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588 Achilles
Achilles ( minor planet designation: 588 Achilles) is a large Jupiter trojan asteroid of the Greek camp. Achilles was the first Jupiter trojan to be discovered, and was discovered by Max Wolf at the Heidelberg Observatory in 1906. Wolf named the minor planet after the legendary hero Achilles from Greek mythology. The dark D-type asteroid measures approximately in diameter which makes it one of the 10 largest Jupiter trojans. It has a rotation period of 7.3 hours and possibly a spherical shape. Discovery ''Achilles'' was discovered on 22 February 1906, by the German astronomer Max Wolf at the Heidelberg-Königstuhl State Observatory in southern Germany. It was the first discovery of a Jupiter trojan, although had been observed as ' two years previously. This body, however, remained unconfirmed as the observation period was not long enough to calculate an orbit. August Kopff, a colleague of Wolf at Heidelberg, then discovered 617 Patroclus eight months after ''Achilles'', ...
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Modelled Shape Of 588 Achilles From Its Light Curve
A model is a person with a role either to promote, display or advertise commercial products (notably fashion clothing in fashion shows) or to serve as a visual aid for people who are creating works of art or to pose for photography. Though models are predominantly female, there are also male models, especially to model clothing. Models may work professionally or casually. Modelling ("modeling" in American English) is considered to be different from other types of public performance, such as acting or dancing. Although the difference between modelling and performing is not always clear, appearing in a film or a play is not generally considered to be "modelling". Similarly, appearing in a TV advertisement is generally not considered modelling. Modelling generally does not involve speaking. Personal opinions are generally not expressed and a model's reputation and image are considered critical. Types of modelling include: fashion, glamour, fitness, bikini, fine art, body-part, ...
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Heidelberg Observatory
Heidelberg (; Palatine German: '''') is a city in the German state of Baden-Württemberg, situated on the river Neckar in south-west Germany. As of the 2016 census, its population was 159,914, of which roughly a quarter consisted of students. Located about south of Frankfurt, Heidelberg is the fifth-largest city in Baden-Württemberg. Heidelberg is part of the densely populated Rhine-Neckar Metropolitan Region. Heidelberg University, founded in 1386, is Germany's oldest and one of Europe's most reputable universities. Heidelberg is a scientific hub in Germany and home to several internationally renowned research facilities adjacent to its university, including the European Molecular Biology Laboratory and four Max Planck Institutes. The city has also been a hub for the arts, especially literature, throughout the centuries, and it was designated a "City of Literature" by the UNESCO Creative Cities Network. Heidelberg was a seat of government of the former Electora ...
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Joseph Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaJoseph-Louis Lagrange, comte de l’Empire
''Encyclopædia Britannica''
or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an and , later naturalized
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Three-body Problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the -body problem. Unlike two-body problems, no general closed-form solution exists, as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun. In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles. Mathematical description The mathematical statement of the three-body problem can be given in terms of the Newtonian equations of motion for vector positions \mathbf = (x_i, y_i, z_i) ...
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Ecliptic
The ecliptic or ecliptic plane is the orbital plane of the 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. Sun's apparent motion The ecliptic is the apparent path of 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) the Sun about four minutes later each day than it would if Earth did not orbit; a day on Earth is therefore 24 hours ...
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Orbital Inclination
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°. Orbits The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the orbital plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator. For pl ...
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Orbital Eccentricity
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy. Definition In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: * circular orbit: ''e'' = 0 * elliptic orbit: 0 < ''e'' < 1 *
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Semi-major Axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the cente ...
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Jupiter
Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth the mass of the Sun. Jupiter is the third brightest natural object in the Earth's night sky after the Moon and Venus, and it has been observed since prehistoric times. It was named after the Roman god Jupiter, the king of the gods. Jupiter is primarily composed of hydrogen, but helium constitutes one-quarter of its mass and one-tenth of its volume. It probably has a rocky core of heavier elements, but, like the other giant planets in the Solar System, it lacks a well-defined solid surface. The ongoing contraction of Jupiter's interior generates more heat than it receives from the Sun. Because of its rapid rotation, the planet's shape is an oblate spheroid: it has a slight but noticeable bulge around the equator. The outer atmosphere i ...
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Lagrangian Point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem in which two bodies are far more massive than the third. Normally, the two massive bodies exert an unbalanced gravitational force at a point, altering the orbit of whatever is at that point. At the Lagrange points, the gravitational forces of the two large bodies and the centrifugal force balance each other. This can make Lagrange points an excellent location for satellites, as few orbit corrections are needed to maintain the desired orbit. Small objects placed in orbit at Lagrange points are in equilibrium in at least two directions relative to the center of mass of the large bodies. For any combination of two orbital bodies there are five Lagrange points, L1 to L5, all in the orbital plane of the two ...
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624 Hektor
624 Hektor is the largest Jupiter trojan and the namesake of the Hektor family, with a highly elongated shape equivalent in volume to a sphere of approximately 225 to 250 kilometers diameter. It was discovered on 10 February 1907, by astronomer August Kopff at Heidelberg Observatory in southwest Germany, and named after the Trojan prince Hector, from Greek mythology. It has one small 12-kilometer sized satellite, Skamandrios, discovered in 2006. Description ''Hektor'' is a D-type asteroid, dark and reddish in colour. It lies in Jupiter's leading Lagrangian point, , called the Greek camp after one of the two sides in the legendary Trojan War. Hektor is named after the Trojan hero Hektor and is thus one of two trojan asteroids that is "misplaced" in the wrong camp (the other one being 617 Patroclus in the Trojan camp). Contact-binary hypothesis Hektor is one of the most elongated bodies of its size in the Solar System, being approximately 403 km in its longest ...
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617 Patroclus
617 Patroclus ( ) is a large binary Jupiter trojan asteroid. It is a dark D-type asteroid and a slow rotator, due to the 103-hour orbital period of its two components. It is one of five Jovian asteroids targeted by the ''Lucy'' space probe, and is scheduled for a flyby in 2033. Patroclus was discovered on 17 October, 1906, by astronomer August Kopff at the Heidelberg Observatory in Germany, and was named after Patroclus in Greek mythology. It was the second trojan to be discovered and the only member of the Trojan camp named after a Greek figure, as the convention of naming one 'camp' after Greek figures of the Trojan War and the other after Trojan figures had not yet been established. Patroclus was long thought to be one of the largest Jupiter trojans, with a diameter on the order of 150 km. However, in 2001 it was discovered to be a binary asteroid of two similarly sized objects. The name ''Patroclus'' is now assigned to the larger component, some 110–115 km in diame ...
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