Planet
A planet is an astronomical body orbiting a star or stellar remnant, massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, has cleared its neighbouring region of planetesimals. The term planet is ancient, with ties to history, science and religion. Five planets in the Solar System are visible to the naked eye; these were regarded by many early cultures as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, incorporating a number of disparate objects. In 2006, the International Astronomical Union adopted a resolution defining planets within the Solar System; this definition is controversial because it excludes many objects of planetary mass based on where or what they orbit. Although eight of the planetary bodies discovered before 1950 remain "planets" under the modern definition, some celestial bodies, such as Ceres, Pallas and Vesta, Pluto, that were once considered planets by the scientific community, are no longer viewed as such.
The planets were thought by Ptolemy to orbit Earth in epicycle motions. Although the idea that the planets orbited the Sun had been suggested many times, it was not until the 17th century that this view was supported by evidence from the first telescopic astronomical observations, performed by Galileo Galilei. About the same time, by careful analysis of pre-telescopic observational data collected by Tycho Brahe, Johannes Kepler found the planets' orbits were elliptical rather than circular; as observational tools improved, astronomers saw that, like Earth, each of the planets rotated around an axis tilted with respect to its orbital pole, some shared such features as ice caps and seasons. Since the dawn of the Space Age, close observation by space probes has found that Earth and the other planets share characteristics such as volcanism, hurricanes and hydrology. Planets are divided into two main types: large low-density giant planets, smaller rocky terrestrials. There are eight planets in the Solar System.
In order of increasing distance from the Sun, they are the four terrestrials, Venus and Mars the four giant planets, Saturn and Neptune. Six of the planets are orbited by one or more natural satellites. Several thousands of planets around other stars have been discovered in the Milky Way; as of 1 April 2019, 4,023 known extrasolar planets in 3,005 planetary systems, ranging in size from just above the size of the Moon to gas giants about twice as large as Jupiter have been discovered, out of which more than 100 planets are the same size as Earth, nine of which are at the same relative distance from their star as Earth from the Sun, i.e. in the circumstellar habitable zone. On December 20, 2011, the Kepler Space Telescope team reported the discovery of the first Earth-sized extrasolar planets, Kepler-20e and Kepler-20f, orbiting a Sun-like star, Kepler-20. A 2012 study, analyzing gravitational microlensing data, estimates an average of at least 1.6 bound planets for every star in the Milky Way.
Around one in five Sun-like stars is thought to have an Earth-sized planet in its habitable zone. The idea of planets has evolved over its history, from the divine lights of antiquity to the earthly objects of the scientific age; the concept has expanded to include worlds not only in the Solar System, but in hundreds of other extrasolar systems. The ambiguities inherent in defining planets have led to much scientific controversy; the five classical planets, being visible to the naked eye, have been known since ancient times and have had a significant impact on mythology, religious cosmology, ancient astronomy. In ancient times, astronomers noted how certain lights moved across the sky, as opposed to the "fixed stars", which maintained a constant relative position in the sky. Ancient Greeks called these lights πλάνητες ἀστέρες or πλανῆται, from which today's word "planet" was derived. In ancient Greece, China and indeed all pre-modern civilizations, it was universally believed that Earth was the center of the Universe and that all the "planets" circled Earth.
The reasons for this perception were that stars and planets appeared to revolve around Earth each day and the common-sense perceptions that Earth was solid and stable and that it was not moving but at rest. The first civilization known to have a functional theory of the planets were the Babylonians, who lived in Mesopotamia in the first and second millennia BC; the oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BC copy of a list of observations of the motions of the planet Venus, that dates as early as the second millennium BC. The MUL. APIN is a pair of cuneiform tablets dating from the 7th century BC that lays out the motions of the Sun and planets over the course of the year; the Babylonian astrologers laid the foundations of what would become Western astrology. The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BC, comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.
Venus and the outer planets Mars and Saturn were all identified by Babylonian astronomers. These would remain the only known planets until the invention of the telescope in early modern times; the ancient Greeks did not attach as much significance to the planets as the Babylonians. The Pythagoreans, in the 6th and 5t
Orbital eccentricity
The orbital eccentricity of an astronomical object is a 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, 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 used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy. 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. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p = 1 − 2 r a r p + 1 where: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
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Isaac Newton
Sir Isaac Newton was an English mathematician, astronomer and author, recognised as one of the most influential scientists of all time, a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton made seminal contributions to optics, shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. In Principia, Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to prove Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity, he demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was confirmed by the geodetic measurements of Maupertuis, La Condamine, others, convincing most European scientists of the superiority of Newtonian mechanics over earlier systems.
Newton built the first practical reflecting telescope and developed a sophisticated theory of colour based on the observation that a prism separates white light into the colours of the visible spectrum. His work on light was collected in his influential book Opticks, published in 1704, he formulated an empirical law of cooling, made the first theoretical calculation of the speed of sound, introduced the notion of a Newtonian fluid. In addition to his work on calculus, as a mathematician Newton contributed to the study of power series, generalised the binomial theorem to non-integer exponents, developed a method for approximating the roots of a function, classified most of the cubic plane curves. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, he was a devout but unorthodox Christian who rejected the doctrine of the Trinity. Unusually for a member of the Cambridge faculty of the day, he refused to take holy orders in the Church of England.
Beyond his work on the mathematical sciences, Newton dedicated much of his time to the study of alchemy and biblical chronology, but most of his work in those areas remained unpublished until long after his death. Politically and tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02, he was knighted by Queen Anne in 1705 and spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint, as well as president of the Royal Society. Isaac Newton was born on Christmas Day, 25 December 1642 "an hour or two after midnight", at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire, his father named Isaac Newton, had died three months before. Born prematurely, Newton was a small child; when Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough.
Newton disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them." Newton's mother had three children from her second marriage. From the age of about twelve until he was seventeen, Newton was educated at The King's School, which taught Latin and Greek and imparted a significant foundation of mathematics, he was removed from school, returned to Woolsthorpe-by-Colsterworth by October 1659. His mother, widowed for the second time, attempted to make him an occupation he hated. Henry Stokes, master at The King's School, persuaded his mother to send him back to school. Motivated by a desire for revenge against a schoolyard bully, he became the top-ranked student, distinguishing himself by building sundials and models of windmills. In June 1661, he was admitted to Trinity College, Cambridge, on the recommendation of his uncle Rev William Ayscough, who had studied there.
He started as a subsizar—paying his way by performing valet's duties—until he was awarded a scholarship in 1664, guaranteeing him four more years until he could get his MA. At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers such as Descartes, astronomers such as Galileo and Thomas Street, through whom he learned of Kepler's work, he set down in his notebook a series of "Quaestiones" about mechanical philosophy. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that became calculus. Soon after Newton had obtained his BA degree in August 1665, the university temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus and the law of gravitation. In April 1667, he returned in October was elected as a fellow of Trinity.
Fellows were required to become ordained priests, although this was no
Escape velocity
In physics, escape velocity is the minimum speed needed for a free object to escape from the gravitational influence of a massive body. It is slower the further away from the body an object is, slower for less massive bodies; the escape velocity from Earth is about 11.186 km/s at the surface. More escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. With escape velocity in a direction pointing away from the ground of a massive body, the object will move away from the body, slowing forever and approaching, but never reaching, zero speed. Once escape velocity is achieved, no further impulse need to be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body, continually slowing, will asymptotically approach zero speed as the object's distance approaches infinity, never to come back. Speeds higher than escape velocity have a positive speed at infinity.
Note that the minimum escape velocity assumes that there is no friction, which would increase the required instantaneous velocity to escape the gravitational influence, that there will be no future acceleration or deceleration, which would change the required instantaneous velocity. For a spherically symmetric, massive body such as a star, or planet, the escape velocity for that body, at a given distance, is calculated by the formula v e = 2 G M r, where G is the universal gravitational constant, M the mass of the body to be escaped from, r the distance from the center of mass of the body to the object; the relationship is independent of the mass of the object escaping the massive body. Conversely, a body that falls under the force of gravitational attraction of mass M, from infinity, starting with zero velocity, will strike the massive object with a velocity equal to its escape velocity given by the same formula; when given an initial speed V greater than the escape speed v e, the object will asymptotically approach the hyperbolic excess speed v ∞, satisfying the equation: v ∞ 2 = V 2 − v e 2.
In these equations atmospheric friction is not taken into account. A rocket moving out of a gravity well does not need to attain escape velocity to escape, but could achieve the same result at any speed with a suitable mode of propulsion and sufficient propellant to provide the accelerating force on the object to escape. Escape velocity is only required to send a ballistic object on a trajectory that will allow the object to escape the gravity well of the mass M; the existence of escape velocity is a consequence of conservation of energy and an energy field of finite depth. For an object with a given total energy, moving subject to conservative forces it is only possible for the object to reach combinations of locations and speeds which have that total energy. By adding speed to the object it expands the possible locations that can be reached, with enough energy, they become infinite. For a given gravitational potential energy at a given position, the escape velocity is the minimum speed an object without propulsion needs to be able to "escape" from the gravity.
Escape velocity is a speed because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field. The simplest way of deriving the formula for escape velocity is to use conservation of energy. For the sake of simplicity, unless stated otherwise, we assume that an object is attempting to escape from a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity. In its initial state, i, imagine that a spaceship of mass m is at a distance r from the center of mass of the planet, whose mass is M, its initial speed is equal to v e. At its final state, f, it will be an infinite distance away from the planet, its speed will be negligibly small and assumed to be 0. Kinetic energy K and gravitational potential energy Ug are the only types of energy that we will deal with, so by the conservation of energy, i = f Kƒ = 0 because final velocity is zero, Ugƒ = 0 because its final distance is infinity, so ⇒ 1 2 m v e 2 + − G M m r
Moon
The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, the largest among planetary satellites relative to the size of the planet that it orbits; the Moon is after Jupiter's satellite Io the second-densest satellite in the Solar System among those whose densities are known. The Moon is thought to have formed not long after Earth; the most accepted explanation is that the Moon formed from the debris left over after a giant impact between Earth and a Mars-sized body called Theia. The Moon is in synchronous rotation with Earth, thus always shows the same side to Earth, the near side; the near side is marked by dark volcanic maria that fill the spaces between the bright ancient crustal highlands and the prominent impact craters. After the Sun, the Moon is the second-brightest visible celestial object in Earth's sky, its surface is dark, although compared to the night sky it appears bright, with a reflectance just higher than that of worn asphalt.
Its gravitational influence produces the ocean tides, body tides, the slight lengthening of the day. The Moon's average orbital distance is 1.28 light-seconds. This is about thirty times the diameter of Earth; the Moon's apparent size in the sky is the same as that of the Sun, since the star is about 400 times the lunar distance and diameter. Therefore, the Moon covers the Sun nearly during a total solar eclipse; this matching of apparent visual size will not continue in the far future because the Moon's distance from Earth is increasing. The Moon was first reached in September 1959 by an unmanned spacecraft; the United States' NASA Apollo program achieved the only manned lunar missions to date, beginning with the first manned orbital mission by Apollo 8 in 1968, six manned landings between 1969 and 1972, with the first being Apollo 11. These missions returned lunar rocks which have been used to develop a geological understanding of the Moon's origin, internal structure, the Moon's history. Since the Apollo 17 mission in 1972, the Moon has been visited only by unmanned spacecraft.
Both the Moon's natural prominence in the earthly sky and its regular cycle of phases as seen from Earth have provided cultural references and influences for human societies and cultures since time immemorial. Such cultural influences can be found in language, lunar calendar systems and mythology; the usual English proper name for Earth's natural satellite is "the Moon", which in nonscientific texts is not capitalized. The noun moon is derived from Old English mōna, which stems from Proto-Germanic *mēnô, which comes from Proto-Indo-European *mḗh₁n̥s "moon", "month", which comes from the Proto-Indo-European root *meh₁- "to measure", the month being the ancient unit of time measured by the Moon; the name "Luna" is used. In literature science fiction, "Luna" is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of Earth's moon; the modern English adjective pertaining to the Moon is lunar, derived from the Latin word for the Moon, luna. The adjective selenic is so used to refer to the Moon that this meaning is not recorded in most major dictionaries.
It is derived from the Ancient Greek word for the Moon, σελήνη, from, however derived the prefix "seleno-", as in selenography, the study of the physical features of the Moon, as well as the element name selenium. Both the Greek goddess Selene and the Roman goddess Diana were alternatively called Cynthia; the names Luna and Selene are reflected in terminology for lunar orbits in words such as apolune and selenocentric. The name Diana comes from the Proto-Indo-European *diw-yo, "heavenly", which comes from the PIE root *dyeu- "to shine," which in many derivatives means "sky and god" and is the origin of Latin dies, "day"; the Moon formed 4.51 billion years ago, some 60 million years after the origin of the Solar System. Several forming mechanisms have been proposed, including the fission of the Moon from Earth's crust through centrifugal force, the gravitational capture of a pre-formed Moon, the co-formation of Earth and the Moon together in the primordial accretion disk; these hypotheses cannot account for the high angular momentum of the Earth–Moon system.
The prevailing hypothesis is that the Earth–Moon system formed after an impact of a Mars-sized body with the proto-Earth. The impact blasted material into Earth's orbit and the material accreted and formed the Moon; the Moon's far side has a crust, 30 mi thicker than that of the near side. This is thought to be; this hypothesis, although not perfect best explains the evidence. Eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, Jeff Taylor challenged fellow lunar scientists: "You have eighteen months. Go back to your Apollo data, go back to your computer, do whatever you have to, but make up your mind. Don't come to our conference unless you have something to say about the Moon's birth." At the 1984 conference at Kona, the giant impact hypothesis emerged as the most consensual theory. Before the conference, there were parti
Apsis
The term apsis refers to an extreme point in the orbit of an object. It denotes either the respective distance of the bodies; the word comes via Latin from Greek, there denoting a whole orbit, is cognate with apse. Except for the theoretical possibility of one common circular orbit for two bodies of equal mass at diametral positions, there are two apsides for any elliptic orbit, named with the prefixes peri- and ap-/apo-, added in reference to the body being orbited. All periodic orbits are, according to Newton's Laws of motion, ellipses: either the two individual ellipses of both bodies, with the center of mass of this two-body system at the one common focus of the ellipses, or the orbital ellipses, with one body taken as fixed at one focus, the other body orbiting this focus. All these ellipses share a straight line, the line of apsides, that contains their major axes, the foci, the vertices, thus the periapsis and the apoapsis; the major axis of the orbital ellipse is the distance of the apsides, when taken as points on the orbit, or their sum, when taken as distances.
The major axes of the individual ellipses around the barycenter the contributions to the major axis of the orbital ellipses are inverse proportional to the masses of the bodies, i.e. a bigger mass implies a smaller axis/contribution. Only when one mass is sufficiently larger than the other, the individual ellipse of the smaller body around the barycenter comprises the individual ellipse of the larger body as shown in the second figure. For remarkable asymmetry, the barycenter of the two bodies may lie well within the bigger body, e.g. the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If the smaller mass is negligible compared to the larger the orbital parameters are independent of the smaller mass. For general orbits, the terms periapsis and apoapsis are used. Pericenter and apocenter are equivalent alternatives, referring explicitly to the respective points on the orbits, whereas periapsis and apoapsis may refer to the smallest and largest distances of the orbiter and its host.
For a body orbiting the Sun, the point of least distance is the perihelion, the point of greatest distance is the aphelion. The terms become apastron when discussing orbits around other stars. For any satellite of Earth, including the Moon, the point of least distance is the perigee and greatest distance the apogee, from Ancient Greek Γῆ, "land" or "earth". For objects in lunar orbit, the point of least distance is sometimes called the pericynthion and the greatest distance the apocynthion. Perilune and apolune are used. In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body. However, in the case of a spacecraft, the terms are used to refer to the orbital altitude of the spacecraft above the surface of the central body; these formulae characterize the pericenter and apocenter of an orbit: Pericenter Maximum speed, v per = μ a, at minimum distance, r per = a. Apocenter Minimum speed, v ap = μ a, at maximum distance, r ap = a.
While, in accordance with Kepler's laws of planetary motion and the conservation of energy, these two quantities are constant for a given orbit: Specific relative angular momentum h = μ a Specific orbital energy ε = − μ 2 a where: a is the semi-major axis: a = r per + r ap 2 μ is the standard gravitational parameter e is the eccentricity, defined as e = r ap − r per r ap + r per = 1 − 2 r ap r per + 1 Note t
Orbit
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Orbit refers to a repeating trajectory, although it may refer to a non-repeating trajectory. To a close approximation and satellites follow elliptic orbits, with the central 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 motion; the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached.
It assumed the heavens were fixed apart from the motion of the spheres, was developed without any understanding of gravity. After the planets' motions were more measured, theoretical mechanisms such as deferent and epicycles were added. Although the model was capable of reasonably predicting the planets' positions in the sky and more epicycles were required as the measurements became more accurate, hence the model became unwieldy. Geocentric it was modified by Copernicus to place the Sun at the centre to help simplify the model; the model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our Solar System are elliptical, not circular, as had been believed, that the Sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had been thought, but rather that the speed depends on the planet's distance from the Sun.
Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are about 5.2 and 0.723 AU distant from the Sun, their orbital periods about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, that those bodies orbit their common center of mass. Where one body is much more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.
Advances in Newtonian mechanics were used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. Albert Einstein in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes propagate instantaneously; this led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are approximated well by the Newtonian predictions but the differences are measurable.
All the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is easier to use and sufficiently accurate. Within a planetary system, dwarf planets and other minor planets and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet. Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time.
Mercury, the smallest planet in the Solar System, has the most eccentric orbit