Vicarious Hypothesis
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Vicarious Hypothesis
The Vicarious Hypothesis, or ''hypothesis vicaria'', was a planetary hypothesis proposed by Johannes Kepler to describe the motion of Mars. The hypothesis adopted the circular orbit and equant of Ptolemy's planetary model as well as the heliocentrism of the Copernican model. Calculations using the Vicarious Hypothesis did not support a circular orbit for Mars, leading Kepler to propose elliptical orbits as one of three laws of planetary motion in '' Astronomia Nova''. History In 1600, Johannes Kepler met and began working with Tycho Brahe at Benátky, a town north of Prague where Brahe's new observatory was being built. Brahe assigned Kepler the task of modeling the motion of Mars using only data that Brahe had collected himself. Upon the death of Brahe in 1601, all of Brahe's data was willed to Kepler. Brahe's observational data was among the most accurate of his time, which Kepler used in the construction of the Vicarious Hypothesis. Predecessors Ptolemy Claudius Pto ...
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Planetary Habitability
Planetary habitability is the measure of a planet's or a natural satellite's potential to develop and maintain environments hospitable to life. Life may be generated directly on a planet or satellite endogenously or be transferred to it from another body, through a hypothetical process known as panspermia. Environments do not need to contain life to be considered habitable nor are accepted habitable zones (HZ) the only areas in which life might arise. As the existence of life beyond Earth is unknown, planetary habitability is largely an extrapolation of conditions on Earth and the characteristics of the Sun and Solar System which appear favorable to life's flourishing. Of particular interest are those factors that have sustained complex, multicellular organisms on Earth and not just simpler, unicellular creatures. Research and theory in this regard is a component of a number of natural sciences, such as astronomy, planetary science and the emerging discipline of astrobio ...
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Ptolemaic Elements
Ptolemaic is the adjective formed from the name Ptolemy, and may refer to: Pertaining to the Ptolemaic dynasty * Ptolemaic dynasty, the Macedonian Greek dynasty that ruled Egypt founded in 305 BC by Ptolemy I Soter * Ptolemaic Kingdom Pertaining to a certain ancient writer *Relating to Ptolemy, 2nd-century AD geographer and astronomer/astrologer *Ptolemaic system, a geocentric model of the universe developed in detail by the astronomer Claudius Ptolemaeus See also * Ptolemy (name) Ptolemy is a name derived from Ancient Greek. Common variants include Ptolemaeus (Latin), Tolomeo (Italian) and Talmai (Hebrew). Etymology Ptolemy is the English form of the Ancient Greek name Πτολεμαῖος (''Ptolemaios''), a derivative o ...
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Minute And Second Of Arc
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol , is of an arcminute, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship. To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astr ...
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Radius
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the spoke of a chariot wheel. as a function of axial position ../nowiki>" Spherical coordinates In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial direction on a reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane. See also *Bend radius *Filling radius in Riemannian geometry *Radius of convergence * Radius of convexity *Radius of curvature *Radius of gyration ''Radius of gyration'' or gyradius of a body about the axis of r ...
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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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Opposition (astronomy)
In positional astronomy, two astronomical objects are said to be in opposition when they are on opposite sides of the celestial sphere, as observed from a given body (usually Earth). A planet (or asteroid or comet) is said to be "in opposition" or "at opposition" when it is in opposition to the Sun. Because most orbits in the Solar System are nearly coplanar to the ecliptic, this occurs when the Sun, Earth, and the body are configured in an approximately straight line, or syzygy; that is, Earth and the body are in the same direction as seen from the Sun. Opposition occurs only for superior planets (see the diagram). The instant of opposition is defined as that when the apparent geocentric celestial longitude of the body differs by 180° from the apparent geocentric longitude of the Sun. At that time, a body is: * in apparent retrograde motion * visible almost all night – rising around sunset, culminating around midnight, and setting around sunrise * at the point in its ...
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Longitude
Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, England on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows ...
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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 of orbi ...
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Geocentric Model
In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many European ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt. Two observations supported the idea that Earth was the center of the Universe: * First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographic poles of Earth. * Second, Earth seems to be unmoving from the perspective of an earthbound observer; it feels solid, stable, and stationary. ...
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Nicolaus Copernicus
Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic Church, Catholic canon (priest), canon, who formulated a mathematical model, model of Celestial spheres#Renaissance, the universe that placed heliocentrism, the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier. The publication of Copernicus's model in his book ' (''On the Revolutions of the Celestial Spheres''), just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland (1385 ...
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Copernican Heliocentrism Theory Diagram
Copernican means of or pertaining to the astronomer Nicolaus Copernicus (1473–1543). Copernican may also refer to: Science * Copernican heliocentrism, the astronomical model developed by Copernicus * Copernican principle, in physical cosmology * Copernican period, in lunar geology Politics * Copernican federalism, a US political model * Copernican paradigm, an Australian political model Music * Symphony No. 2 (Górecki) Symphony No. 2, the "Copernican," Op. 31 ''(II Symfonia "Kopernikowska")'' () is a choral symphony composed by Henryk Górecki in 1972 to celebrate the 500th anniversary of the birth of astronomer Nicolaus Copernicus. Composed in a monumental style ..., a symphony by Henryk Górecki known as the ''Copernican'' Symphony, Op. 31 See also * Copernicus (other) {{disambig ...
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Angular Velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object rotates or revolves relative to a point or axis). The magnitude of the pseudovector represents the ''angular speed'', the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.(EM1) There are two types of angular velocity. * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular ve ...
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