angles. If a straight transversal line intersects two parallel lines, corresponding (alternate) angles at the two points of intersection are equal; adjacent angles are supplementary, that is they add to π radians or 180°.

A formal definition

A Euclidean angle is completely determined by the corresponding right triangle. In particular, if

\theta

is a Euclidean angle, it is true that :

\cos \theta = \frac

and :

\sin \theta = \frac

for two numbers

x

and

y

. So an angle can be legitimately given by two numbers

x

and

y

, or by a ratio

\frac

. What's more, to any such ratio there corresponds exactly one angle, since :

\frac = \frac = \frac

(i.e., changing the ratio will necessarily change the sin and cos, which in the geometric range

0 < \theta < 2\pi

are one-to-one - one sin or cos corresponds to one

\theta

Angles in different contexts

In the Euclidean plane, the angle θ between two vectors u and v is related to their dot product and their lengths by the formula :

\mathbf \cdot \mathbf = \cos(\theta)\ \|\mathbf\|\ \|\mathbf\|.

This allows one to define angles in any real inner product space, replacing the Euclidean dot product · by the Hilbert space inner product <·,·>. The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr. ἀμφί, on both sides, κυρτόσ, convex) or cissoidal (Gr. κισσόσ, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίσ, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis, biconcave. Two intersecting planes form an angle, called their dihedral angle. It is defined as the angle between two lines normal to the planes. Also a plane and an intersecting line form an angle. This angle is equal to π/2 radians minus the angle between the intersecting line and the line that goes through the point of intersection and is perpendicular to the plane.

Angles in Riemannian geometry

In Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and g_ij are the components of the metric tensor G, :

\cos \theta = \frac
.

Angles in astronomy

In astronomy, one can measure the angular separation of two stars by imagining two lines through the Earth, each one intersecting one of the stars. Then the angle between those lines can be measured; this is the angular separation between the two stars. Astronomers also measure the apparent size of objects. For example, the full moon has an angular measurement of approximately 0.5°, when viewed from Earth. One could say, "The Moon subtends an angle of half a degree." The small-angle formula can be used to convert such an angular measurement into a distance/size ratio.

Angles in maritime navigation

The modern format of angle used to indicate longitude or latitude is hemisphere degree minute.decimal, where there are 60 minutes in a degree, for instance N 51 23.438 or E 090 58.928. The obsolete (but still commonly used) format of angle used to indicate longitude or latitude is hemisphere degree minute' second", where there are 60 minutes in a degree and 60 seconds in a minute, for instance N 51 23′26″ or E 090 58′57″

External links

- [http://www.unitconversion.org/unit_converter/angle.html Online Angle Converter - convert between various units of angle, such as degree, radian, grad, gon, minute, second, sign, mil, and so on]
- [http://www.unitconversion.org/unit_converter/angle-v.html Interactive Angle Conversion Table - convert selected unit to all other units of angle]
- [http://www.cut-the-knot.org/triangle/ABisector.shtml Angle Bisectors] at cut-the-knot
- [http://www.cut-the-knot.org/Curriculum/Geometry/PerpBiInQuadri.shtml Angle Bisectors and Perpendiculars in a Quadrilateral] at cut-the-knot
- [http://www.cut-the-knot.org/Curriculum/Geometry/CyQuadri.shtml Angle Bisectors in a Quadrilateral] at cut-the-knot
- [http://www.cut-the-knot.org/triangle/TriangleFromBisectors.shtml Constructing a triangle from its angle bisectors] at cut-the-knot
- [http://calc.skyrocket.de/en/ Online Unit Converter - Conversion of many different units] Category:Elementary geometry Category:Trigonometry
- ko:각도 ja:角度 simple:Angle

Orbital parameter

.]] :For other meanings of the term "orbit", see orbit (disambiguation) In physics, an orbit is the path that an object makes around another object while under the influence of a source of centripetal force, such as gravity.

History

Orbits were first analysed mathematically by Johannes Kepler who formulated his results in his laws of planetary motion. He found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies responding to the force of gravity were conic sections. Newton showed that a pair of bodies follow orbits of dimensions that are in inverse proportion to their masses about their common center of mass. Where one body is much more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.

Planetary orbits

Within a planetary system, planets, asteroids, comets and space debris orbit the central star in elliptical orbits. Any comet in a parabolic or hyperbolic orbit about the central star is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. To date, no comet has been observed in our solar system with a distinctly hyperbolic orbit. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about that planet. Due to mutual gravitational perturbations, the eccentricities of the orbits of the planets in our solar system vary over time. Pluto and Mercury have the most eccentric orbits. At the present epoch, Mars has the next largest eccentricity while the smallest eccentricities are those of the orbits of Venus and Neptune. As an object orbits another, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other. In the elliptical orbit, the centre of mass of the orbiting-orbited system will sit at one focus of both orbits, with nothing present at the other focus. As a planet approaches periapsis, the planet will increase in velocity. As a planet approaches apoapsis, the planet will decrease in velocity. See also: Kepler's laws of planetary motion

Understanding orbits

There are a few common ways of understanding orbits.
- As the object moves sideways, it falls toward the orbited object. However it moves so quickly that the curvature of the orbited object will fall away beneath it.
- A force, such as gravity, pulls the object into a curved path as it attempts to fly off in a straight line.
- As the object falls, it moves sideways fast enough (has enough tangential velocity) to miss the orbited object. This understanding is particularly useful for mathematical analysis, because the object's motion can be described as the sum of the three one-dimensional coordinates oscillating around a gravitational center. As an illustration of the orbit around a planet (eg Earth), the much-used cannon model may prove useful (see image below). Imagine a cannon sitting on top of a (very) tall mountain, which fires a cannonball horizontally. The mountain needs to be very tall, so that the cannon will be above the Earth's atmosphere and we can ignore the effects of air friction on the cannon ball. 300px If the cannon fires its ball with a low initial velocity, the trajectory of the ball will curve downwards and hit the ground (A). As the firing velocity is increased, the cannonball will hit the ground further (B) and further (C) away from the cannon, because while the ball is still falling towards the ground, the ground is curving away from it (see first point, above). If the cannonball is fired with sufficient velocity, the ground will curve away from the ball at the same rate as the ball falls - it is now in orbit (D). The orbit may be circular like (D) or if the firing velocity is increased even more, the orbit may become more (E) and more (F) elliptical. At a certain even faster velocity (called the escape velocity) the motion changes from an elliptical orbit to a parabola.

Newton's laws of motion

For a system of only two bodies that are only influenced by their mutual gravity, their orbits can be exactly calculated by Newton's laws of motion and gravity. Briefly, the sum of the forces will equal the mass times its acceleration. Gravity is proportional to mass, and falls off proportionally to the square of distance. To calculate, it is convenient to describe the motion in a coordinate system that is centered on the heavier body, and we can say that the lighter body is in orbit around the heavier body. An unmoving body that's far from a large object has more energy than one that's close. This is because it can fall farther. This is called "potential energy" because it is not yet actual. With two bodies, an orbit is a flat curve. The orbit can be open (so the object never returns) or closed (returning), depending on the total kinetic + potential energy of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less. The path of a free-falling (orbiting) body is always a conic section. An open orbit has the shape of a hyperbola (or in the limiting case, a parabola); the bodies approach each other for a while, curve around each other around the time of their closest approach, and then separate again forever. This is often the case with comets that occasionally approach the Sun. A closed orbit has the shape of an ellipse (or in the limiting case, a circle). The point where the orbiting body is closest to Earth is the perigee, called periapsis (less properly, "perifocus" or "pericentron") when the orbit is around a body other than Earth. The point where the satellite is farthest from Earth is called apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part. Orbiting bodies in closed orbits repeat their path after a constant period of time. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows: # The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal points of the ellipse. Therefore the orbit lies in a plane, called the orbital plane. The point on the orbit closest to the attracting body is the periapsis. The point farthest from the attracting body is called the apoapsis. There are also specific terms for orbits around particular bodies; things orbiting the Sun have a perihelion and aphelion, things orbiting the Earth have a perigee and apogee, and things orbiting the Moon have a perilune and apolune (or, synonymously, periselene and aposelene). An orbit around any star, not just the Sun, has a periastron and an apastron # As the planet moves around its orbit during a fixed amount of time, the line from Sun to planet sweeps a constant area of the orbital plane, regardless of which part of its orbit the planet traces during that period of time. This means that the planet moves faster near its perihelion than near its aphelion, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time." # For each planet, the ratio of the 3rd power of its semi-major axis to the 2nd power of its period is the same constant value for all planets. Except for special cases like Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies. The 2-body solutions were published by Newton in Principia in 1687. In 1912, K. F. Sundman developed a converging infinite series that solves the 3-body problem, however it converges too slowly to be of much use. Instead, orbits can be approximated with arbitrarily high accuracy. These approximations take two forms. One form takes the pure elliptic motion as a basis, and adds perturbation terms to account for the gravitational influence of multiple bodies. This is convenient for calculating the positions of astronomical bodies. The equations of motion of the moon, planets and other bodies are known with great accuracy, and are used to generate tables for celestial navigation. The differential equation form is used for scientific or mission-planning purposes. According to Newton's laws, the sum of all the forces will equal the mass times its acceleration (F = ma). Therefore accelerations can be expressed in terms of positions. The perturbation terms are much easier to describe in this form. Predicting subsequent positions and velocities from initial ones corresponds to solving an initial value problem. Numerical methods calculate the positions and velocities of the objects a tiny time in the future, then repeat this. However, tiny arithmetic errors from the limited accuracy of a computer's math accumulate, limiting the accuracy of this approach. Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large objects have been simulated.

Analysis of orbital motion

(see also orbit equation and Kepler's first law) To analyse the motion of a body moving under the influence of a force which is always directed towards a fixed point, it is convenient to use polar coordinates with the origin coinciding with the centre of force. In such coordinates the radial and transverse components of the acceleration are, respectively: :

\frac - r\left( \frac \right)^2

and :

\frac\frac\left( r^2\frac \right)

. Since the force is always radial, the transverse acceleration is zero, and it follows that: :

\frac = hu^2

, where h is a constant of integration and we have introduced the auxiliary variable u defined as 1/r. If magnitude of the radial force is f(r) per unit mass of the orbiting body, then the elimination of the time variable from the radial component of the equation of motion yields: :

\frac + u = \frac

. In the case of an inverse square force law the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). The equation of the orbit described by the particle is thus: :

r = \frac = \frac

, where φ and e are constants of integration and L is the Semi-latus rectum. This can be recognised as the equation of a conic section in polar coordinates.

Orbital parameters

See: Orbital elements For a general elliptic orbit, the relations between the axis, eccentricity, and least and largest distance are: :Semimajor axis = (periapsis + apoapsis)/2 = mean of the extreme radii :Periapsis = semimajor axis × (1 - eccentricity) = least distance :Apoapsis = semimajor axis × (1 + eccentricity) = largest distance Note that there are alternative definitions for a "mean radius" or "average distance": if you average the radius over time for one orbit (mean anomaly), or over the orbital angle as observed by the primary (true anomaly), then you get a different result. See here for details.

Orbital period

See: orbital period

Orbital decay

If some part of a body's orbit enters an atmosphere, its orbit can decay because of drag. At each periapsis, the object scrapes the air, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. Eventually, the orbit circularises and then the object spirals into the atmosphere. The bounds of an atmosphere vary wildly. During solar maxima, the Earth's atmosphere causes drag up to a hundred kilometres higher than during solar minimums. Some satellites with long conductive tethers can also decay because of electromagnetic drag from the Earth's magnetic field. Basically, the wire cuts the magnetic field, and acts as a generator. The wire moves electrons from the near vacuum on one end to the near-vacuum on the other end. The orbital energy is converted to heat in the wire. Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input, and so can be used indefinitely. See statite for one such proposed use. Orbital decay can also occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the solar system are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years. Finally, orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely.

Earth orbits

See Earth orbit for more details.
- Low Earth orbit
- High Earth Orbit
- Intermediate circular orbit
- Geostationary orbit
- Geosynchronous orbit
- Geostationary transfer orbit
- Molniya orbit
- Polar orbit
- Polar Sun Synchronous Orbit (this is not a complete list).

Scaling in gravity

The gravitational constant G is defined to be:
- 6.6742 × 10⁻¹¹ N·m²/kg²
- 6.6742 × 10⁻¹¹ m³/(kg·s²)
- 6.6742 × 10⁻¹¹(kg/m³)^-1s^-2. Thus the constant has dimension density^-1 time^-2. This corresponds to the following properties. Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the earth. When all densities are multiplied by four, orbits are the same, but with orbital velocities doubled. When all densities are multiplied by four, and all sizes are halved, orbits are similar, with the same orbital velocities. These properties are illustrated in the formula :

GT^2 \sigma = 3\pi \left( \frac \right)^3,

for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density σ, where T is the orbital period.

Role in the evolution of atomic theory

When atomic structure was first probed experimentally early in the twentieth century, an early picture of the atom portrayed it as a miniature solar system bound by the coulomb force rather than by gravity. This was inconsistent with electrodynamics and the model was progressively refined as quantum theory evolved, but there is a legacy of the picture in the term orbital for the wave function of an energetically bound electron state.

External links

- An on-line orbit plotter: http://www.bridgewater.edu/departments/physics/ISAW/PlanetOrbit.html
- [http://www.braeunig.us/space/orbmech.htm Orbital Mechanics] (Rocket and Space Technology) Category:Celestial mechanics Category:Solar System als:Umlaufbahn ja:軌道 (力学) simple:Orbit th:วงโคจร

Angle

Units of measure for angles

Conventions on measurement

Types of angles

Some facts

A formal definition

A Euclidean angle is completely determined by the corresponding right triangle. In particular, if

\theta

is a Euclidean angle, it is true that :

\cos \theta = \frac

and :

\sin \theta = \frac

for two numbers

x

and

y

. So an angle can be legitimately given by two numbers

x

and

y

, or by a ratio

\frac

. What's more, to any such ratio there corresponds exactly one angle, since :

\frac = \frac = \frac

(i.e., changing the ratio will necessarily change the sin and cos, which in the geometric range

0 < \theta < 2\pi

are one-to-one - one sin or cos corresponds to one

\theta

Angles in different contexts

In the Euclidean plane, the angle θ between two vectors u and v is related to their dot product and their lengths by the formula :

\mathbf \cdot \mathbf = \cos(\theta)\ \|\mathbf\|\ \|\mathbf\|.

Angles in Riemannian geometry

In Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and g_ij are the components of the metric tensor G, :

\cos \theta = \frac
.

Angles in astronomy

Angles in maritime navigation

External links

Equator

The equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. The equator divides the planet into a Northern Hemisphere and the Southern Hemisphere. The latitude of the equator is, by definition, 0°. The length of Earth's equator is about 40,075.0 km, or 24,901.5 miles. The equator is one of the five main circles of latitude based on the relationship of the Earth's rotation and plane of orbit around the sun. Additionally, the equator is the only line of latitude which is also a great circle The Sun, in its seasonal movement through the sky, passes directly over the equator twice each year on the Vernal and Autumnal Equinoxes, which occur in March and September (respectively). At the equator, the rays of the sun are perpendicular to the surface of the earth on these dates. Places near the equator experience the quickest rates of sunrise and sunset in the world, taking minutes. Such places also have a relatively constant amount of day/night time on every day throughout the year compared with more northerly or southerly places.

Equatorial climate

In many tropical regions people identify two seasons, wet and dry, but most places very close to the equator are wet throughout the year, although seasons can vary depending on a variety of factors including elevation and proximity to an ocean. ocean The surface of the Earth at the equator is mainly ocean. The highest point on the Equator is 4,690 m, at 77° 59' 31" W on the south slopes of Volcán Cayambe (summit 5,790 m) in Ecuador. This is a short distance above the snow line, and is the only point on the Equator where snow lies on the ground (Google Earth satellite data and photos).

Equatorial countries

The equator traverses the land and/or water of 13 countries in total:
- São Tomé and Príncipe - passing through Ilhéu das Rolas, an islet in this archipelago
- Gabon
- Republic of the Congo
- Democratic Republic of Congo
- Uganda
- Kenya
- Somalia
- Maldives - misses every island, passing between Gaafu Dhaalu Atoll and Gnaviyani Atoll
- Indonesia
- Sumatra - also small islands Tanah Masa to the West and Lingga to the East
- Borneo - Kalimantan
- Sulawesi
- Halmahera - also small islands Kayoa to the West and Gebe to the East
- Kawe, a small island near Waigeo - and other islets throughout Indonesia
- Kiribati - misses every island
- Gilbert Islands - passing between Aranuka and Nonouti Atolls
- Line Islands - passing between Kiritimati Island and Malden Island, though neither is very close to the equator
- Ecuador
- Galapagos Islands - passing through Isabela Island.
- Mainland Ecuador
- Colombia
- Brazil

Degree (angle)

:This article describes "degree" as a unit of angle. For alternative meanings, see degree (disambiguation). ---- A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1／360 of a full rotation. When that angle is with respect to a reference meridian, it indicates a location along a great circle of a sphere (such as Earth, Mars, or the celestial sphere).

History

The number 360 was probably adopted because of the number of days in a year. Primitive calendars, such as the Persian Calendar used 360 days for a year. This was most likely due to watching stars revolve around the North Star forming a circle one degree per day. Its application to measuring angles in geometry can possibly be traced to Thales who popularized geometry among the Greeks and lived in Anatolia (modern western Turkey) among people who had dealings with Egypt and Babylon. The degree and its subdivisions are the only units in use which are written without a separating space between the number and unit symbol (e.g. 15° 30', not 15 ° 30 ').

Further justification

360 is also readily divisible: 360 has 24 divisors (including 1 and 360), including every number from 1 to 10 except 7. For the number of degrees in a circle to be divisible by every number from 1 to 10, there would need to be 2520 degrees in a circle, which is a much less convenient number. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for latitudes and longitudes on the Earth, degree measurements may be written with decimal places, but the traditional sexagesimal unit subdivision is commonly seen. One degree is divided into 60 minutes (of arc), and one minute into 60 seconds (of arc). These units, also called the arcminute and arcsecond, are respectively represented as a single and double prime, or if necessary by a single and double closing quotation mark: for example, 40.1875° = 40° 11' 15". If still more accuracy is required, decimal divisions of the second are normally used, rather than thirds of 1／60 second, fourths of 1／60 of a third, and so on. These (rarely used) subdivisions were noted by writing the Roman numeral for the number of sixtieths in superscript: 1^I for a "prime" (minute of arc), 1^II for a second, 1^III for a third, 1^IV for a fourth, etc. Hence the modern symbols for the minute and second of arc.

Radians

In mathematics, angles in degrees are rarely used, as the convenient divisibility of the number 360 is not so important. For various reasons, mathematicians typically prefer to use the radian (symbol rad, an angle corresponding to an arc of a circle whose length equals the circle's radius (as opposed to its radius of curvature, or arcradius). Thus 180° = π rad, 1° ≈ 0.0174533 rad, and 1 rad ≈ 57.29578°. The radian is also the SI unit of angle.

Metric "decimal" degree

With the invention of the metric system, based on powers of ten, there was an attempt to define a "decimal degree" (grad or gon), so that the number of decimal degrees in a right angle would be 100, and there would be 400 degrees in a circle. Whilst this idea did not gain much momentum, most scientific calculators still support it.

Planet

A planet is generally considered to be a relatively large mass of accreted matter in orbit around a star that is not a star itself. The name comes from the Greek term πλανήτης, planētēs, meaning "wanderer", as ancient astronomers noted how certain lights moved across the sky in relation to the other stars. Based on historical consensus, the International Astronomical Union (IAU) lists nine planets in our solar system. Since the term "planet" has no precise scientific definition, however, many astronomers contest that figure. Some say it should be lowered to eight by removing Pluto from the list, whilst others claim it should be raised to fifteen, twenty, or even higher.

Planetary formation

It is not known with certainty how planets are formed. The prevailing theory is that they are formed from those remnants of a nebula that don't condense under gravity to form a protostar. Instead, these remnants become a thin disc of dust and gas revolving around the protostar and begin to condense about local concentrations of mass within the disc. These concentrations become ever more dense until they collapse inward under gravity to form protoplanets. When the protostar has grown such that it ignites to form a star, its solar wind blows away most of the disc's remaining material. Thereafter there still may be many protoplanets orbiting the star or each other, but over time many will collide, either to form a single larger planet or release material for other larger protoplanets or planets to absorb. Meanwhile, protoplanets that have avoided collisions may become moons of larger planets. With the discovery and observation of planetary systems around stars other than our own, it is becoming possible to elaborate, revise or even replace this account.

Within our solar system

Main article: Solar system The process of naming planets and their features is known as planetary nomenclature. All the currently accepted planets in the solar system are named after Roman gods, except for Uranus (named after a Greek god) and the Earth, which was not seen as a planet by the ancients but rather the centre of the universe. The designated planetary names are near-universal in the Western world, but some non-European languages, such as Chinese, use their own. Moons are also named after gods and characters from classical mythology, or, in the case of Uranus, after Shakespearean characters. Asteroids can be named after anybody or anything at the discretion of their discoverers, subject to approval by the IAU's nomenclature panel.

Accepted planets

Asteroid According to the authority of the IAU, there are nine planets in our solar system. In increasing distance from the Sun they are: #Mercury (astronomical symbol ) #Venus () #Earth () with one confirmed natural satellite, Luna (the Moon) #Mars () with two confirmed natural satellites, Deimos and Phobos #Jupiter () with sixty-three confirmed natural satellites #Saturn () with forty-six confirmed natural satellites #Uranus (Uranus) with twenty-seven confirmed natural satellites #Neptune () with thirteen confirmed natural satellites #Pluto () with three confirmed natural satellites (Charon, S/2005 P 1, S/2005 P 2) However, there is some pressure for Pluto to be reclassified as a Kuiper Belt object, especially in light of the discovery of . This object, however, has not yet received a definitive classification from the IAU.

Other candidates

When Ceres was found orbiting between Mars and Jupiter in 1801, it was initially touted as a planet, but after many smaller objects were found with a similar orbit, it was classified as an asteroid. However, due to its large size (relative to the other asteroids), and its roughly spherical shape, Ceres would be considered a planet by some astronomers' definitions. Similarly, since 1992 many objects have been found in the predicted Kuiper Belt that exists beyond Neptune. Several of the largest of these have challenged the planetary status quo, as they are both spherical and larger than the bodies in the Mars-Jupiter asteroid belt, and are similar in size, orbit and composition to Pluto. However, as yet none have been accepted as planets by the IAU. The most significant of these are (in order of increasing distance from the Sun) 90482 Orcus, , 50000 Quaoar, , , 28978 Ixion, 20000 Varuna, 19521 Chaos, and 90377 Sedna. (However, it should be noted that Sedna is often considered to be beyond the Kuiper Belt; being either a member of the scattered disc or the inner Oort Cloud). Like Ceres before it, Sedna was widely touted as a planet when it was discovered in 2003, as it was the largest object found since Pluto. However, mainly due to its size still being smaller than Pluto's, it did not achieve planetary status from the IAU. However, the discovery in 2005 of (nicknamed Xena), with a size and mass larger than Pluto seems to have forced the issue. As of September 2005 it has not yet been accepted as a planet, but the IAU is expected to announce a definition of a planet by the end of the year, which will either see become a planet, or have Pluto stripped of its status.

Extrasolar planets

:Main article: Extrasolar planet. Of the 173 extrasolar planets (those outside our solar system) discovered to date (October 2005) most have masses which are about the same or larger than Jupiter's. Exceptions include a number of planets discovered orbiting burned-out star remnants called pulsars, such as PSR B1257+12, the planets orbiting the stars Mu Arae, 55 Cancri and GJ 436 which are approximately Neptune-sized [http://www.eso.org/outreach/press-rel/pr-2004/pr-22-04_pf.html], and a planet orbiting Gliese 876 that is estimated to be about 6 to 8 times as massive as the Earth and is probably rocky in origin. It is far from clear if the newly discovered large planets would resemble the gas giants in our solar system or if they are of an entirely different type as yet unknown, like ammonia giants or carbon planets. In particular, some of the newly discovered planets, known as hot Jupiters, orbit extremely close to their parent stars, in nearly circular orbits. They therefore receive much more stellar radiation than the gas giants in our solar system, which makes it questionable whether they are the same type of planet at all. There is also a class of hot Jupiters that orbit so close to their star that their atmospheres are slowly blown away in a comet-like tail: the Chthonian planets. The National Aeronautics and Space Administration of the United States has a program underway to develop a Terrestrial Planet Finder artificial satellite, which would be capable of detecting the planets with masses comparable to terrestrial planets. The frequency of occurrence of these planets is one of the variables in the Drake equation which estimates the number of intelligent, communicating civilizations that exist in our galaxy. Astronomers have recently [http://www.nature.com/news/2005/050711/full/050711-6.html] [http://www.jpl.nasa.gov/news/news.cfm?release=2005-115] detected a planet in a triple star system, a finding that challenges current theories of planetary formation. The planet, a gas giant slightly larger than Jupiter, orbits the main star of the HD 188753 system, in the constellation Cygnus, and is hence known as HD 188753 Ab. The stellar trio (yellow, orange, and red) is about 149 light-years from Earth. The planet, which is at least 14% larger than Jupiter, orbits the main star (HD 188753 A) once every 80 hours or so (3.3 days), at a distance of about 8 Gm, a twentieth of the distance between Earth and the Sun. The other two stars whirl tightly around each other in 156 days, and circle the main star every 25.7 years at a distance from the main star that would put them between Saturn and Uranus in our own Solar System. The latter stars invalidate the leading hot Jupiter formation theory, which holds these planets form at "normal" distances and then migrate inward through some debatable mechanism. This could not have occurred here, the outer star pair disrupting outer planet formation.

Brown dwarf "planets"

The discovery of a planet-sized satellite of a brown dwarf has blurred the distinction between "planet" and "moon." A brown dwarf, though a star in theory, in practice is often described as in between a planet and a star. It is formally defined by the IAU by its official statement that "Substellar objects with true masses above the limiting mass for thermonuclear fusion of deuterium are "brown dwarfs", no matter how they formed nor where they are located." To the IAU, the question of whether an object in orbit around a brown dwarf is a "planet" or a "moon" was simply not relevant, as it does not use the term "moon," only "satellite" and as yet has no official definition for "planet."

Interstellar planets

Interstellar planets are rogues in interstellar space, not gravitationally linked to any given solar system. No interstellar planet is known to date, but their existence is considered a likely hypothesis based on computer simulations of the origin and evolution of planetary systems, which often include the ejection of bodies of significant mass. Such objects are not formally called planets, however, since the IAU has not defined the term "planet".

Definition and classification of planets

Much like "continent", "planet" is a word without a precise definition, with history and culture playing as much of a role as geology and astrophysics. Recent definitions have been vague and imprecise; The American Heritage Dictionary, for instance, formerly defined a planet as: :A nonluminous celestial body larger than an asteroid or comet, illuminated by light from a star, such as the sun, around which it revolves. In the solar system there are nine known planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.' However, for some time that definition has been viewed by many as inadequate. The eight largest planets (which are also the eight nearest to the Sun) are universally recognised as such, and for this reason are often universally referred to as "major planets", but there is controversy over Pluto and other smaller objects.
Suggested wide definitions
Since the discoveries of many of the objects in the Kuiper belt and around other stars, there has been a concerted push amongst scientists to come up with a precise definition of what constitutes a planet. In 1999, the IAU set up a working group to develop a scientifically plausible recommendation, but as of August, 2005 they had not reached a conclusion. After the discovery of (informally called "Xena"), a member of the committee, Alan Stern, has said that the group wanted "to get something done, pronto". He also informed journalists that a "consensus" in the group was moving towards the following definition: :A planet is a body that directly orbits a star, is large enough to be round because of self gravity, and is not so large that it triggers nuclear fusion in its interior. Note that this definition also covers disputes at the upper end of a planet's size, which provides the extra benefit of forming a barrier between planets and brown dwarfs. Many consider this definition the best option as it sets up divisions based on physical characteristics rather than an arbitrary size limit. It is also somewhat universal in its application where other definitions have been crafted mainly to sort our own solar system into simple categories (such as placing the size limit as just under Mars, Mercury or Pluto). Depending how it is interpreted, objects counted as planets under such a new system would include some or all of the objects listed above, with potentially many more yet to be found. Gibor Basri, head of astronomy at the University of Berkeley, has suggested a similar definition and has also proposed the terms "fusor" (any object that achieves fusion in its core) and "planemo" (an object that is round from self-gravity but not a fusor) to help improve the astronomical nomenclature. Under Basri's definition: :A planet is a planemo orbiting a fusor These definitions have the advantage of creating a group including larger moons (which share many characteristics with the smaller planets) and also covering large free-roaming objects, which some astronomers think should be included in the definition of a planet. Basri has also suggested 'liberal use of adjectives' such as "major", "beltway", "dwarf", "giant", "super" and "historical".[http://astron.berkeley.edu/%7Ebasri/defineplanet/Mercury.htm] Others have suggested categories of planet/planemo based on composition such as "rock" (composed mainly of silicate), "gas" (composed mainly of hydrogen and helium), and "ice" (composed mainly of oxygen and carbon).
Suggested narrow definitions
There are alternate suggestions which would instead reduce the number of planets in the system. Upon his discovery of Sedna, Mike Brown of Caltech suggested a definition which would exclude both Sedna and Pluto from being classified as planets, proposing the following: :A planet is any body in the solar system that is more massive than the total mass of all of the other bodies in a similar orbit [http://www.gps.caltech.edu/~mbrown/sedna/#What%20is%20the%20definition%20of%20a%20planet?] This definition generally plays down the importance of size, but instead focuses on the formation of the proposed planet. Under this definition, no Kuiper Belt objects (including Pluto) would be considered planets. Brown's wish to "demote" Pluto prompted many to criticize him for setting out to create a purely scientific definition for a term which had an existing popular (albeit 'flawed') application. Upon his discovery of , Brown indicated he had become a convert to this way of thinking, and proposed that whatever definition of planet be adopted, it should include both Pluto and any Kuiper Belt object found to be larger than Pluto. [http://www.gps.caltech.edu/~mbrown/planetlila/index.html]
Further classification
Astronomers distinguish between minor planets, such as asteroids, comets, and trans-Neptunian objects; and major (or true) planets. Planets within Earth's solar system can be divided into categories according to composition.
- Terrestrial or rocky: Planets that are similar to Earth — with bodies largely composed of rock: Mercury, Venus, Earth, Mars
- Jovian or gas giant: Those with a composition largely made up of gaseous material: Jupiter, Saturn, Uranus, Neptune. Uranian planets, or ice giants, are a sub-class of gas giants, distinguished from true Jovians by their depletion in hydrogen and helium and a significant composition of rock and ice.
- Icy: Sometimes a third category is added to include bodies like Pluto, whose composition is primarily ice; this category of "icy" bodies also includes many non-planetary bodies such as the icy moons of the outer planets of our solar system (e.g. Triton). Many consider the Earth and its Moon to be a double planet, for several reasons:
- The Moon, as measured by its diameter, is 1.5 times larger than Pluto.
- The gravitational force of the Sun on the Moon is larger than the gravitational force of the Earth on the Moon by a factor of approx. 2.2. (This is not a unique situation in the solar system. The Sun's gravity is also stronger than the primary's on Jupiter's moon S/2003 J 2; Uranus' moon S/2001 U 2; Neptune's moons S/2002 N 4 and Psamathe; and several asteroid moons. However, Luna is the sole case of this phenomenon affecting an object of planetary mass.)
See also

- Definition of planet
- Planetary habitability
- Planetary science
- Planemo
- Planetoid
- Brown Dwarf
- Planets in science fiction
- Prograde and retrograde motion
- Skies of other planets
References

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External links

- [http://www.nineplanets.org/ NinePlanets.org] - tour of the solar system
- [http://www.iau.org International Astronomical Union]
- [http://www.fourmilab.ch/cgi-bin/uncgi/Solar/ Solar System Live] (an interactive orrery)
- [http://janus.astro.umd.edu/javadir/orbits/ssv.html Solar System Viewer] (animation)
- [http://www.sky-pics.net/ Pictures of the solar system]
- [http://gw.marketingden.com/planets/sun.html Renderings of the planets]
- [http://planetquest.jpl.nasa.gov/ NASA Planet Quest]
- [http://www.ciw.edu/IAU/div3/wgesp/definition.html Working definition of "planet"] from IAU WGESP — the lower bound remained a matter of consensus in February 2003
- Dan Green's page on [http://cfa-www.harvard.edu/cfa/ps/icq/ICQPluto.html planet classification]
- [http://www.spacedaily.com/news/outerplanets-04b.html Gravity Rules: The Nature and Meaning of Planethood]; S. Alan Stern; March 22, 2004
- [http://www.iau.org/IAU/FAQ/PlutoPR.html On the status of Pluto]; IAU, February 3, 1999
- als:Planet ko:행성 ms:Planet ja:惑星 simple:Planet th:ดาวเคราะห์ zh-min-nan:He̍k-chheⁿ

Sun

:: For the astrological significance of the Sun, see Solar system in astrology. ::"Solar" redirects here; for the superhero by that name, see Solar (comics). The Sun (or Sol) is the star at the center of our Solar system. Earth orbits the Sun, as do many other bodies, including other planets, asteroids, meteoroids, comets and dust. Its heat and light support almost all life on Earth. The Sun is a ball of plasma with a mass of about 2 kg, which is somewhat higher than that of an average star. About 74% of its mass is hydrogen, with 25% helium and the rest made up of trace quantities of heavier elements. It is thought that the Sun is about 5 billion years old, and is about halfway through its main sequence evolution, during which nuclear fusion reactions in its core fuse hydrogen into helium. In about 5 billion years time the Sun will become a white dwarf. Although it is the nearest star to Earth and has been intensively studied by scientists, many questions about the Sun remain unanswered, such as why its outer atmosphere has a temperature of over 10⁶ K when its visible surface (the photosphere) has a temperature of just 6,000 K. Looking directly at the Sun can damage the retina and one's eyesight. See below for details.

General information

See below The Sun is classified as a main sequence star, which means it is in a state of "hydrostatic balance", neither contracting nor expanding, and is generating its energy through nuclear fusion of hydrogen nuclei into helium. The Sun has a spectral class of G2V, with the G2 meaning that its color is yellow and its spectrum contains spectral lines of ionized and neutral metals as well as very weak hydrogen lines [http://www.astro.uiuc.edu/~kaler/sow/spectra.html#classes], and the V signifying that it, like most stars, is a "dwarf" star on the main sequence[http://www.physics.uq.edu.au/people/ross/phys2080/spec/analyz.htm]. The Sun has a predicted main sequence lifetime of about 10 billion years. Its current age is thought to be about 4.5 billion years, a figure which is determined using computer models of stellar evolution, and nucleocosmochronology . The Sun orbits the center of the Milky Way galaxy at a distance of about 25,000 to 28,000 light-years from the galactic centre, completing one revolution in about 226 million years. The orbital speed is 217 km/s, equivalent to one light year every 1400 years, and one AU every 8 days. The astronomical symbol for the Sun is a circle with a point at its centre (Image:Sol.gif).

Structure

Image:Sol.gif The Sun is a near-perfect sphere, with an oblateness estimated at about 9 millionths, which means the polar diameter differs from the equatorial by about 10 km. This is because the centrifugal effect of the Sun's slow rotation is 18 million times weaker than its surface gravity (at the equator). Tidal effects from the planets do not significantly affect the shape of the Sun, although the Sun itself orbits the center of mass of the solar system, which is offset from the Sun's center mostly because of the large mass of Jupiter. The mass of the Sun is so comparatively great that the center of mass of the solar system is generally within the bounds of the Sun itself. The Sun does not have a definite boundary as rocky planets do, as the density of its gases drops off following an approximately exponential relationship with distance from the centre of the Sun. Nevertheless, the Sun has well defined interior structure, described below. The Sun's radius is measured from centre to the edges of the photosphere. The solar interior is not directly observable and the Sun itself is opaque to electromagnetic radiation. However, just as the study of the waves generated by earthquakes (seismology) can be used to study the interior structure of the Earth, helioseismology, the study of sound waves that travel through the Sun's interior, has also contributed greatly to our understanding of the Sun's structure . Computer modeling of the Sun is also used as a theoretical tool to investigate its deep layers.

Core

At the center of the Sun, where its density reaches up to 150,000 kg/m³ (150 times the density of water on Earth), thermonuclear reactions (nuclear fusion) convert hydrogen into helium, producing the energy that keeps the Sun in a state of equilibrium. About 8.9 protons (hydrogen nuclei) are converted to helium nuclei every second, releasing energy at the matter-energy conversion rate of 4.26 million tonnes per second or 383 yottawatts (9.15 tons of TNT per second). The core extends from the center of the Sun to about 0.2 solar radii, and is the only part of the Sun where an appreciable amount of heat is produced by fusion: the rest of the star is heated by energy that is transferred outward. All of the energy of the interior fusion must travel through the successive layers to the solar photosphere, before it escapes to space. The high-energy photons (gamma and X rays) released in fusion reactions take a long time to reach the Sun's surface, slowed down by the indirect path taken, as well as constant absorption and re-emission at lower energies in the solar mantle (see below). Estimates of the "photon travel time" range from as much as 50 million years (Richard S. Lewis, The Illustrated Encyclopedia of the Universe, Harmony Books, New York, 1983, p. 65) to as little as 17,000 years [http://www.badastronomy.com/bitesize/solar_system/sun.html]. Upon reaching the surface after a final trip through the convective outer layer, the photons escape as visible light. Neutrinos are also released in the fusion reactions in the core, but unlike photons they very rarely interact with matter, and so almost all are able to escape the Sun immediately.

Radiation zone

From about 0.2 to about 0.7 solar radii, the material is hot and dense enough that thermal radiation is sufficient to transfer the intense heat of the core outward. In this zone, there is no thermal convection: while the material grows cooler with altitude, this temperature gradient is slower than the adiabatic lapse rate and hence cannot drive convection. Heat is transferred by ions of hydrogen and helium emitting photons, which travel a brief distance before being re-absorbed by other ions. Because of this, it can take a photon nearly 1,000,000 years to reach the photosphere.

Convection zone

photosphere From about 0.7 solar radii to 1.0 solar radii, the material in the Sun is not dense enough or hot enough to transfer the heat energy of the interior outward via radiation. As a result, thermal convection occurs as thermal columns carry hot material to the surface (photosphere) of the Sun. Once the material cools off at the surface, it plunges back downward to the base of the convection zone, to receive more heat from the top of the radiative zone. Convective overshoot is thought to occur at the base of the convection zone, carrying turbulent downflows into the outer layers of the radiative zone. The thermal columns in the convection zone form an imprint on the surface of the Sun, in the form of the solar granulation and supergranulation. The turbulent convection of this outer part of the solar interior gives rise to a 'small-scale' dynamo that produces magnetic north and south poles all over the surface of the Sun.

Photosphere

The visible surface of the Sun, the photosphere, is the layer below which the Sun becomes opaque to visible light. Above the photosphere, sunlight is free to propagate into space and its energy escapes the Sun entirely. Sunlight has approximately a black-body spectrum that indicates its temperature is about 6,000 K, interspersed with atomic absorption lines from the tenuous layers above the photosphere. The photosphere has a particle density of about 10²³/m³ (this is about 1% of the particle density of Earth's atmosphere at sea level). The parts of the Sun above the photosphere are referred to collectively as the solar atmosphere. They can be viewed with telescopes operating across the electromagnetic spectrum, from radio through visible light to gamma rays.

Temperature minimum

The coolest layer of the Sun is the temperature minimum region about 500 km above the photosphere. It is about 4,000 K. It is the only part of the Sun cool enough to support simple molecules such as carbon monoxide and water; all other parts of the Sun are hot enough to break chemical bonds.

Chromosphere

Above the visible surface of the Sun is a thin layer, about 2,000 km thick, that is dominated by a spectrum of emission and absorption lines. It is called the chromosphere from the Greek root chromos, meaning color, because the chromosphere is visible as a colored flash at the beginning and end of total eclipses of the Sun.

Corona

The corona is the extended outer atmosphere of the Sun, which is much larger in volume than the Sun itself. The corona merges smoothly with the solar wind that fills the solar system and heliosphere. The low corona, which is very near the surface of the Sun, has a particle density of 10¹¹/m³ (Earth's atmosphere near sea level has a particle density of about 2x10²⁵/m³). The temperature of the corona is several megakelvins.

Theoretical problems

Solar neutrino problem

megakelvin For some time it was thought that the number of neutrinos produced by the nuclear reactions in the Sun was only a third of the number predicted by theory, a result that was termed the solar neutrino problem. Several neutrino observatories were constructed, including the Sudbury Neutrino Observatory and Kamiokande to try to measure the solar neutrino flux. It has recently been found that neutrinos have rest mass, and can therefore transform into harder-to-detect varieties of neutrinos while en route from the Sun to Earth in a process known as neutrino oscillation . Thus, measurement and theory have been reconciled.

Coronal heating problem

The optical surface of the Sun (the photosphere) is known to have a temperature of about 6,000 K. Above it lies the solar corona with a temperature of one million kelvins. The high temperature of the corona suggests that it is heated by something other than the photosphere. It is thought that the energy necessary to heat the corona is provided by turbulent motion in the convection zone below the photosphere. Two main mechanisms have been proposed to explain coronal heating: Wave heating, in which sound, gravitational and magnetohydrodynamic waves are produced by turbulence in the convection zone. These waves travel upward and dissipate in the corona, depositing their energy in the ambient gas in the form of heat. The other proposed mechanism is flare heating, in which magnetic energy is continuously built up by photospheric motion and released through magnetic reconnection in the form of solar flares and waves. , , , . Currently, it is unclear whether waves are an efficient heating mechanism. All waves except Alfven waves have been found to dissipate or refract before reaching the corona (, ). In addition, Alfven waves do not easily dissipate in the corona . Current research focus has therefore shifted towards flare heating mechanisms. One possible candidate to explain coronal heating is continuous flaring at small scales , but this is still an open topic of investigation.

Faint young sun problem

Theoretical models of the sun's development suggest that 3.8 to 2.5 billion years ago, during the Archean period, the Sun was only about 75 percent as bright as it is today. Such a weak star would not have been able to sustain liquid water on the Earth's surface, and thus life should not have been able to develop. However, the geologic record shows that the Earth has remained at a fairly constant temperature throughout its history. In fact, the young Earth was actually warmer than it is today. Some scientists have suggested that the young Earth's atmosphere contained much larger quantities of greenhouse gases such as carbon dioxide and/or ammonia than are present today . Others suggest that cosmic rays might strongly influence the Earth's climate, and that their flux was much higher in the early history of the solar system .

Magnetic field

cosmic ray's rotating magnetic field on the plasma in the interplanetary medium (Solar Wind) [http://quake.stanford.edu/~wso/gifs/HCS.html]. (click to enlarge)]] All matter in the Sun is in the form of gas and plasma due to its high temperatures. This makes it possible for the Sun to rotate faster at its equator (about 25 days) than it does at higher latitudes (28 days near its poles). The differential rotation of the Sun's latitudes causes its magnetic field lines to become twisted together over time, causing magnetic field loops to erupt from the Sun's surface and trigger the formation of the Sun's dramatic sunspots and solar prominences. (See magnetic reconnection.) The solar activity cycle includes old magnetic fields being stripped off the Sun's surface starting from one pole and ending at the other. The magnetic field of the sun reverses once for each 11-year sunspot cycle. The influence of the Sun's rotating magnetic field on the plasma in the interplanetary medium creates the largest structure in the Solar System, the Heliospheric current sheet. The plasma in the interplanetary medium is also responsible for the strength of the Sun's magnetic field at the orbit of the Earth being over 100 times greater than originally anticipated. If space were a vacuum, then the Sun's 10^-4 tesla magnetic dipole field would reduce with the cube of the distance to about 10^-11 tesla. But satellite observations show that it is about 100 times greater at around 10^-9 tesla. Magnetohydrodynamic (MHD) theory predicts that the motion of a conducting fluid (e.g. the interplanetary medium) in a magnetic field, induces electric currents which in turn generates magnetic fields, and in this respect it behaves like an MHD dynamo.

Position of the Sun through the year

The path of the Sun across the sky varies throughout the year. The shape described by the Sun's position, considered at the same time each day for a complete year, is called the analemma, and resembles a figure 8, aligned along the North/South direction. The most obvious variation in the Sun's apparent position through the year is a North/South swing over 47 degrees of angle, due to the 23.5 degree tilt of the Earth, but there is an East/West component as well. The North/South swing in apparent angle is the main source of seasons on Earth.

Solar space missions

seasons using UV light from the He⁺ emission line at 30.4 nm. (Animation (980 kB MPEG))]] To obtain an uninterrupted view of the Sun, the European Space Agency and NASA cooperatively launched the Solar and Heliospheric Observatory (SOHO) on December 2, 1995. Originally a two-year mission, SOHO is now over ten years old (as of late 2005). It has proved so useful that a follow-on mission, the Solar Dynamics Observatory, is planned for launch in 2008. Elemental abundances in the photosphere are well known from spectroscopic studies, but the composition of the interior of the Sun is much less well known. A solar wind sample return mission, Genesis, was designed to allow astronomers to directly measure the composition of solar material. It returned to Earth in 2004 and is undergoing analysis, but it was damaged by crash-landing when its parachute failed to deploy on reentry to Earth's atmosphere.

History and future of the Sun

The Sun is thought to be a second-generation star, whose formation may have been triggered by shockwaves from a nearby supernova. This is suggested by a high abundance of heavy elements such as iron, gold and uranium in the solar system: the most plausible ways that these elements could be produced are by endothermic nuclear reactions during a supernova or by transmutation via neutron absorption inside a massive first generation star. Our Sun does not have enough mass to explode as a supernova, and its mass is below the Chandrasekhar limit. Instead, in 4-5 billion years it will enter its red giant phase, its outer layers expanding as the hydrogen fuel in the core is consumed and the core contracts and heats up. Helium fusion will begin when the core temperature reaches about 3 K. While it is likely that the expansion of the outer layers of the Sun will reach the current position of Earth's orbit, recent r