Hirayama Family
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Hirayama Family
A Hirayama family of asteroids is a group of minor planets that share similar orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. Strictly speaking, families and their membership are identified by analysing the so-called proper orbital elements rather than the current osculating orbital elements, which regularly fluctuate on timescales of tens of thousands of years. The ''proper elements'' are related constants of motion that are thought to remain almost constant for times of at least tens of millions of years. The Japanese astronomer Kiyotsugu Hirayama (1874–1943) pioneered the estimation of proper elements for asteroids, and first identified several of the most prominent families in 1918. Kiyotsugu Hirayama initially identified the Koronis, Eos, and Themis families, and later recognized also the Flora and Maria Maria may refer to: People * Mary, mother ...
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Asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. Of the roughly one million known asteroids the greatest number are located between the orbits of Mars and Jupiter, approximately 2 to 4 AU from the Sun, in the main asteroid belt. Asteroids are generally classified to be of three types: C-type, M-type, and S-type. These were named after and are generally identified with carbonaceous, metallic, and silicaceous compositions, respectively. The size of asteroids varies greatly; the largest, Ceres, is almost across and qualifies as a dwarf planet. The total mass of all the asteroids combined is only 3% that of Earth's Moon. The majority of main belt asteroids follow slightly elliptical, stable orbits, revolving in the same direction as the Earth and taking from three to six years to comple ...
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Minor Planet
According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor planet'', but that year's meeting reclassified minor planets and comets into dwarf planets and small Solar System bodies (SSSBs).Press release, IAU 2006 General Assembly: Result of the IAU Resolution votes
International Astronomical Union, August 24, 2006. Accessed May 5, 2008.
Minor planets include asteroids (

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Orbital Elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics. A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time. Keplerian elements The traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the common center of mass. When viewed from a non-inertial frame centered on one of the bodies, only the traj ...
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Semimajor 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 center t ...
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Eccentricity (orbit)
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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Inclination
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a Plane of reference, reference plane and the orbital plane or Axis of rotation, 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 degree (angle), degrees. For a satellite orbiting a planet, the plane of reference is usually ...
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Proper Orbital Elements
__NOTOC__ The proper orbital elements or proper elements of an orbit are constants of motion of an object in space that remain practically unchanged over an astronomically long timescale. The term is usually used to describe the three quantities: *''proper semimajor axis'' (''ap''), *''proper eccentricity'' (''ep''), and *''proper inclination'' (''ip''). The proper elements can be contrasted with the osculating Keplerian orbital elements observed at a particular time or epoch, such as the semi-major axis, eccentricity, and inclination. Those osculating elements change in a quasi-periodic and (in principle) predictable manner due to such effects as perturbations from planets or other bodies, and precession (e.g. perihelion precession). In the Solar System, such changes usually occur on timescales of thousands of years, while proper elements are meant to be practically constant over at least tens of millions of years. For most bodies, the osculating elements are relatively close ...
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Osculating Orbit
In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturbations were absent. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity). Etymology The word '' osculate'' is Latin for "kiss". In mathematics, two curves osculate when they just touch, without (necessarily) crossing, at a point, where both have the same position and slope, i.e. the two curves "kiss". Kepler elements An osculating orbit and the object's position upon it can be fully described by the six standard Kepler orbital elements (osculating elements), which are easy to calculate as long as one knows the object's position and velocity relative to the central body. The osculating elements would remain constant in the absence of perturbations. Real astronomical orbits experience pert ...
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Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north toward the East China Sea, Philippine Sea, and Taiwan in the south. Japan is a part of the Ring of Fire, and spans Japanese archipelago, an archipelago of List of islands of Japan, 6852 islands covering ; the five main islands are Hokkaido, Honshu (the "mainland"), Shikoku, Kyushu, and Okinawa Island, Okinawa. Tokyo is the Capital of Japan, nation's capital and largest city, followed by Yokohama, Osaka, Nagoya, Sapporo, Fukuoka, Kobe, and Kyoto. Japan is the List of countries and dependencies by population, eleventh most populous country in the world, as well as one of the List of countries and dependencies by population density, most densely populated and Urbanization by country, urbanized. About three-fourths of Geography of Japan, the c ...
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Astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, galaxies – in either observational astronomy, observational (by analyzing the data) or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, Sun, solar astronomy, the Star formation, origin or stellar evolution, evolution of stars, or the galaxy formation and evolution, formation of galaxies. A related but distinct subject is physical cosmology, which studies the Universe as a whole. Types Astronomers usually fall under either of two main types: observational astronomy, observational and theoretical astronomy, theoretical. Observational astronomers make direct observations of Astronomical object, celestial objects and analyze the data. In contrast, theoretical astronomers create and investigate C ...
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Kiyotsugu Hirayama
was a Japanese astronomer, best known for his discovery that many asteroid orbits were more similar to one another than chance would allow, leading to the concept of asteroid families, now called " Hirayama families" in his honour. Biography Hirayama studied astronomy at Imperial University of Tokyo and graduated in 1897. He taught astronomy in the engineering school of the General Staff Office of the Japanese Army between 1897 and 1901. In 1906 he became Assistant Professor of Astronomy at Tokyo Imperial University; in 1919 he became a Professor. From 1906 to 1907 Hirayama was a member of the Committee that determined the latitude border at Sakhalin after the Russo–Japanese War. In 1911 he received a doctoral degree "with several papers about latitude variation". Hirayama started working on asteroids in 1905; in 1918 he published papers "Researches on the distribution of the mean motions of the asteroids" and "Groups of asteroids probably of common origin", and, later "Famil ...
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Koronis Family
] The Koronis or Koronian family (), also known as the Lacrimosa family, is a very large asteroid family of S-type asteroid, stony asteroids, located in the Kirkwood gap, outer region of the asteroid belt. They are thought to have been formed at least two billion years ago in a catastrophic collision between two larger bodies. The family is named after 158 Koronis, and the largest known member (208 Lacrimosa) is about in diameter. The Koronis family travels in a cluster along the same orbit. It has 5949 members. This family has two subfamilies. The Karin family () was formed remarkably recently in a catastrophic collision (destroying the parent body), with an estimated age of 5.72 million years. The Koronis(2) family () with 246 members is the other. It formed 15 million years ago by a non-catastrophic collision with 158 Koronis. On August 28, 1993, the Galileo spacecraft visited a member of this family, 243 Ida. A photo of Ida (and its tiny moon Dactyl) is part of the composite i ...
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