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Commensurability (astronomy)
Commensurability is the property of two orbiting objects, such as planets, satellites, or asteroids, whose orbital periods are in a rational proportion. Examples include the 2:3 commensurability between the orbital periods of Neptune and Pluto, the 3:4 commensurability between the orbital periods of the Saturnian satellites Titan and Hyperion, the orbital periods associated with the Kirkwood gaps in the asteroid belt relative to that of Jupiter, and the 2:1 commensurability between Gliese 876 b and Gliese 876 c. Commensurabilities are normally the result of an orbital resonance, rather than being due to coincidence. See also *Harmonic *Ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ... References {{DEFAULTSORT:Commensurability (Astronomy) Asteroids Celestial mechan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asteroid Belt
The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called asteroids or minor planets. This asteroid belt is also called the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. The asteroid belt is the smallest and innermost known circumstellar disc in the Solar System. About 60% of its mass is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea. The total mass of the asteroid belt is calculated to be 3% that of the Moon. Ceres, the only object in the asteroid belt large enough to be a dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas, and Hygiea have mean diameters less than 600 km. The remaining bodies range down to the size of a dust par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbits
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. History Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687. The name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics." The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term "celestial mechanics." Prior to Kepler there was little connection between exact, quantitative prediction of planetary positions, using geometrical or arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler Johannes Kepler (1571–1630) was the first to closely integrate the predictive geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asteroids
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 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the other harmonics are known as ''higher harmonics''. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a '' harmonic series''. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. In music, harmonics are used on string instruments and wind ins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Resonance
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects (binary resonance). The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an ''unstable'' interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gliese 876 C
Gliese 876 c is an exoplanet orbiting the red dwarf Gliese 876, taking about 30 days to complete an orbit. The planet was discovered in April 2001 and is the second planet in order of increasing distance from its star. Discovery At the time of discovery, Gliese 876 was already known to host an extrasolar planet designated Gliese 876 b. On January 9, 2001, it was announced that further analysis of the star's radial velocity had revealed the existence of a second planet in the system, which was designated Gliese 876 c. The orbital period of Gliese 876 c was found to be exactly half that of the outer planet, which meant that the radial velocity signature of the second planet was initially interpreted as a higher eccentricity of the orbit of Gliese 876 b. Orbit and mass Gliese 876 c is in a 1:2:4 Laplace resonance with the outer planets Gliese 876 b and Gliese 876 e: for every orbit of planet e, planet b completes two orbits and planet c completes four. This leads to strong gravit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gliese 876 B
Gliese 876 b is an exoplanet orbiting the red dwarf Gliese 876. It completes one orbit in approximately 61 days. Discovered in June 1998, Gliese 876 b was the first planet to be discovered orbiting a red dwarf. Discovery Gliese 876 b was initially announced by Geoffrey Marcy on June 22, 1998 at a symposium of the International Astronomical Union in Victoria, British Columbia, Canada. The discovery was made using data from the Keck and Lick observatories. Only 2 hours after his announcement, he was shown an e-mail from the Geneva Extrasolar Planet Search team confirming the planet. The Geneva team used telescopes at the Haute-Provence Observatory in France and the European Southern Observatory in La Serena, Chile. Like the majority of early extrasolar planet discoveries it was discovered by detecting variations in its star's radial velocity as a result of the planet's gravity. This was done by making sensitive measurements of the Doppler shift of the spectral lines of Gliese 87 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 atmosphe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirkwood Gap
A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter. For example, there are very few asteroids with semimajor axis near 2.50 AU, period 3.95 years, which would make three orbits for each orbit of Jupiter (hence, called the 3:1 orbital resonance). Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiter's. The weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family ''(see List of asteroid families)''. The gaps were first noticed in 1866 by Daniel Kirkwood, who also correctly explained their origin in the orbital resonances with Jupiter while a professor at Jefferson College in Canonsburg, Pennsylvania. Most of the Kirkwood gaps are depleted, unlike the mean-motion resonan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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