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44-466: The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun . From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars . The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system . The ecliptic is the apparent path of

88-498: A particular equinox, that is, the equinox of a particular date, known as an epoch ; the coordinates are referred to the direction of the equinox at that date. For instance, the Astronomical Almanac lists the heliocentric position of Mars at 0h Terrestrial Time , 4 January 2010 as: longitude 118°09′15.8″, latitude +1°43′16.7″, true heliocentric distance 1.6302454 AU, mean equinox and ecliptic of date. This specifies

132-476: A relatively short time span, perhaps several centuries. J. Laskar computed an expression to order T good to 0.04″ /1000 years over 10,000 years. All of these expressions are for the mean obliquity, that is, without the nutation of the equator included. The true or instantaneous obliquity includes the nutation. Most of the major bodies of the Solar System orbit the Sun in nearly the same plane. This

176-507: A short-duration time span, perhaps a few centuries, is represented to high accuracy. Some long ephemerides cover several millennia to medium accuracy. They are published by the Jet Propulsion Laboratory as Development Ephemeris . The latest releases include DE430 which covers planetary and lunar ephemeris from Dec 21, 1549 to Jan 25, 2650 with high precision and is intended for general use for modern time periods . DE431

220-551: A span of decades by many researchers. The independent variable of the ephemeris is always time. In the case of the most current ephemerides, it is a relativistic coordinate time scale equivalent to the IAU definition of TCB . In the past, mean solar time (before the discovery of the non-uniform rotation of the Earth ) and ephemeris time (before the implementation of relativistic gravitational equations ) were used. The remainder of

264-529: Is a simplification. Periodic motions of the Moon and apparent periodic motions of the Sun (actually of Earth in its orbit) cause short-term small-amplitude periodic oscillations of Earth's axis, and hence the celestial equator, known as nutation . This adds a periodic component to the position of the equinoxes; the positions of the celestial equator and (March) equinox with fully updated precession and nutation are called

308-477: Is also used occasionally; the x -axis is directed toward the March equinox, the y -axis 90° to the east, and the z -axis toward the north ecliptic pole; the astronomical unit is the unit of measure. Symbols for ecliptic coordinates are somewhat standardized; see the table. Ecliptic coordinates are convenient for specifying positions of Solar System objects, as most of the planets' orbits have small inclinations to

352-488: Is divided into 12 signs of 30° longitude, each of which approximates the Sun's motion in one month. In ancient times, the signs corresponded roughly to 12 of the constellations that straddle the ecliptic. These signs are sometimes still used in modern terminology. The " First Point of Aries " was named when the March equinox Sun was actually in the constellation Aries ; it has since moved into Pisces because of precession of

396-471: Is likely due to the way in which the Solar System formed from a protoplanetary disk . Probably the closest current representation of the disk is known as the invariable plane of the Solar System . Earth's orbit, and hence, the ecliptic, is inclined a little more than 1° to the invariable plane, Jupiter's orbit is within a little more than ½° of it, and the other major planets are all within about 6°. Because of this, most Solar System bodies appear very close to

440-533: Is near an ascending or descending node at the same time it is at conjunction ( new ) or opposition ( full ). The ecliptic is so named because the ancients noted that eclipses only occur when the Moon is crossing it. The exact instants of equinoxes and solstices are the times when the apparent ecliptic longitude (including the effects of aberration and nutation ) of the Sun is 0°, 90°, 180°, and 270°. Because of perturbations of Earth's orbit and anomalies of

484-410: Is projected outward to the celestial sphere , forming the celestial equator , it crosses the ecliptic at two points known as the equinoxes . The Sun, in its apparent motion along the ecliptic, crosses the celestial equator at these points, one from south to north, the other from north to south. The crossing from south to north is known as the March equinox , also known as the first point of Aries and

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528-581: The Bureau des Longitudes was founded in 1795 to publish the Connaissance des Temps . The early fundamental ephemerides of these publications came from many different sources and authors as the science of celestial mechanics matured. At the end of the 19th century, the analytical methods of general perturbations reached the probable limits of what could be accomplished by hand calculation. The planetary "theories" of Newcomb and Hill formed

572-514: The ascending node of the ecliptic on the celestial equator. The crossing from north to south is the September equinox or descending node . The orientation of Earth's axis and equator are not fixed in space, but rotate about the poles of the ecliptic with a period of about 26,000 years, a process known as lunisolar precession , as it is due mostly to the gravitational effect of the Moon and Sun on Earth's equatorial bulge . Likewise,

616-460: The Solar System is a model of the objects of the system in space, with all of their positions and motions accurately represented. It is intended to be a high-precision primary reference for prediction and observation of those positions and motions, and which provides a basis for further refinement of the model. It is generally not intended to cover the entire life of the Solar System; usually

660-399: The equations of motion on early computing machines for purposes of producing fundamental ephemerides for the Astronomical Almanac . Jupiter, Saturn, Uranus, Neptune, and Pluto were based on the work of Eckert, et al . and Clemence through 1983. The fundamental ephemeris of the Moon, always a difficult problem in celestial mechanics, remained a work-in-progress through the early 1980s. It

704-407: The mean equinox of 4 January 2010 0h TT as above , without the addition of nutation. Because the orbit of the Moon is inclined only about 5.145° to the ecliptic and the Sun is always very near the ecliptic, eclipses always occur on or near it. Because of the inclination of the Moon's orbit, eclipses do not occur at every conjunction and opposition of the Sun and Moon, but only when the Moon

748-446: The true equator and equinox ; the positions without nutation are the mean equator and equinox . Obliquity of the ecliptic is the term used by astronomers for the inclination of Earth's equator with respect to the ecliptic, or of Earth's rotation axis to a perpendicular to the ecliptic. It is about 23.4° and is currently decreasing 0.013 degrees (47 arcseconds) per hundred years because of planetary perturbations. The angular value of

792-399: The Sun about four minutes later each day than it would if Earth did not orbit; a day on Earth is therefore 24 hours long rather than the approximately 23-hour 56-minute sidereal day . Again, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun. The actual speed with which Earth orbits the Sun varies slightly during the year, so the speed with which

836-502: The Sun seems to move along the ecliptic also varies. For example, the Sun is north of the celestial equator for about 185 days of each year, and south of it for about 180 days. The variation of orbital speed accounts for part of the equation of time . Because of the movement of Earth around the Earth–Moon center of mass , the apparent path of the Sun wobbles slightly, with a period of about one month . Because of further perturbations by

880-449: The Sun throughout the course of a year . Because Earth takes one year to orbit the Sun, the apparent position of the Sun takes one year to make a complete circuit of the ecliptic. With slightly more than 365 days in one year, the Sun moves a little less than 1° eastward every day. This small difference in the Sun's position against the stars causes any particular spot on Earth's surface to catch up with (and stand directly north or south of)

924-624: The Sun, Moon, and planets. From 2003 onward (as of Feb 2012), JPL's DE405/LE405 , an integrated ephemeris referred to the International Celestial Reference Frame , has been used. In France, the Bureau des Longitudes began using their machine-generated semi-analytical theory VSOP82 in 1984, and their work continued with the founding of the Institut de mécanique céleste et de calcul des éphémérides in 1998 and

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968-457: The calendar , the dates of these are not fixed. The ecliptic currently passes through the following thirteen constellations : There are twelve constellations that are not on the ecliptic, but are close enough that the Moon and planets can occasionally appear in them. The ecliptic forms the center of the zodiac , a celestial belt about 20° wide in latitude through which the Sun, Moon, and planets always appear to move. Traditionally, this region

1012-408: The celestial equator. Spherical coordinates , known as ecliptic longitude and latitude or celestial longitude and latitude, are used to specify positions of bodies on the celestial sphere with respect to the ecliptic. Longitude is measured positively eastward 0° to 360° along the ecliptic from the March equinox, the same direction in which the Sun appears to move. Latitude is measured perpendicular to

1056-474: The course of a year. In other cases, for instance a moon or artificial satellite orbiting another planet, it is convenient to define the inclination of the Moon's orbit as the angle between its orbital plane and the planet's equatorial plane . The coordinate system defined that uses the orbital plane as the x y {\displaystyle xy} plane is known as the perifocal coordinate system . For launch vehicles and artificial satellites,

1100-405: The ecliptic in the sky. The invariable plane is defined by the angular momentum of the entire Solar System, essentially the vector sum of all of the orbital and rotational angular momenta of all the bodies of the system; more than 60% of the total comes from the orbit of Jupiter. That sum requires precise knowledge of every object in the system, making it a somewhat uncertain value. Because of

1144-409: The ecliptic itself is not fixed. The gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of Earth's orbit, and hence of the ecliptic, known as planetary precession . The combined action of these two motions is called general precession , and changes the position of the equinoxes by about 50 arc seconds (about 0.014°) per year. Once again, this

1188-412: The ecliptic, and therefore always appear relatively close to it on the sky. Because Earth's orbit, and hence the ecliptic, moves very little, it is a relatively fixed reference with respect to the stars. Because of the precessional motion of the equinox , the ecliptic coordinates of objects on the celestial sphere are continuously changing. Specifying a position in ecliptic coordinates requires specifying

1232-436: The ecliptic, to +90° northward or −90° southward to the poles of the ecliptic, the ecliptic itself being 0° latitude. For a complete spherical position, a distance parameter is also necessary. Different distance units are used for different objects. Within the Solar System, astronomical units are used, and for objects near Earth , Earth radii or kilometers are used. A corresponding right-handed rectangular coordinate system

1276-548: The ephemeris can consist of either the mathematical equations and initial conditions which describe the motions of the bodies of the Solar System, of tabulated data calculated from those equations and conditions, or of condensed mathematical representations of the tabulated data. A fundamental ephemeris is the basis from which apparent ephemerides, phenomena, and orbital elements are computed for astronomical, nautical, and surveyors' almanacs. Apparent ephemerides give positions and motions of Solar System bodies as seen by observers from

1320-414: The equinoxes . Orbital plane The orbital plane is defined in relation to a reference plane by two parameters : inclination ( i ) and longitude of the ascending node (Ω). By definition, the reference plane for the Solar System is usually considered to be Earth's orbital plane, which defines the ecliptic , the circular path on the celestial sphere that the Sun appears to follow over

1364-617: The fundamental ephemerides of the Nautical Almanac at that time. For the Sun, Mercury, Venus, and Mars, the tabulations of the Astronomical Almanac continued to be derived from the work of Newcomb and Ross through 1983. In France, the works of LeVerrier and Gaillot formed the fundamental ephemeris of the Connaissance des Temps . From the mid 20th century, work began on numerical integration of

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1408-426: The most current knowledge of all relevant physical forces and effects. Current fundamental ephemerides are typically released with exact descriptions of all mathematical models, methods of computation, observational data, and adjustment to the observations at the time of their announcement. This may not have been the case in the past, as fundamental ephemerides were then computed from a collection of methods derived over

1452-495: The motion of a body at a particular instant, used for further short-time-span calculation of the body's position when high accuracy is not required. Astronomers have been tasked with computing accurate ephemerides, originally for purposes of sea navigation, from at least the 18th century. In England, Charles II founded the Royal Observatory in 1675, which began publishing The Nautical Almanac in 1766. In France,

1496-441: The obliquity is found by observation of the motions of Earth and other planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived. Until 1983 the obliquity for any date was calculated from work of Newcomb , who analyzed positions of

1540-477: The orbital plane is a defining parameter of an orbit; as in general, it will take a very large amount of propellant to change the orbital plane of an object. Other parameters, such as the orbital period , the eccentricity of the orbit and the phase of the orbit are more easily changed by propulsion systems. Orbital planes of satellites are perturbed by the non-spherical nature of the Earth's gravity . This causes

1584-477: The orbital plane of the satellite's orbit to slowly rotate around the Earth, depending on the angle the plane makes with the Earth's equator. For planes that are at a critical angle this can mean that the plane will track the Sun around the Earth, forming a Sun-synchronous orbit . A launch vehicle's launch window is usually determined by the times when the target orbital plane intersects the launch site. Fundamental ephemeris A fundamental ephemeris of

1628-401: The other planets of the Solar System , the Earth–Moon barycenter wobbles slightly around a mean position in a complex fashion. Because Earth's rotational axis is not perpendicular to its orbital plane , Earth's equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23.4°, which is known as the obliquity of the ecliptic . If the equator

1672-512: The planets until about 1895: ε = 23°27′08.26″ − 46.845″ T − 0.0059″ T + 0.00181″ T where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question. From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac . Obliquity based on DE200, which analyzed observations from 1911 to 1979,

1716-466: The sky's distant background. The ecliptic forms one of the two fundamental planes used as reference for positions on the celestial sphere, the other being the celestial equator . Perpendicular to the ecliptic are the ecliptic poles , the north ecliptic pole being the pole north of the equator. Of the two fundamental planes, the ecliptic is closer to unmoving against the background stars, its motion due to planetary precession being roughly 1/100 that of

1760-461: The surface of Earth, and are useful for astronomers, navigators, and surveyors in planning observations and in reducing the data acquired, although much of the work of latter two has been supplanted by GPS technology. Phenomena are events related to the configurations of Solar System bodies, for instance rise and set times, phases , eclipses and occultations , and have many civil and scientific applications. Orbital elements are descriptions of

1804-399: The uncertainty regarding the exact location of the invariable plane, and because the ecliptic is well defined by the apparent motion of the Sun, the ecliptic is used as the reference plane of the Solar System both for precision and convenience. The only drawback of using the ecliptic instead of the invariable plane is that over geologic time scales, it will move against fixed reference points in

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1848-441: Was based originally on the work of Brown, with updates and corrections by Clemence, et al . and Eckert, et al . Starting in 1984, a revolution in the methods of producing fundamental ephemerides began. From 1984 through 2002, the fundamental ephemeris of the Astronomical Almanac was the Jet Propulsion Laboratory 's DE200/LE200 , a fully numerically-integrated ephemeris fitted to modern position and velocity observations of

1892-435: Was calculated: ε = 23°26′21.45″ − 46.815″ T − 0.0006″ T + 0.00181″ T where hereafter T is Julian centuries from J2000.0 . JPL's fundamental ephemerides have been continually updated. The Astronomical Almanac for 2010 specifies: ε = 23°26′21.406″ − 46.836769″ T − 0.0001831″ T + 0.00200340″ T − 0.576×10″ T − 4.34×10″ T These expressions for the obliquity are intended for high precision over

1936-651: Was created to cover a longer time period Aug 15, -13200 to March 15, 17191 with slightly less precision for use with historic observations and far reaching forecasted positions. DE432 was released as a minor update to DE430 with improvements to the Pluto barycenter in support of the New Horizons mission. The set of physical laws and numerical constants used in the calculation of the ephemeris must be self-consistent and precisely specified. The ephemeris must be calculated strictly in accordance with this set, which represents

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