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129-496: There are interrelated observational and theoretical branches of planetary science. Observational research can involve combinations of space exploration , predominantly with robotic spacecraft missions using remote sensing , and comparative, experimental work in Earth-based laboratories . The theoretical component involves considerable computer simulation and mathematical modelling . Planetary scientists are generally located in

258-413: A Legendre transformation on the generalized coordinates, velocities and momenta; therefore, both contain the same information for describing the dynamics of a system. There are other formulations such as Hamilton–Jacobi theory , Routhian mechanics , and Appell's equation of motion . All equations of motion for particles and fields, in any formalism, can be derived from the widely applicable result called

387-521: A gravity assist from Jupiter . Its closest approach to Pluto was on 14 July 2015; scientific observations of Pluto began five months prior to closest approach and continued for 16 days after the encounter. The New Horizons mission also performed a flyby of the small planetesimal Arrokoth , in the Kuiper belt , in 2019. This was its first extended mission. Although many comets have been studied from Earth sometimes with centuries-worth of observations, only

516-484: A magnetosphere around a planet. Early space probes discovered the gross dimensions of the terrestrial magnetic field, which extends about 10 Earth radii towards the Sun. The solar wind , a stream of charged particles, streams out and around the terrestrial magnetic field, and continues behind the magnetic tail, hundreds of Earth radii downstream. Inside the magnetosphere, there are relatively dense regions of solar wind particles,

645-602: A better appreciation of the Red Planet but also yield further insight into the past, and possible future, of Earth. The exploration of Mars has come at a considerable financial cost with roughly two-thirds of all spacecraft destined for Mars failing before completing their missions, with some failing before they even began. Such a high failure rate can be attributed to the complexity and large number of variables involved in an interplanetary journey, and has led researchers to jokingly speak of The Great Galactic Ghoul which subsists on

774-491: A body's position during its motion. In physical systems, however, some structure or other system usually constrains the body's motion from taking certain directions and pathways. So a full set of Cartesian coordinates is often unneeded, as the constraints determine the evolving relations among the coordinates, which relations can be modeled by equations corresponding to the constraints. In the Lagrangian and Hamiltonian formalisms,

903-461: A close flyby of Saturn's moon Titan, resulting in a trajectory incompatible with a Pluto flyby. Voyager 2 never had a plausible trajectory for reaching Pluto. After an intense political battle, a mission to Pluto dubbed New Horizons was granted funding from the United States government in 2003. New Horizons was launched successfully on 19 January 2006. In early 2007 the craft made use of

1032-405: A complicated mechanical system requires a unifying basis from which they follow. This is provided by various variational principles : behind each set of equations there is a principle that expresses the meaning of the entire set. Given a fundamental and universal quantity called action , the principle that this action be stationary under small variation of some other mechanical quantity generates

1161-574: A conspicuous anticyclone storm system rivaled in size only by Jupiter's Great Red Spot . Neptune also proved to have the fastest winds of any planet in the Solar System, measured as high as 2,100 km/h. Voyager 2 also examined Neptune's ring and moon system . It discovered 900 complete rings and additional partial ring "arcs" around Neptune. In addition to examining Neptune's three previously known moons, Voyager 2 also discovered five previously unknown moons, one of which, Proteus , proved to be

1290-484: A diet of Mars probes. This phenomenon is also informally known as the " Mars Curse ". In contrast to overall high failure rates in the exploration of Mars, India has become the first country to achieve success of its maiden attempt. India's Mars Orbiter Mission (MOM) is one of the least expensive interplanetary missions ever undertaken with an approximate total cost of ₹ 450 Crore ( US$ 73 million ). The first mission to Mars by any Arab country has been taken up by

1419-472: A few clouds in the images of the planet. The magnetosphere of Uranus, however, proved to be unique, being profoundly affected by the planet's unusual axial tilt. In contrast to the bland appearance of Uranus itself, striking images were obtained of the Moons of Uranus, including evidence that Miranda had been unusually geologically active. The exploration of Neptune began with the 25 August 1989 Voyager 2 flyby,

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1548-650: A few comets have been closely visited. In 1985, the International Cometary Explorer conducted the first comet fly-by ( 21P/Giacobini-Zinner ) before joining the Halley Armada studying the famous comet. The Deep Impact probe smashed into 9P/Tempel to learn more about its structure and composition and the Stardust mission returned samples of another comet's tail. The Philae lander successfully landed on Comet Churyumov–Gerasimenko in 2014 as part of

1677-791: A force across reversible displacements is zero, which is the work done by a force consistent with ideal constraints of the system. The idea of a constraint is useful – since this limits what the system can do, and can provide steps to solving for the motion of the system. The equation for D'Alembert's principle is: δ W = Q ⋅ δ q = 0 , {\displaystyle \delta W={\boldsymbol {\mathcal {Q}}}\cdot \delta \mathbf {q} =0\,,} where Q = ( Q 1 , Q 2 , … , Q N ) {\displaystyle {\boldsymbol {\mathcal {Q}}}=({\mathcal {Q}}_{1},{\mathcal {Q}}_{2},\dots ,{\mathcal {Q}}_{N})} are

1806-518: A large number of Earth observation satellites have been deployed specifically to explore Earth from a space-based perspective. These satellites have significantly contributed to the understanding of a variety of Earth-based phenomena. For instance, the hole in the ozone layer was found by an artificial satellite that was exploring Earth's atmosphere, and satellites have allowed for the discovery of archeological sites or geological formations that were difficult or impossible to otherwise identify. The Moon

1935-415: A mountain as tall as, for example, 15 km (9 mi), would develop so much pressure at its base, due to gravity, that the rock there would become plastic , and the mountain would slump back to a height of roughly 10 km (6 mi) in a geologically insignificant time. Some or all of these geologic principles can be applied to other planets besides Earth. For instance on Mars, whose surface gravity

2064-599: A planned crewed landing to occur with Artemis III . The rise of the private space industry also began in earnest in the 2010s with the development of private launch vehicles, space capsules and satellite manufacturing. In the 2000s, China initiated a successful crewed spaceflight program while India launched the Chandrayaan programme , while the European Union and Japan have also planned future crewed space missions. The two primary global programs gaining traction in

2193-490: A set of 2 N first-order ordinary differential equations, one for each q i ( t ) and p i ( t ). Another result from the Legendre transformation relates the time derivatives of the Lagrangian and Hamiltonian: which is often considered one of Hamilton's equations of motion additionally to the others. The generalized momenta can be written in terms of the generalized forces in the same way as Newton's second law: Analogous to

2322-488: A smooth and polished surface" suggested that it and other worlds might appear "just like the face of the Earth itself". Advances in telescope construction and instrumental resolution gradually allowed increased identification of the atmospheric as well as surface details of the planets. The Moon was initially the most heavily studied, due to its proximity to the Earth, as it always exhibited elaborate features on its surface, and

2451-566: A sort of bubble of particles made in the Galaxy by the Sun's solar wind . The Sun is a major focus of space exploration. Being above the atmosphere in particular and Earth's magnetic field gives access to the solar wind and infrared and ultraviolet radiations that cannot reach Earth's surface. The Sun generates most space weather , which can affect power generation and transmission systems on Earth and interfere with, and even damage, satellites and space probes. Numerous spacecraft dedicated to observing

2580-537: A very wide range of problems indeed. Development of analytical mechanics has two objectives: (i) increase the range of solvable problems by developing standard techniques with a wide range of applicability, and (ii) understand the mathematical structure of mechanics. In the long run, however, (ii) can help (i) more than a concentration on specific problems for which methods have already been designed. In Newtonian mechanics , one customarily uses all three Cartesian coordinates , or other 3D coordinate system , to refer to

2709-555: A wide range of peer reviewed journals . Some planetary scientists work at private research centres and often initiate partnership research tasks. The history of planetary science may be said to have begun with the Ancient Greek philosopher Democritus , who is reported by Hippolytus as saying The ordered worlds are boundless and differ in size, and that in some there is neither sun nor moon, but that in others, both are greater than with us, and yet with others more in number. And that

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2838-426: Is a collection of closely related formulations of classical mechanics . Analytical mechanics uses scalar properties of motion representing the system as a whole—usually its kinetic energy and potential energy . The equations of motion are derived from the scalar quantity by some underlying principle about the scalar's variation . Analytical mechanics was developed by many scientists and mathematicians during

2967-522: Is a useful shorthand (see matrix calculus for this notation). If the curvilinear coordinate system is defined by the standard position vector r , and if the position vector can be written in terms of the generalized coordinates q and time t in the form: r = r ( q ( t ) , t ) {\displaystyle \mathbf {r} =\mathbf {r} (\mathbf {q} (t),t)} and this relation holds for all times t , then q are called holonomic constraints . Vector r

3096-642: Is an important transitional zone between the solid planetary surface and the higher rarefied ionizing and radiation belts. Not all planets have atmospheres: their existence depends on the mass of the planet, and the planet's distance from the Sun ;– too distant and frozen atmospheres occur. Besides the four giant planets , three of the four terrestrial planets ( Earth , Venus , and Mars ) have significant atmospheres. Two moons have significant atmospheres: Saturn 's moon Titan and Neptune 's moon Triton . A tenuous atmosphere exists around Mercury . The effects of

3225-417: Is believed to have orbited Earth at a height of about 250 km (160 mi). It had two radio transmitters (20 and 40 MHz), which emitted "beeps" that could be heard by radios around the globe. Analysis of the radio signals was used to gather information about the electron density of the ionosphere, while temperature and pressure data was encoded in the duration of radio beeps. The results indicated that

3354-455: Is called a phase path , a particular curve ( q ( t ), p ( t )) subject to the required initial conditions. The set of all phase paths, the general solution to the differential equations, is the phase portrait : All dynamical variables can be derived from position q , momentum p , and time t , and written as a function of these: A = A ( q , p , t ). If A ( q , p , t ) and B ( q , p , t ) are two scalar valued dynamical variables,

3483-410: Is called a (configuration) path or trajectory , i.e. one particular q ( t ) subject to the required initial conditions . The general solutions form a set of possible configurations as functions of time: The configuration space can be defined more generally, and indeed more deeply, in terms of topological manifolds and the tangent bundle . The Legendre transformation of the Lagrangian replaces

3612-421: Is explicitly dependent on t in cases when the constraints vary with time, not just because of q ( t ) . For time-independent situations, the constraints are also called scleronomic , for time-dependent cases they are called rheonomic . The introduction of generalized coordinates and the fundamental Lagrangian function: where T is the total kinetic energy and V is the total potential energy of

3741-446: Is false even for such simple system as rotations of a solid body . In more complicated systems, the vectorial approach cannot give an adequate description. The analytical approach simplifies problems by treating mechanical systems as ensembles of particles that interact with each other, rather considering each particle as an isolated unit. In the vectorial approach, forces must be determined individually for each particle, whereas in

3870-403: Is meant by 'solving' a set of differential equations. A problem is regarded as solved when the particles coordinates at time t are expressed as simple functions of t and of parameters defining the initial positions and velocities. However, 'simple function' is not a well-defined concept: nowadays, a function f ( t ) is not regarded as a formal expression in t ( elementary function ) as in

3999-497: Is much less, the largest volcano, Olympus Mons , is 27 km (17 mi) high at its peak, a height that could not be maintained on Earth. The Earth geoid is essentially the figure of the Earth abstracted from its topographic features. Therefore, the Mars geoid ( areoid ) is essentially the figure of Mars abstracted from its topographic features. Surveying and mapping are two important fields of application of geodesy. An atmosphere

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4128-528: Is the total kinetic energy of the system, and the notation ∂ ∂ q = ( ∂ ∂ q 1 , ∂ ∂ q 2 , … , ∂ ∂ q N ) {\displaystyle {\frac {\partial }{\partial \mathbf {q} }}=\left({\frac {\partial }{\partial q_{1}}},{\frac {\partial }{\partial q_{2}}},\dots ,{\frac {\partial }{\partial q_{N}}}\right)}

4257-482: Is to solve mechanical problems, such as arise in physics and engineering. Starting from a physical system—such as a mechanism or a star system—a mathematical model is developed in the form of a differential equation. The model can be solved numerically or analytically to determine the motion of the system. Newton's vectorial approach to mechanics describes motion with the help of vector quantities such as force , velocity , acceleration . These quantities characterise

4386-421: Is used widely, from fundamental physics to applied mathematics , particularly chaos theory . The methods of analytical mechanics apply to discrete particles, each with a finite number of degrees of freedom. They can be modified to describe continuous fields or fluids, which have infinite degrees of freedom. The definitions and equations have a close analogy with those of mechanics. The goal of mechanical theory

4515-586: The Apollo astronauts for the field geology they would encounter on their lunar missions. Overlapping sequences were identified on images taken by the Lunar Orbiter program , and these were used to prepare a lunar stratigraphic column and geological map of the Moon. One of the main problems when generating hypotheses on the formation and evolution of objects in the Solar System is the lack of samples that can be analyzed in

4644-467: The Cassini spacecraft, which lasted from 2004 until 2017. Saturn has at least 62 known moons , although the exact number is debatable since Saturn's rings are made up of vast numbers of independently orbiting objects of varying sizes. The largest of the moons is Titan , which holds the distinction of being the only moon in the Solar System with an atmosphere denser and thicker than that of Earth. Titan holds

4773-498: The HED meteorites back to a specific asteroid in the main belt, 4 Vesta . The comparatively few known Martian meteorites have provided insight into the geochemical composition of the Martian crust, although the unavoidable lack of information about their points of origin on the diverse Martian surface has meant that they do not provide more detailed constraints on theories of the evolution of

4902-657: The International Space Station (ISS). With the substantial completion of the ISS following STS-133 in March 2011, plans for space exploration by the U.S. remained in flux. The Constellation program aiming for a return to the Moon by 2020 was judged unrealistic by an expert review panel reporting in 2009. Constellation ultimately was replaced with the Artemis Program , of which the first mission occurred in 2022 , with

5031-545: The Poisson bracket is defined by the generalized coordinates and momenta: Calculating the total derivative of one of these, say A , and substituting Hamilton's equations into the result leads to the time evolution of A : This equation in A is closely related to the equation of motion in the Heisenberg picture of quantum mechanics , in which classical dynamical variables become quantum operators (indicated by hats (^)), and

5160-647: The Van Allen radiation belts . Planetary geophysics includes, but is not limited to, seismology and tectonophysics , geophysical fluid dynamics , mineral physics , geodynamics , mathematical geophysics , and geophysical surveying . Planetary geodesy (also known as planetary geodetics) deals with the measurement and representation of the planets of the Solar System, their gravitational fields and geodynamic phenomena ( polar motion in three-dimensional, time-varying space). The science of geodesy has elements of both astrophysics and planetary sciences. The shape of

5289-470: The asteroids , the new planets Uranus and Neptune , and many more satellites . The Orbiting Astronomical Observatory 2 was the first space telescope launched 1968, but the launching of Hubble Space Telescope in 1990 set a milestone. As of 1 December 2022, there were 5,284 confirmed exoplanets discovered. The Milky Way is estimated to contain 100–400 billion stars and more than 100 billion planets . There are at least 2 trillion galaxies in

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5418-436: The biosphere , but those meteorites collected in the last few decades from Antarctica are almost entirely pristine. The different types of meteorites that originate from the asteroid belt cover almost all parts of the structure of differentiated bodies: meteorites even exist that come from the core-mantle boundary ( pallasites ). The combination of geochemistry and observational astronomy has also made it possible to trace

5547-641: The dwarf planets Ceres and Pluto were orbited by Dawn and passed by New Horizons , respectively. This accounts for flybys of each of the eight planets in the Solar System , the Sun , the Moon , and Ceres and Pluto (two of the five recognized dwarf planets ). The first interplanetary surface mission to return at least limited surface data from another planet was the 1970 landing of Venera 7 , which returned data to Earth for 23 minutes from Venus . In 1975, Venera 9

5676-418: The far side of the Moon . India's Chandrayaan-3 in 2023 achieved the world's first landing on the lunar south pole region. Crewed exploration of the Moon began in 1968 with the Apollo 8 mission that successfully orbited the Moon, the first time any extraterrestrial object was orbited by humans. In 1969, the Apollo 11 mission marked the first time humans set foot upon another world. Crewed exploration of

5805-681: The generalized forces (script Q instead of ordinary Q is used here to prevent conflict with canonical transformations below) and q are the generalized coordinates. This leads to the generalized form of Newton's laws in the language of analytical mechanics: Q = d d t ( ∂ T ∂ q ˙ ) − ∂ T ∂ q , {\displaystyle {\boldsymbol {\mathcal {Q}}}={\frac {d}{dt}}\left({\frac {\partial T}{\partial \mathbf {\dot {q}} }}\right)-{\frac {\partial T}{\partial \mathbf {q} }}\,,} where T

5934-451: The gravity fields of the planets to be mapped. For example, in the 1970s, the gravity field disturbances above lunar maria were measured through lunar orbiters, which led to the discovery of concentrations of mass, mascons , beneath the Imbrium, Serenitatis, Crisium, Nectaris and Humorum basins. If a planet's magnetic field is sufficiently strong, its interaction with the solar wind forms

6063-459: The motion of a body idealised as a "mass point" or a " particle " understood as a single point to which a mass is attached. Newton's method has been successfully applied to a wide range of physical problems, including the motion of a particle in Earth 's gravitational field and the motion of planets around the Sun. In this approach, Newton's laws describe the motion by a differential equation and then

6192-591: The observable universe . HD1 is the most distant known object from Earth, reported as 33.4 billion light-years away. MW 18014 was a German V-2 rocket test launch that took place on 20 June 1944, at the Peenemünde Army Research Center in Peenemünde . It was the first human-made object to reach outer space , attaining an apogee of 176 kilometers, which is well above the Kármán line . It

6321-542: The principle of least action . One result is Noether's theorem , a statement which connects conservation laws to their associated symmetries . Analytical mechanics does not introduce new physics and is not more general than Newtonian mechanics. Rather it is a collection of equivalent formalisms which have broad application. In fact the same principles and formalisms can be used in relativistic mechanics and general relativity , and with some modifications, quantum mechanics and quantum field theory . Analytical mechanics

6450-399: The rotation rate of a planet about its axis can be seen in atmospheric streams and currents. Seen from space, these features show as bands and eddies in the cloud system and are particularly visible on Jupiter and Saturn. Exoplanetology studies exoplanets , the planets existing outside our Solar System . Until recently, the means of studying exoplanets have been extremely limited, but with

6579-863: The time derivative (here denoted by an overdot) of this tuple give the generalized velocities : d q d t = ( d q 1 d t , d q 2 d t , … , d q N d t ) ≡ q ˙ = ( q ˙ 1 , q ˙ 2 , … , q ˙ N ) . {\displaystyle {\frac {d\mathbf {q} }{dt}}=\left({\frac {dq_{1}}{dt}},{\frac {dq_{2}}{dt}},\dots ,{\frac {dq_{N}}{dt}}\right)\equiv \mathbf {\dot {q}} =({\dot {q}}_{1},{\dot {q}}_{2},\dots ,{\dot {q}}_{N}).} D'Alembert's principle states that infinitesimal virtual work done by

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6708-399: The 18th century and onward, after Newtonian mechanics . Newtonian mechanics considers vector quantities of motion, particularly accelerations , momenta , forces , of the constituents of the system; it can also be called vectorial mechanics . A scalar is a quantity, whereas a vector is represented by quantity and direction. The results of these two different approaches are equivalent, but

6837-817: The 2020s are the Chinese-led International Lunar Research Station and the US-led Artemis Program, with its plan to build the Lunar Gateway and the Artemis Base Camp , each having its own set of international partners. The first telescope is said to have been invented in 1608 in the Netherlands by an eyeglass maker named Hans Lippershey , but their first recorded use in astronomy was by Galileo Galilei in 1609. In 1668 Isaac Newton built his own reflecting telescope ,

6966-422: The Earth is to a large extent the result of its rotation, which causes its equatorial bulge , and the competition of geologic processes such as the collision of plates and of vulcanism , resisted by the Earth's gravity field. These principles can be applied to the solid surface of Earth ( orogeny ; Few mountains are higher than 10 km (6 mi), few deep sea trenches deeper than that because quite simply,

7095-581: The Hamiltonian in one set of coordinates q and momenta p to be transformed into a new set Q = Q ( q , p , t ) and P = P ( q , p , t ), in four possible ways: With the restriction on P and Q such that the transformed Hamiltonian system is: the above transformations are called canonical transformations , each function G n is called a generating function of the " n th kind" or "type- n ". The transformation of coordinates and momenta can allow simplification for solving Hamilton's equations for

7224-505: The Martian lithosphere . As of July 24, 2013, 65 samples of Martian meteorites have been discovered on Earth. Many were found in either Antarctica or the Sahara Desert. During the Apollo era, in the Apollo program , 384 kilograms of lunar samples were collected and transported to the Earth, and three Soviet Luna robots also delivered regolith samples from the Moon. These samples provide

7353-532: The Middle East. The total mass of recognized lunar meteorites is close to 50 kg. Space probes made it possible to collect data in not only the visible light region but in other areas of the electromagnetic spectrum. The planets can be characterized by their force fields: gravity and their magnetic fields, which are studied through geophysics and space physics. Measuring the changes in acceleration experienced by spacecraft as they orbit has allowed fine details of

7482-548: The Moon began with the Ranger 4 impactor in 1962. Starting in 1966, the Soviets successfully deployed a number of landers to the Moon which were able to obtain data directly from the Moon's surface; just four months later, Surveyor 1 marked the debut of a successful series of U.S. landers. The Soviet uncrewed missions culminated in the Lunokhod program in the early 1970s, which included

7611-426: The Moon did not continue for long. The Apollo 17 mission in 1972 marked the sixth landing and the most recent human visit. Artemis II is scheduled to complete a crewed flyby of the Moon in 2025, and Artemis III will perform the first lunar landing since Apollo 17 with it scheduled for launch no earlier than 2026. Robotic missions are still pursued vigorously. The exploration of Mars has been an important part of

7740-407: The Moon, entering in a lunar orbit on 3 April 1966. The first crewed landing on another celestial body was performed by Apollo 11 on 20 July 1969, landing on the Moon. There have been a total of six spacecraft with humans landing on the Moon starting from 1969 to the last human landing in 1972. The first interplanetary flyby was the 1961 Venera 1 flyby of Venus , though the 1962 Mariner 2

7869-460: The Moon. Also, probes were sent throughout the known Solar System, and into Solar orbit. Uncrewed spacecraft have been sent into orbit around Saturn, Jupiter, Mars, Venus, and Mercury by the 21st century, and the most distance active spacecraft, Voyager 1 and 2 traveled beyond 100 times the Earth-Sun distance. The instruments were enough though that it is thought they have left the Sun's heliosphere,

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7998-507: The Poisson bracket is replaced by the commutator of operators via Dirac's canonical quantization : Following are overlapping properties between the Lagrangian and Hamiltonian functions. Action is another quantity in analytical mechanics defined as a functional of the Lagrangian: A general way to find the equations of motion from the action is the principle of least action : where

8127-475: The Solar System and extrasolar planetary systems. Observing exoplanets and determining their physical properties, exoplanetology , is a major area of research besides Solar System studies. Every planet has its own branch. In planetary science, the term geology is used in its broadest sense, to mean the study of the surface and interior parts of planets and moons, from their core to their magnetosphere. The best-known research topics of planetary geology deal with

8256-423: The Solar System are accomplished at a cost in energy, which is described by the net change in velocity of the spacecraft, or delta-v . Due to the relatively high delta-v to reach Mercury and its proximity to the Sun, it is difficult to explore and orbits around it are rather unstable. Venus was the first target of interplanetary flyby and lander missions and, despite one of the most hostile surface environments in

8385-539: The Solar System, has had more landers sent to it (nearly all from the Soviet Union) than any other planet in the Solar System. The first flyby was the 1961  Venera 1 , though the 1962  Mariner 2  was the first flyby to successfully return data. Mariner 2 has been followed by several other flybys by multiple space agencies often as part of missions using a Venus flyby to provide a gravitational assist en route to other celestial bodies. In 1967, Venera 4 became

8514-690: The Sun, beginning with the Apollo Telescope Mount , have been launched and still others have had solar observation as a secondary objective. Parker Solar Probe , launched in 2018, will approach the Sun to within 1/9th the orbit of Mercury. Mercury remains the least explored of the Terrestrial planets . As of May 2013, the Mariner 10 and MESSENGER missions have been the only missions that have made close observations of Mercury. MESSENGER entered orbit around Mercury in March 2011, to further investigate

8643-408: The Sun, or the geomorphology of the surfaces of the terrestrial planets, to give only a few examples. The main comparison that can be made is to features on the Earth, as it is much more accessible and allows a much greater range of measurements to be made. Earth analog studies are particularly common in planetary geology, geomorphology, and also in atmospheric science. The use of terrestrial analogs

8772-528: The United Arab Emirates. Called the Emirates Mars Mission , it was launched on 19 July 2020 and went into orbit around Mars on 9 February 2021. The uncrewed exploratory probe was named "Hope Probe" and was sent to Mars to study its atmosphere in detail. The Russian space mission Fobos-Grunt , which launched on 9 November 2011, experienced a failure leaving it stranded in low Earth orbit . It

8901-410: The analytical approach it is enough to know one single function which contains implicitly all the forces acting on and in the system. Such simplification is often done using certain kinematic conditions which are stated a priori . However, the analytical treatment does not require the knowledge of these forces and takes these kinematic conditions for granted. Still, deriving the equations of motion of

9030-468: The analytical mechanics approach has many advantages for complex problems. Analytical mechanics takes advantage of a system's constraints to solve problems. The constraints limit the degrees of freedom the system can have, and can be used to reduce the number of coordinates needed to solve for the motion. The formalism is well suited to arbitrary choices of coordinates, known in the context as generalized coordinates . The kinetic and potential energies of

9159-543: The asteroid 4 Vesta , two of the three largest asteroids, were visited by NASA's Dawn spacecraft , launched in 2007. Hayabusa was a robotic spacecraft developed by the Japan Aerospace Exploration Agency to return a sample of material from the small near-Earth asteroid 25143 Itokawa to Earth for further analysis. Hayabusa was launched on 9 May 2003 and rendezvoused with Itokawa in mid-September 2005. After arriving at Itokawa, Hayabusa studied

9288-428: The asteroid's shape, spin, topography, color, composition, density, and history. In November 2005, it landed on the asteroid twice to collect samples. The spacecraft returned to Earth on 13 June 2010. The exploration of Jupiter has consisted solely of a number of automated NASA spacecraft visiting the planet since 1973. A large majority of the missions have been "flybys", in which detailed observations are taken without

9417-425: The astronomy and physics or Earth sciences departments of universities or research centres, though there are several purely planetary science institutes worldwide. Generally, planetary scientists study one of the Earth sciences , astronomy , astrophysics , geophysics , or physics at the graduate level and concentrate their research in planetary science disciplines. There are several major conferences each year, and

9546-460: The broader Rosetta mission . Deep space exploration is the branch of astronomy , astronautics and space technology that is involved with the exploration of distant regions of outer space. Physical exploration of space is conducted both by human spaceflights (deep-space astronautics) and by robotic spacecraft . Analytical dynamics In theoretical physics and mathematical physics , analytical mechanics , or theoretical mechanics

9675-420: The class of all solutions, that is, the mathematical structure of the problem. Moreover, an accurate mental or drawn picture can be made for the motion of two bodies, and it can be as real and accurate as the real bodies moving and interacting. In the three-body problem, parameters can also be assigned specific values; however, the solution at these assigned values or a collection of such solutions does not reveal

9804-508: The configuration space, the set of all momenta is the generalized momentum space : ("Momentum space" also refers to " k -space"; the set of all wave vectors (given by De Broglie relations ) as used in quantum mechanics and theory of waves ) The set of all positions and momenta form the phase space : that is, the Cartesian product of the configuration space and generalized momentum space. A particular solution to Hamilton's equations

9933-433: The constraints are incorporated into the motion's geometry, reducing the number of coordinates to the minimum needed to model the motion. These are known as generalized coordinates , denoted q i ( i = 1, 2, 3...). Generalized coordinates incorporate constraints on the system. There is one generalized coordinate q i for each degree of freedom (for convenience labelled by an index i = 1, 2... N ), i.e. each way

10062-410: The current rate of innovation in research technology , exoplanetology has become a rapidly developing subfield of astronomy . Planetary science frequently makes use of the method of comparison to give a greater understanding of the object of study. This can involve comparing the dense atmospheres of Earth and Saturn's moon Titan , the evolution of outer Solar System objects at different distances from

10191-414: The departure t 1 and arrival t 2 times are fixed. The term "path" or "trajectory" refers to the time evolution of the system as a path through configuration space C {\displaystyle {\mathcal {C}}} , in other words q ( t ) tracing out a path in C {\displaystyle {\mathcal {C}}} . The path for which action is least is the path taken by

10320-684: The distinction of being the only object in the Outer Solar System that has been explored with a lander, the Huygens probe deployed by the Cassini spacecraft. The exploration of Uranus has been entirely through the Voyager 2 spacecraft, with no other visits currently planned. Given its axial tilt of 97.77°, with its polar regions exposed to sunlight or darkness for long periods, scientists were not sure what to expect at Uranus. The closest approach to Uranus occurred on 24 January 1986. Voyager 2 studied

10449-533: The energy required at launch to reach Jupiter, albeit at the cost of a significantly longer flight duration. Jupiter has 95 known moons , many of which have relatively little known information about them. Saturn has been explored only through uncrewed spacecraft launched by NASA, including one mission ( Cassini–Huygens ) planned and executed in cooperation with other space agencies. These missions consist of flybys in 1979 by Pioneer 11 , in 1980 by Voyager 1 , in 1982 by Voyager 2 and an orbital mission by

10578-461: The entire system, then either following the calculus of variations or using the above formula – lead to the Euler–Lagrange equations ; which are a set of N second-order ordinary differential equations , one for each q i ( t ). This formulation identifies the actual path followed by the motion as a selection of the path over which the time integral of kinetic energy is least, assuming

10707-407: The exploration of space is currently carried out mainly by astronomers with telescopes , its physical exploration is conducted both by uncrewed robotic space probes and human spaceflight . Space exploration, like its classical form astronomy , is one of the main sources for space science . While the observation of objects in space, known as astronomy , predates reliable recorded history , it

10836-472: The features on planetary surfaces and reconstructs the history of their formation, inferring the physical processes that acted on the surface. Planetary geomorphology includes the study of several classes of surface features: The history of a planetary surface can be deciphered by mapping features from top to bottom according to their deposition sequence , as first determined on terrestrial strata by Nicolas Steno . For example, stratigraphic mapping prepared

10965-504: The first human spaceflight ( Yuri Gagarin aboard Vostok 1 ) in 1961, the first spacewalk (by Alexei Leonov ) on 18 March 1965, the first automatic landing on another celestial body in 1966, and the launch of the first space station ( Salyut 1 ) in 1971. After the first 20 years of exploration, focus shifted from one-off flights to renewable hardware, such as the Space Shuttle program , and from competition to cooperation as with

11094-403: The first fully functional telescope of this kind, and a landmark for future developments due to its superior features over the previous Galilean telescope . A string of discoveries in the Solar System (and beyond) followed, then and in the next centuries : the mountains of the Moon , the phases of Venus , the main satellites of Jupiter and Saturn , the rings of Saturn , many comets ,

11223-458: The first of which was Galileo , which flew past two: 951 Gaspra in 1991, followed by 243 Ida in 1993. Both of these lay near enough to Galileo' s planned trajectory to Jupiter that they could be visited at acceptable cost. The first landing on an asteroid was performed by the NEAR Shoemaker probe in 2000, following an orbital survey of the object, 433 Eros . The dwarf planet Ceres and

11352-506: The first probe to enter and directly examine the atmosphere of Venus. In 1970, Venera 7 became the first successful lander to reach the surface of Venus and by 1985 it had been followed by eight additional successful Soviet Venus landers which provided images and other direct surface data. Starting in 1975, with the Soviet orbiter Venera 9 , some ten successful orbiter missions have been sent to Venus, including later missions which were able to map

11481-412: The first uncrewed rovers and also successfully brought lunar soil samples to Earth for study. This marked the first (and to date the only) automated return of extraterrestrial soil samples to Earth. Uncrewed exploration of the Moon continues with various nations periodically deploying lunar orbiters. China's Chang'e 4 in 2019 and Chang'e 6 in 2024 achieved the world's first landing and sample return on

11610-416: The generalized coordinates and velocities ( q , q̇ ) with ( q , p ); the generalized coordinates and the generalized momenta conjugate to the generalized coordinates: and introduces the Hamiltonian (which is in terms of generalized coordinates and momenta): where ⋅ {\displaystyle \cdot } denotes the dot product , also leading to Hamilton's equations : which are now

11739-407: The intervals between the ordered worlds are unequal, here more and there less, and that some increase, others flourish and others decay, and here they come into being and there they are eclipsed. But that they are destroyed by colliding with one another. And that some ordered worlds are bare of animals and plants and all water. In more modern times, planetary science began in astronomy, from studies of

11868-403: The laboratory, where a large suite of tools are available, and the full body of knowledge derived from terrestrial geology can be brought to bear. Direct samples from the Moon, asteroids and Mars are present on Earth, removed from their parent bodies, and delivered as meteorites . Some of these have suffered contamination from the oxidising effect of Earth's atmosphere and the infiltration of

11997-459: The last largest moon in the system. Data from Voyager 2 supported the view that Neptune's largest moon, Triton , is a captured Kuiper belt object. The dwarf planet Pluto presents significant challenges for spacecraft because of its great distance from Earth (requiring high velocity for reasonable trip times) and small mass (making capture into orbit difficult at present). Voyager 1 could have visited Pluto, but controllers opted instead for

12126-523: The longest ever Soviet planetary surface mission. Venus and Mars are the two planets outside of Earth on which humans have conducted surface missions with uncrewed robotic spacecraft . Salyut 1 was the first space station of any kind, launched into low Earth orbit by the Soviet Union on 19 April 1971. The International Space Station (ISS) is currently the largest and oldest of the 2 current fully functional space stations, inhabited continuously since

12255-466: The lunar surface, and 400,171 km (248,655 mi) from Earth, marking the record for the farthest humans have ever traveled from Earth in 1970. As of 26 November 2022 Voyager 1 was at a distance of 159 AU (23.8 billion km; 14.8 billion mi) from Earth. It is the most distant human-made object from Earth. Starting in the mid-20th century probes and then human missions were sent into Earth orbit, and then on to

12384-486: The mathematical structure of the problem. As in many other problems, the mathematical structure can be elucidated only by examining the differential equations themselves. Analytical mechanics aims at even more: not at understanding the mathematical structure of a single mechanical problem, but that of a class of problems so wide that they encompass most of mechanics. It concentrates on systems to which Lagrangian or Hamiltonian equations of motion are applicable and that include

12513-462: The modern methods of computer modelling which provide arithmetical solutions to mechanical problems to any desired degree of accuracy, the differential equations being replaced by difference equations . Still, though lacking precise definitions, it is obvious that the two-body problem has a simple solution, whereas the three-body problem has not. The two-body problem is solved by formulas involving parameters; their values can be changed to study

12642-614: The most comprehensive record of the composition of any Solar System body besides the Earth. The numbers of lunar meteorites are growing quickly in the last few years – as of April 2008 there are 54 meteorites that have been officially classified as lunar. Eleven of these are from the US Antarctic meteorite collection, 6 are from the Japanese Antarctic meteorite collection and the other 37 are from hot desert localities in Africa, Australia, and

12771-418: The number of generalized coordinates required to define the configuration of the system), following the general rule: For a system with N degrees of freedom, the generalized coordinates can be collected into an N - tuple : q = ( q 1 , q 2 , … , q N ) {\displaystyle \mathbf {q} =(q_{1},q_{2},\dots ,q_{N})} and

12900-494: The observations made by Mariner 10 in 1975 (Munsell, 2006b). A third mission to Mercury, scheduled to arrive in 2025, BepiColombo is to include two probes . BepiColombo is a joint mission between Japan and the European Space Agency . MESSENGER and BepiColombo are intended to gather complementary data to help scientists understand many of the mysteries discovered by Mariner 10's flybys . Flights to other planets within

13029-426: The planet's unique atmosphere and magnetosphere . Voyager 2 also examined its ring system and the moons of Uranus including all five of the previously known moons, while discovering an additional ten previously unknown moons. Images of Uranus proved to have a uniform appearance, with no evidence of the dramatic storms or atmospheric banding evident on Jupiter and Saturn. Great effort was required to even identify

13158-512: The planetary bodies in the near vicinity of the Earth: the Moon , and the two neighboring planets: Venus and Mars . Of these, the Moon was studied first, using methods developed earlier on the Earth. Planetary geology focuses on celestial objects that exhibit a solid surface or have significant solid physical states as part of their structure. Planetary geology applies geology , geophysics and geochemistry to planetary bodies. Geomorphology studies

13287-586: The probe landing or entering orbit; such as in Pioneer and Voyager programs. The Galileo and Juno spacecraft are the only spacecraft to have entered the planet's orbit. As Jupiter is believed to have only a relatively small rocky core and no real solid surface, a landing mission is precluded. Reaching Jupiter from Earth requires a delta-v of 9.2 km/s, which is comparable to the 9.7 km/s delta-v needed to reach low Earth orbit. Fortunately, gravity assists through planetary flybys can be used to reduce

13416-534: The problem is reduced to the solving of that equation. When a mechanical system contains many particles, however (such as a complex mechanism or a fluid ), Newton's approach is difficult to apply. Using a Newtonian approach is possible, under proper precautions, namely isolating each single particle from the others, and determining all the forces acting on it. Such analysis is cumbersome even in relatively simple systems. Newton thought that his third law "action equals reaction" would take care of all complications. This

13545-466: The rate of new discoveries is very high, partly due to the large number of interplanetary spacecraft currently exploring the Solar System. Planetary science studies observational and theoretical astronomy, geology ( astrogeology ), atmospheric science , and an emerging subspecialty in planetary oceans , called planetary oceanography . This is both an observational and a theoretical science. Observational researchers are predominantly concerned with

13674-536: The reason NASA was created was as a response to Sputnik I. The launch of the first human-made object to orbit Earth , the Soviet Union's Sputnik 1 , on 4 October 1957, and the first Moon landing by the American Apollo 11 mission on 20 July 1969 are often taken as landmarks for this initial period. The Soviet space program achieved many of the first milestones, including the first living being in orbit in 1957,

13803-399: The required set of differential equations. The statement of the principle does not require any special coordinate system , and all results are expressed in generalized coordinates . This means that the analytical equations of motion do not change upon a coordinate transformation , an invariance property that is lacking in the vectorial equations of motion. It is not altogether clear what

13932-414: The satellite was not punctured by a meteoroid . Sputnik 1 was launched by an R-7 rocket. It burned up upon re-entry on 3 January 1958. The first successful human spaceflight was Vostok 1 ("East 1"), carrying the 27-year-old Russian cosmonaut , Yuri Gagarin , on 12 April 1961. The spacecraft completed one orbit around the globe, lasting about 1 hour and 48 minutes. Gagarin's flight resonated around

14061-428: The sole visit to the system as of 2024. The possibility of a Neptune Orbiter has been discussed, but no other missions have been given serious thought. Although the extremely uniform appearance of Uranus during Voyager 2 ' s visit in 1986 had led to expectations that Neptune would also have few visible atmospheric phenomena, the spacecraft found that Neptune had obvious banding, visible clouds, auroras , and even

14190-436: The space exploration programs of the Soviet Union (later Russia), the United States, Europe, Japan and India. Dozens of robotic spacecraft , including orbiters , landers , and rovers , have been launched toward Mars since the 1960s. These missions were aimed at gathering data about current conditions and answering questions about the history of Mars. The questions raised by the scientific community are expected to not only give

14319-474: The study of the small bodies of the Solar System: those that are observed by telescopes, both optical and radio, so that characteristics of these bodies such as shape, spin, surface materials and weathering are determined, and the history of their formation and evolution can be understood. Theoretical planetary astronomy is concerned with dynamics : the application of the principles of celestial mechanics to

14448-664: The surface of Venus using radar to pierce the obscuring atmosphere. Space exploration has been used as a tool to understand Earth as a celestial object. Orbital missions can provide data for Earth that can be difficult or impossible to obtain from a purely ground-based point of reference. For example, the existence of the Van Allen radiation belts was unknown until their discovery by the United States' first artificial satellite, Explorer 1 . These belts contain radiation trapped by Earth's magnetic fields, which currently renders construction of habitable space stations above 1000 km impractical. Following this early unexpected discovery,

14577-699: The system are expressed using these generalized coordinates or momenta, and the equations of motion can be readily set up, thus analytical mechanics allows numerous mechanical problems to be solved with greater efficiency than fully vectorial methods. It does not always work for non- conservative forces or dissipative forces like friction , in which case one may revert to Newtonian mechanics. Two dominant branches of analytical mechanics are Lagrangian mechanics (using generalized coordinates and corresponding generalized velocities in configuration space ) and Hamiltonian mechanics (using coordinates and corresponding momenta in phase space ). Both formulations are equivalent by

14706-433: The system can change its configuration ; as curvilinear lengths or angles of rotation. Generalized coordinates are not the same as curvilinear coordinates. The number of curvilinear coordinates equals the dimension of the position space in question (usually 3 for 3d space), while the number of generalized coordinates is not necessarily equal to this dimension; constraints can reduce the number of degrees of freedom (hence

14835-469: The system. From this principle, all equations of motion in classical mechanics can be derived. This approach can be extended to fields rather than a system of particles (see below), and underlies the path integral formulation of quantum mechanics , and is used for calculating geodesic motion in general relativity . The invariance of the Hamiltonian (under addition of the partial time derivative of an arbitrary function of p , q , and t ) allows

14964-494: The technological improvements gradually produced more detailed lunar geological knowledge. In this scientific process, the main instruments were astronomical optical telescopes (and later radio telescopes ) and finally robotic exploratory spacecraft , such as space probes . The Solar System has now been relatively well-studied, and a good overall understanding of the formation and evolution of this planetary system exists. However, there are large numbers of unsolved questions, and

15093-419: The time of Newton but most generally as a quantity determined by t , and it is not possible to draw a sharp line between 'simple' and 'not simple' functions. If one speaks merely of 'functions', then every mechanical problem is solved as soon as it has been well stated in differential equations, because given the initial conditions and t determine the coordinates at t . This is a fact especially at present with

15222-474: The total energy to be fixed, and imposing no conditions on the time of transit. The Lagrangian formulation uses the configuration space of the system, the set of all possible generalized coordinates: where R N {\displaystyle \mathbb {R} ^{N}} is N -dimensional real space (see also set-builder notation ). The particular solution to the Euler–Lagrange equations

15351-409: The unresolved planets. In this sense, the original planetary astronomer would be Galileo , who discovered the four largest moons of Jupiter , the mountains on the Moon , and first observed the rings of Saturn , all objects of intense later study. Galileo's study of the lunar mountains in 1609 also began the study of extraterrestrial landscapes: his observation "that the Moon certainly does not possess

15480-423: The world; it was a demonstration of the advanced Soviet space program and it opened an entirely new era in space exploration: human spaceflight . The first artificial object to reach another celestial body was Luna 2 reaching the Moon in 1959. The first soft landing on another celestial body was performed by Luna 9 landing on the Moon on 3 February 1966. Luna 10 became the first artificial satellite of

15609-433: The year 2000. The other, Tiangong space station built by China, is now fully crewed and operational. Voyager 1 became the first human-made object to leave the Solar System into interstellar space on 25 August 2012. The probe passed the heliopause at 121 AU to enter interstellar space . The Apollo 13 flight passed the far side of the Moon at an altitude of 254 kilometers (158 miles; 137 nautical miles) above

15738-628: Was a vertical test launch. Although the rocket reached space, it did not reach orbital velocity , and therefore returned to Earth in an impact, becoming the first sub-orbital spaceflight . In 1949, the Bumper-WAC reached an altitude of 393 kilometres (244 mi), becoming the first human-made object to enter space, according to NASA . The first successful orbital launch was of the Soviet uncrewed Sputnik 1 ("Satellite 1") mission on 4 October 1957. The satellite weighed about 83 kg (183 lb), and

15867-517: Was driven by a " Space Race " between the Soviet Union and the United States . A driving force of the start of space exploration was during the Cold War. After the ability to create nuclear weapons, the narrative of defense/offense left land and the power to control the air the focus. Both the Soviet Union and the U.S. were racing to prove their superiority in technology through exploring space. In fact,

15996-425: Was first described by Gilbert (1886). This non-exhaustive list includes those institutions and universities with major groups of people working in planetary science. Alphabetical order is used. Smaller workshops and conferences on particular fields occur worldwide throughout the year. Space exploration Space exploration is the use of astronomy and space technology to explore outer space . While

16125-434: Was the development of large and relatively efficient rockets during the mid-twentieth century that allowed physical space exploration to become a reality. Common rationales for exploring space include advancing scientific research, national prestige, uniting different nations, ensuring the future survival of humanity, and developing military and strategic advantages against other countries. The early era of space exploration

16254-399: Was the first celestial body to be the object of space exploration. It holds the distinctions of being the first remote celestial object to be flown by, orbited, and landed upon by spacecraft, and the only remote celestial object ever to be visited by humans. In 1959, the Soviets obtained the first images of the far side of the Moon , never previously visible to humans. The U.S. exploration of

16383-435: Was the first flyby of Venus to return data (closest approach 34,773 kilometers). Pioneer 6 was the first satellite to orbit the Sun , launched on 16 December 1965. The other planets were first flown by in 1965 for Mars by Mariner 4 , 1973 for Jupiter by Pioneer 10 , 1974 for Mercury by Mariner 10 , 1979 for Saturn by Pioneer 11 , 1986 for Uranus by Voyager 2 , 1989 for Neptune by Voyager 2 . In 2015,

16512-477: Was the first to return images from the surface of another planet, returning images from Venus. In 1971, the Mars 3 mission achieved the first soft landing on Mars returning data for almost 20 seconds. Later, much longer duration surface missions were achieved, including over six years of Mars surface operation by Viking 1 from 1975 to 1982 and over two hours of transmission from the surface of Venus by Venera 13 in 1982,

16641-480: Was to begin exploration of the Phobos and Martian circumterrestrial orbit, and study whether the moons of Mars, or at least Phobos, could be a "trans-shipment point" for spaceships traveling to Mars. Until the advent of space travel , objects in the asteroid belt were merely pinpricks of light in even the largest telescopes, their shapes and terrain remaining a mystery. Several asteroids have now been visited by probes,

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