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Cassini's Laws
Cassini's laws provide a compact description of the motion of the Moon. They were established in 1693 by Giovanni Domenico Cassini, a prominent scientist of his time.For the original statement of the laws, see Refinements of these laws to include physical librations have been made, and they have been generalized to treat other satellites and planets. Cassini's laws # The Moon has a 1:1 spin–orbit resonance. This means that the rotation–orbit ratio of the Moon is such that the same side of it always faces the Earth. # The Moon's rotational axis maintains a constant angle of inclination from the ecliptic plane. The Moon's rotational axis precesses so as to trace out a cone that intersects the ecliptic plane as a circle. # A plane formed from a normal to the ecliptic plane and a normal to the Moon's orbital plane will contain the Moon's rotational axis. In the case of the Moon, its rotational axis always points some 1.5 degrees away from the North ecliptic pole. The normal t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of Australia). The Moon is a planetary-mass object with a differentiated rocky body, making it a satellite planet under the geophysical definitions of the term and larger than all known dwarf planets of the Solar System. It lacks any significant atmosphere, hydrosphere, or magnetic field. Its surface gravity is about one-sixth of Earth's at , with Jupiter's moon Io being the only satellite in the Solar System known to have a higher surface gravity and density. The Moon orbits Earth at an average distance of , or about 30 times Earth's diameter. Its gravitational influence is the main driver of Earth's tides and very slowly lengthens Earth's day. The Moon's orbit around Earth has a sidereal period of 27.3 days. During each s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecliptic Pole
An orbital pole is either point at the ends of an imaginary line segment that runs through the center of an orbit (of a revolving body like a planet, moon or satellite) and is perpendicular to the orbital plane. Projected onto the celestial sphere, orbital poles are similar in concept to celestial poles, but are based on the body's orbit instead of its equator. The north orbital pole of a revolving body is defined by the right-hand rule. If the fingers of the right hand are curved along the direction of orbital motion, with the thumb extended and oriented to be parallel to the orbital axis, then the direction the thumb points is defined to be the orbital north. The poles of Earth's orbit are referred to as the ecliptic poles. For the remaining planets, the orbital pole in ecliptic coordinates is given by the longitude of the ascending node (☊) and inclination (''i''): ''l'' = ☊ - 90°, ''b'' = 90° - ''i''. In the following table, the planetary orbit poles are given in bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbit Of The Moon
The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days (a tropical month and sidereal month) and one revolution relative to the Sun in about 29.53 days (a synodic month). Earth and the Moon orbit about their barycentre (common centre of mass), which lies about from Earth's centre (about 73% of its radius), forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds. With a mean orbital velocity of 1.022 km/s (0.635 miles/s, 2,286 miles/h), the Moon covers a distance approximately its diameter, or about half a degree on the celestial sphere, each hour. The Moon differs from most satellites of other planets in that its orbit is close to the ecliptic plane instead of to its primary's (in this case, Earth's) equatorial plane. The Moon's orbital plan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Netherlands
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Astronomical Journal
''The Astronomical Journal'' (often abbreviated ''AJ'' in scientific papers and references) is a peer-reviewed monthly scientific journal owned by the American Astronomical Society (AAS) and currently published by IOP Publishing. It is one of the premier journals for astronomy in the world. Until 2008, the journal was published by the University of Chicago Press on behalf of the AAS. The reasons for the change to the IOP were given by the society as the desire of the University of Chicago Press to revise its financial arrangement and their plans to change from the particular software that had been developed in-house. The other two publications of the society, the ''Astrophysical Journal'' and its supplement series, followed in January 2009. The journal was established in 1849 by Benjamin A. Gould. It ceased publication in 1861 due to the American Civil War, but resumed in 1885. Between 1909 and 1941 the journal was edited in Albany, New York. In 1941, editor Benjamin Boss arrange ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separatrix (mathematics)
In mathematics, a separatrix is the boundary separating two modes of behaviour in a differential equation.Blanchard, Paul, ''Differential Equations'', 4th ed., 2012, Brooks/Cole, Boston, MA, pg. 469. Example Consider the differential equation describing the motion of a simple pendulum: :+ \sin\theta=0. where \ell denotes the length of the pendulum, g the gravitational acceleration and \theta the angle between the pendulum and vertically downwards. In this system there is a conserved quantity H (the Hamiltonian), which is given by H = \frac - \frac\cos\theta. With this defined, one can plot a curve of constant ''H'' in the phase space of system. The phase space is a graph with \theta along the horizontal axis and \dot on the vertical axis – see the thumbnail to the right. The type of resulting curve depends upon the value of ''H''. If H<-\frac then no curve exists (because must be [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retrograde Rotation
Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is, the central object (right figure). It may also describe other motions such as precession or nutation of an object's rotational axis. Prograde or direct motion is more normal motion in the same direction as the primary rotates. However, "retrograde" and "prograde" can also refer to an object other than the primary if so described. The direction of rotation is determined by an inertial frame of reference, such as distant fixed stars. In the Solar System, the orbits around the Sun of all planets and most other objects, except many comets, are prograde. They orbit around the Sun in the same direction as the sun rotates about its axis, which is counterclockwise when observed from above the Sun's north pole. Except for Venus and Uranus, planetary rotations around their axes are also prograde. Most natural satellites have prograde orbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tidal Force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field. In celestial mechanics, the expression ''tidal force'' can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invariable Plane
The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector. In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets (Jupiter, Saturn, Uranus, and Neptune). The invariable plane is within 0.5° of the orbital plane of Jupiter, and may be regarded as the weighted average of all planetary orbital and rotational planes. This plane is sometimes called the "Laplacian" or "Laplace plane" or the "invariable plane of Laplace", though it should not be confused with the Laplace plane, which is the plane about which the individual orbital planes of planetary satellites precess. Both derive from the work of (and are at least sometimes named for) the French astronomer Pierre Simon Laplace. — English translation published in four volumes, 1829–1839; : originally published as in five volumes. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Obliquity
In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane. It differs from orbital inclination. At an obliquity of 0 degrees, the two axes point in the same direction; that is, the rotational axis is perpendicular to the orbital plane. The rotational axis of Earth, for example, is the imaginary line that passes through both the North Pole and South Pole, whereas the Earth's orbital axis is the line perpendicular to the imaginary plane through which the Earth moves as it revolves around the Sun; the Earth's obliquity or axial tilt is the angle between these two lines. Earth's obliquity oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. Based on a continuously updated formula (here Laskar, 1986, though since 2006 the IMCCE and the IAU recommend the P03 model), Earth's mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Plane
The Laplace plane or Laplacian plane of a planetary satellite, named after its discoverer Pierre-Simon Laplace (1749–1827), is a mean or reference plane about whose axis the instantaneous orbital plane of that satellite precesses. Laplace's name is sometimes applied to the invariable plane, which is the plane perpendicular to a system's mean angular momentum vector, but the two should not be confused. They are equivalent only in the case where all perturbers and resonances are far from the precessing body. Definition The axis of this Laplace plane is coplanar with, and between, (a) the polar axis of the parent planet's spin, and (b) the orbital axis of the parent planet's orbit around the Sun. The Laplace plane arises because the equatorial oblateness of the parent planet tends to cause the orbit of the satellite to precess around the polar axis of the parent planet's equatorial plane, while the solar perturbations tend to cause the orbit of the satellite to precess around th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retrograde Motion
Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is, the central object (right figure). It may also describe other motions such as precession or nutation of an object's rotational axis. Prograde or direct motion is more normal motion in the same direction as the primary rotates. However, "retrograde" and "prograde" can also refer to an object other than the primary if so described. The direction of rotation is determined by an inertial frame of reference, such as distant fixed stars. In the Solar System, the orbits around the Sun of all planets and most other objects, except many comets, are prograde. They orbit around the Sun in the same direction as the sun rotates about its axis, which is counterclockwise when observed from above the Sun's north pole. Except for Venus and Uranus, planetary rotations around their axes are also prograde. Most natural satellites have prog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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