# Orbit <!-- SOLSIM:BEGIN g31 — Solar System explorer state (hand-built on wt-core, specs/solar/); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *The orbits (Solar System explorer)* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/solar/Solar_System.html?view=orbits&embed=1" data-title="The orbits (Solar System explorer)"></div> *The Solar System explorer locked on this article's state (`?view=orbits`); every object and population of the [[PORTAL_Solar_System|Solar System portal]] has its own state in the same scene.* <!-- SOLSIM:END --> *Try: set the speed to 1 year/s and watch the inner planets lap the outer ones on their nearly round, nearly flat paths; drag the scene to an edge-on view and pick out the three orbits that leave the common plane, Pluto's at about 17°, Eris's at about 44° and Halley's Comet's at 162°, which carries the comet around the Sun the wrong way; press l to switch the labels on or off while you match each tilted ellipse to its body.* An **orbit** is the path a body follows under the attraction of another mass: a planet around a star, a moon around a planet, a spacecraft around the [[Earth]] or around a point in space where gravitational pulls balance.[^britannica] Most orbits in the [[Planetary_system|planetary systems]] that have been measured are, to a close approximation, [[Ellipse|ellipses]] with the shared centre of mass of the two bodies at one focus, the pattern described by [[Kepler's_laws_of_planetary_motion|Kepler's laws of planetary motion]].[^nasa-bary] The word usually means a path that repeats, although the same mathematics also covers the open, one-pass trajectories of bodies that are not bound to one another. [[Isaac_Newton|Newton's]] mechanics, in which [[Gravity|gravity]] is a force that weakens with the square of distance, predicts orbital motion well enough for nearly every practical purpose.[^kuhn1985] [[General_relativity|General relativity]], which treats gravity as the curvature of spacetime and orbits as [[Geodesic|geodesics]] in it, is more accurate and is needed where fields are strong or precision is extreme.[^kembhavi2020] This article follows the subject from the ancient spheres to the modern equations, the six numbers that fix an orbit, the forces that slowly change it, and the classes of orbit used around Earth. The explorer at the top of this page opens on the orbits of the [[Sun|Sun's]] family: the planets on near-circles close to one plane, and a few smaller bodies on steep or backward paths that stand out against them. ## History Greek astronomy explained the wandering of the planets with nested celestial spheres, an idea associated with Eudoxus and [[Aristotelian_physics|Aristotle]], in which each planet rode a perfect rotating shell and no force was needed to keep it there.[^americo2017] Ptolemy's deferents and epicycles, circles riding on circles, fitted the observed loops, but every gain in measurement demanded more circles.[^mazer2011] Copernicus put the Sun at the centre but kept the circles, and sixteenth-century observers tracked comets passing straight through the supposed spheres.[^boschiero2007][^caspar2012] [[Johannes_Kepler|Johannes Kepler]] replaced the circles with ellipses. His three laws state that each planet moves on an ellipse with the Sun at one focus, that it moves fastest where it is closest to the Sun, and that the cube of a planet's mean distance is proportional to the square of its period for every planet alike.[^hyman1993] The third law can be checked with present values: [[Jupiter]] orbits at about 5.20 [[Astronomical_unit|AU]] with a period of 11.86 years, and 5.20³ ≈ 140.6 while 11.86² ≈ 140.7; [[Venus]] orbits at 0.723 AU in 0.615 years, and both 0.723³ and 0.615² come to about 0.378 (derived).[^nasa-jup][^nasa-ven] Newton showed that all three laws follow from an inverse-square attraction, and that under such a force the possible paths are the conic sections: ellipses, parabolas and hyperbolas.[^macdougal2012][^nauenberg1994] His version of the third law, T² = 4π²a³/(G(M + m)), ties the size a and period T of an orbit to the combined mass of the pair, which orbit their common centre of mass.[^gallant2025][^harper2011] Lagrange later recast mechanics around energy rather than force and, with Euler, found the equilibrium points of the three-body problem that now bear his name.[^goodson2011][^dellantonio2012] The strongest test of the Newtonian programme came in 1846, when Urbain Le Verrier used unexplained irregularities in the motion of [[Uranus]] to predict where an unseen planet should lie; [[Neptune]] was found there.[^krajnovic2016] Einstein's general theory of 1916 removed the assumption that gravity acts instantly and replaced the force with geometry. Its orbits agree with Newton's almost everywhere, but the differences are measurable, and the available evidence favours relativity.[^kembhavi2020] Its first success was the extra advance of [[Mercury_(planet)|Mercury's]] perihelion, about 43 arcseconds per century, which Newtonian perturbations from the other planets could not account for.[^odonnell2014][^clemence1947] Newton's simpler equations remain the working tool for most short-term work.[^kembhavi2020] ## Planetary orbits Inside a planetary system, planets, [[Dwarf_planet|dwarf planets]], [[Asteroid|asteroids]], [[Comet|comets]], [[Meteoroid|meteoroids]] and even debris move on ellipses around the system's barycentre.[^mcsween2019] A comet on a parabolic or hyperbolic path is not bound to the star and so is not counted as a member of its system.[^raymond2023] Moons, ring particles and artificial satellites orbit a barycentre that lies near or inside their planet.[^hahn2020] The shapes of the planetary orbits are not fixed: the planets' mutual pulls make their eccentricities and inclinations drift over long periods.[^pu2018] At present [[Mercury_(planet)|Mercury]] has the most eccentric orbit of the eight planets, e ≈ 0.206, followed by [[Mars]] at about 0.094, while [[Venus]] (0.007) and [[Neptune]] (0.009) have the roundest.[^taylor2001][^nasa-fs] Each orbit has a nearest point, the periapsis, and a farthest, the apoapsis; the straight line through both is the line of apsides, the major axis of the ellipse.[^wells1965][^fairbridge1997] Around Earth they are perigee and apogee, around the Sun perihelion and aphelion, around the [[Moon]] perilune and apolune, and around other stars periastron and apastron.[^gonzalez2025][^spencer2023b] Because the sum of [[Kinetic_energy|kinetic]] and [[Potential_energy|potential energy]] stays constant along an unperturbed orbit, a body speeds up as it falls toward periapsis and slows as it climbs to apoapsis.[^motz2013] [[Earth]] shows a small version of this, moving at about 30.3 km/s at perihelion and 29.3 km/s at aphelion.[^nasa-earth] The explorer draws the planets' orbits from [[NASA]]'s JPL mean elements, so the near-circles and their slight offsets from the Sun are real, while the tilted and backward orbits of [[Pluto]], [[Eris_(dwarf_planet)|Eris]] and [[Halley's_Comet|Halley's Comet]] come from the JPL Small-Body Database.[^jpl-t1][^jpl-sbdb] ## Principles An orbit results from combining [[Newton's_laws_of_motion|Newton's three laws of motion]] with his law of gravitation.[^oxford-newton] Left alone, a body keeps moving in a straight line; a [[Force|force]] toward another body bends that line; and each body pulls the other equally, so both circle their common centre of mass.[^arfken2012] A body moving sideways fast enough keeps falling without ever arriving, and the pull, varying with separation around the path, reproduces Kepler's laws.[^arfken2012] A launch vehicle climbs vertically out of the densest air, then pitches over so that its engines finish firing nearly horizontally.[^wie1998] An orbit that dips into thick air loses speed and eventually re-enters; spacecraft sometimes graze an atmosphere on purpose to shed energy, a manoeuvre called aerobraking.[^cooper1991] ### Illustration Newton's own thought experiment makes the idea concrete: a cannon on a very high mountain, above the air, fires horizontally.[^newton1685] A slow shot falls to the ground nearby. A faster shot lands farther away, because the ground curves away beneath the falling ball. At one particular speed, set by the planet's mass and the height of the mountain, the ground drops away exactly as fast as the ball falls, and the ball circles the planet. Faster still, it traces ellipses whose far point lies opposite the mountain; at the [[Velocity|escape speed]] the path opens into a parabola, and beyond it into a hyperbola, leaving the planet for good but not the Sun.[^weapons1963] Near Earth's surface the circular speed is about 7.9 km/s and the escape speed about 11.2 km/s, their ratio being √2 (the circular value derived from the fact-sheet mass and radius).[^nasa-earth][^openstax] ## Newton's laws ### Gravity and motion In most situations Newton's laws describe motion in a [[Gravitational_field|gravitational field]] with good accuracy; relativistic corrections matter close to a large mass such as a star, or when high precision is required.[^palais2009] A body's acceleration is the net force on it divided by its mass, and the gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of their separation.[^arfken2012] For two isolated, well-separated spheres, the two-body problem, this gives accurate trajectories, written about the heavier body when one dominates and about the common centre of mass when the masses are comparable.[^celletti2007][^fitzpatrick2012] ### Energy and conic sections With potential energy set to zero at infinite separation, it is negative at any finite distance, and the total energy sorts every two-body path.[^ogorodnikov2016] Negative total energy gives a bound, closed orbit, an ellipse, with the circle as the special case in which the two foci coincide; zero total energy gives a parabola, travelled at exactly escape speed; positive total energy gives a hyperbola, on which the bodies swing past each other once and separate.[^curtis2013][^spencer2023a] ### Kepler's laws Closed orbits repeat with a fixed period, and Kepler's three empirical laws, derivable from Newton's, describe them: the orbit is an ellipse lying in a fixed plane with the barycentre at one focus; the line from the Sun to the planet sweeps equal areas in equal times, so the planet moves faster near perihelion; and the cube of the semi-major axis divided by the square of the period is the same for all bodies orbiting the same central mass.[^nasa-kepler] ### Limitations of classical mechanics A perfectly spherical mass with a Newtonian field would hold a bound body on the same ellipse forever. Real orbits drift away from that ellipse because of a primary's flattening, lumpy mass distribution, tides and relativity.[^burnett2022][^harland2008][^cazenave2012][^odonnell2014] Newton published the two-body solution in the *Principia* in 1687; in 1912 Karl Sundman found a series solving the general three-body problem that converges too slowly to use, and the restricted problem, with one massless body, yields the Lagrangian points.[^oxford-newton][^karttunen2007] ## Formulation ### Newtonian analysis of orbital motion With the central mass treated as fixed, the acceleration of the orbiting body is **a** = −(μ/r²) **r̂**, where μ = GM is the standard gravitational parameter.[^dodd2011][^fitzpatrick2023] Written in polar coordinates (r, θ) in the orbital plane, the transverse part of this acceleration must vanish, and that condition integrates to r²θ̇ = h, a constant: the angular momentum per unit mass.[^fitzpatrick2023][^vallado2001] Since the area swept per unit time is h/2, this is Kepler's second law. The radial equation, rewritten with u = 1/r as a function of θ instead of time, becomes u″ + u = μ/h², the equation of a harmonic oscillator with a constant term. Its solution is r = p/(1 + e cos(θ − θ₀)), the polar equation of a conic with the focus at the origin; e is the eccentricity and p = a(1 − e²) for an ellipse, so e = 0 gives a circle of radius a.[^fitzpatrick2023] Combining the period with the swept area gives Kepler's third law in Newton's form, from which the period follows directly from the semi-major axis.[^knudsen2012] ### Relativistic orbital motion The Newtonian analysis ignores frame dragging and gravitational time dilation. Those effects become significant close to large masses, as in the precession of Mercury's orbit, and wherever precision is extreme: the orbit and clock models of GPS satellites must include them.[^odonnell2014][^pogge2017] Relativity also sets a smallest stable circular orbit around a black hole, which depends on the spins involved and, for a non-rotating hole, lies at three times the event-horizon radius.[^jefremov2015][^bardeen1972] ## Specification A two-body orbit is fixed by six numbers, for instance the three components of position and three of velocity at one moment, from which the path can be run forward or backward.[^major2013] An unperturbed orbit lies in a plane fixed in space, and three angles set that plane's orientation against a reference plane. The traditional choice is the set of six Keplerian elements: inclination i, longitude of the ascending node Ω, argument of periapsis ω, eccentricity e, semi-major axis a, and the true anomaly at a reference epoch.[^kluever2018] The explorer shows inclination most plainly. [[Pluto]]'s orbit is inclined about 17° to the [[Ecliptic|ecliptic]] and [[Eris_(dwarf_planet)|Eris]]'s about 44°, while [[Halley's_Comet|Halley's Comet]] has an inclination of about 162°: an inclination above 90° means the body goes around the Sun in the opposite sense to the planets.[^jpl-sbdb] The period follows from the semi-major axis and the masses. The semi-major axis is not the average distance, however: averaged over time, the distance of a body from the focus is a(1 + e²/2), equal to a only for a circle.[^festou2004] For Mercury, with e ≈ 0.206, the time-averaged distance is about 2% larger than a (derived). Real orbits are perturbed, so each element set is quoted for a stated epoch. ## Perturbations A perturbation is a force or impulse, small compared with the main gravitational pull, that changes an orbit's elements over time. Common sources are a primary's departure from a sphere, the pull of third bodies, radiation pressure, atmospheric drag and tides.[^aiaa2002] ### Radial, transverse and normal perturbations A perturbing force can be split into a radial part toward the primary, a transverse part along the direction of motion, and a normal part out of the orbital plane.[^lewis1997] To first order a small radial kick changes the eccentricity but not the period; a kick along or against the motion changes both, a forward push at periapsis raising the apoapsis; a normal kick only tilts the plane. ### Orbital decay A satellite that passes through the outer atmosphere loses energy to [[Drag_(physics)|drag]], mostly near periapsis where it moves fastest, so the apoapsis falls and the orbit becomes rounder until the whole path sinks into denser air and the satellite comes down.[^vukovich2019][^garcia1967] How high drag reaches depends on the planet, and on Earth it varies with solar activity and space weather.[^liu2023][^nwankwo2015] Solar and magnetic sails can hold or reshape an orbit without propellant, and a long conducting tether is slowed by electromagnetic drag in Earth's magnetic field.[^circi2005][^love1992][^ahedo2002] Tides cause decay too. A moon inside its planet's synchronous orbit raises tidal bulges that lag behind it, and their pull slows the moon, so it spirals inward.[^rasio1996][^fortes2025] Mars's inner moon Phobos is the leading example and is expected to crash into [[Mars]] or break into a ring within 20–40 million years.[^black2015] Compact binary stars also lose orbital energy to gravitational waves, significant only where masses are large and accelerations extreme.[^hughes2009] ### Oblateness A uniform sphere, or a body built of uniform concentric shells, attracts like a point mass.[^reed2022] Rotating planets bulge at the equator, which adds a quadrupole term to their field that matters at distances comparable to the planet's radius.[^tremaine2023][^chao2021] For satellites the even zonal harmonics are the important ones, because their effects accumulate over many orbits and turn the orbital plane and the line of apsides, while leaving the semi-major axis unchanged.[^renzetti2013] ### Tidal locking Tides exchange angular momentum and dissipate heat until no net angular momentum passes between two bodies over an orbit, a state that is stable because leaving it would need energy.[^exoplanets2010] Mercury is locked with three rotations every two orbits.[^colombo1965] The [[Moon]] is locked in synchronous rotation, always turning one face to Earth, and [[Pluto]] and [[Charon_(moon)|Charon]] are both locked facing each other.[^michaely2017] ### Multiple gravitating bodies The Moon's orbit cannot be computed accurately from Earth's gravity alone; the Sun's pull must be included.[^barbour2001] A satellite stays reasonably stable if it orbits well inside its planet's [[Hill_sphere|Hill sphere]].[^kisare2024] Over long times, extra bodies turn the line of apsides so that an ellipse traces a rosette; Hipparchus already knew the Moon's apogee circles in about 8.85 years.[^jones1991] In a distant binary, such motion can betray an unseen third star.[^borkovits2019] ### Approaches to many-body problems One method starts from pure Keplerian motion and adds perturbation series for the other bodies, which suits the positions of planets and moons.[^milani2010] The resulting ephemerides are accurate enough to drive celestial navigation tables and spacecraft tracking.[^standish1996] The other method integrates the [[Ordinary_differential_equation|differential equations]] of motion step by step from initial positions and velocities, the standard tool for mission design; rounding errors accumulate, which limits how far ahead it can be trusted.[^pelaez2007] ### Radiation and magnetic fields Small bodies are pushed measurably by sunlight and the stellar wind, and a magnetised body can interact with a planet's magnetosphere.[^vukovich2019] For rotating asteroids, uneven re-emission of absorbed sunlight, the Yarkovsky effect, slowly changes their semi-major axes over millions of years.[^bottke2006] ## Strange orbits Periodic orbits that are not ellipses exist in principle for several bodies, although most are unstable. A stable one was found in 2000: three equal masses chasing one another around a planar figure eight.[^chenciner2000] Later searches found non-planar solutions too, including twelve masses on four interlocking, roughly circular loops arranged like the edges of a cuboctahedron.[^peterson2013] Such configurations are thought to be very unlikely to arise naturally.[^peterson2013] ## Astrodynamics Astrodynamics, or orbital mechanics, applies [[Dynamics_(mechanics)|dynamics]] and celestial mechanics to rockets and spacecraft,.[^hu2015] It is usually computed from Newton's laws and deals with manoeuvres, plane changes and interplanetary transfers, predicting what each burn will do.[^curtis2020] General relativity is used where extra accuracy is needed, as in precise geodetic satellite orbits, or in strong fields close to the Sun or a planet.[^sosnica2025] ## Earth orbits Orbits around Earth are grouped by altitude. Low Earth orbit reaches up to 2,000 km.[^nasa1740] Medium Earth orbit runs from there to just below geosynchronous altitude, typically at about 20,200 km with 12-hour periods, the band used by navigation constellations.[^gcmd] A geosynchronous orbit matches Earth's sidereal rotation, completing one lap per sidereal day, and has a semi-major axis of 42,164 km; a geostationary orbit is the equatorial, circular case, in which a satellite hangs over one point of the equator.[^ippolito2017] High Earth orbits lie above the geosynchronous altitude of 35,786 km.[^gcmd] Kepler's third law links these figures: with Earth's gravitational parameter GM ≈ 398,600 km³/s², an orbit with a = 42,164 km has a period T = 2π√(a³/GM) ≈ 86,160 s, one sidereal day of about 23 h 56 min (derived).[^nasa-earth] ## Scaling in gravity The [[Newton's_law_of_universal_gravitation|gravitational constant]], G ≈ 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻², can be written with units of (density × time²)⁻¹, and that has a useful consequence.[^openstax] For a small body on an orbit of semi-major axis a around a sphere of radius R and mean [[Density|density]] ρ, the period is T = √(3π/(Gρ)) × (a/R)^(3/2) (derived from Kepler's third law). Shrinking every distance while keeping densities the same leaves periods unchanged; raising the density fourfold halves all periods. For a grazing orbit around Earth, with ρ = 5,514 kg/m³, T ≈ 5,060 s, about 84 minutes, independent of Earth's actual size (derived).[^nasa-earth] ## See also - [[Kepler's_laws_of_planetary_motion]] - [[Newton's_law_of_universal_gravitation]] - [[Hill_sphere]] - [[Ecliptic]] - [[Apparent_retrograde_motion]] - Molniya orbit · Polar orbit · Orbit determination ## References [^britannica]: *Encyclopædia Britannica*. "Orbit (astronomy)". https://www.britannica.com/EBchecked/topic/431123/orbit [^nasa-bary]: NASA Space Place. "What is a barycenter?". https://spaceplace.nasa.gov/barycenter/ [^kuhn1985]: Kuhn, T. S. (1985). *The Copernican Revolution*. Harvard University Press, pp. 238, 246–252. ISBN 978-0-674-17103-9. [^kembhavi2020]: Kembhavi, A.; Khare, P. (2020). *Gravitational Waves: A New Window to the Universe*. Springer Nature, pp. 38–42. 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ISBN 978-1-107-02381-9. - Murray, C. D.; Dermott, S. F. (1999). *Solar System Dynamics*. Cambridge University Press. https://doi.org/10.1017/CBO9781139174817 ## External links - NASA Science: Orbits and Kepler's laws — https://science.nasa.gov/solar-system/orbits-and-keplers-laws/ - JPL Solar System Dynamics: planetary orbital elements — https://ssd.jpl.nasa.gov/planets/approx_pos.html - NASA: Basics of Space Flight, chapter 5 "Planetary orbits" — https://science.nasa.gov/learn/basics-of-space-flight/chapter5-1/ ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Orbit) : [Wikitube](https://en.wikitube.io/wiki/Orbit) · pinned revision [1369390584](https://en.wikipedia.org/w/index.php?oldid=1369390584) · 2026-09-18 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Solar_System]]. --- *Solar System portal child articles, wave 1 · 2026-09-18 · drafted · row SOL-004 · explorer state `?view=orbits`.* <!-- hub_tags: Life_Physics · PORTAL_Solar_System -->