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Orbital speed

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Speed at which a body orbits around the barycenter of a system

Not to be confused withEscape velocity.

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Astrodynamics
Part of a series on

Orbital mechanics
Orbital elements Apsis Argument of periapsis Eccentricity Inclination Mean anomaly Orbital nodes Semi-major axis True anomaly
Types oftwo-body orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit Radial orbit Decaying orbit
Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period Orbital velocity Surface gravity Specific orbital energy Vis-viva equation
Celestial mechanics
Gravitational influences Barycenter Hill sphere Perturbations Sphere of influence
N-body orbits Lagrangian points (Halo orbits) Lissajous orbits Lyapunov orbits
Engineering and efficiency
Preflight engineering Mass ratio Payload fraction Propellant mass fraction Tsiolkovsky rocket equation
Efficiency measures Gravity assist Oberth effect
Propulsive maneuvers Orbital maneuver Orbit insertion
v t e

Ingravitationally bound systems, theorbital speed of anastronomical body or object (e.g.planet,moon,artificial satellite,spacecraft, orstar) is thespeed at which itorbits around either thebarycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to thecenter of mass of themost massive body.

The term can be used to refer to either the mean orbital speed (i.e. the average speed over an entire orbit) or its instantaneous speed at a particular point in its orbit. The maximum (instantaneous) orbital speed occurs atperiapsis (perigee, perihelion, etc.), while the minimum speed for objects in closed orbits occurs at apoapsis (apogee, aphelion, etc.). In idealtwo-body systems, objects in open orbits continue to slow down forever as their distance to the barycenter increases.

When a system approximates a two-body system, instantaneous orbital speed at a given point of the orbit can be computed from its distance to the central body and the object'sspecific orbital energy, sometimes called "total energy". Specific orbital energy is constant and independent of position.^[1]

Radial trajectories

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In the following, it is assumed that the system is a two-body system and the orbiting object has a negligible mass compared to the larger (central) object. In real-world orbital mechanics, it is the system's barycenter, not the larger object, which is at the focus.

Specific orbital energy, or total energy, is equal toE_k − E_p (the difference between kinetic energy and potential energy). The sign of the result may be positive, zero, or negative and the sign tells us something about the type of orbit:^[1]

If thespecific orbital energy is positive the orbit is unbound, or open, and will follow ahyperbola with the larger body thefocus of the hyperbola. Objects in open orbits do not return; once past periapsis their distance from the focus increases without bound. Seeradial hyperbolic trajectory
If the total energy is zero, (E_k = E_p): the orbit is aparabola withfocus at the other body. Seeradial parabolic trajectory. Parabolic orbits are also open.
If the total energy is negative,E_k −E_p < 0: The orbit is bound, or closed. The motion will be on anellipse with onefocus at the other body. Seeradial elliptic trajectory,free-fall time. Planets have bound orbits around the Sun.

Transverse orbital speed

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Thetransverse orbital speed is inversely proportional to the distance to the central body because of the law of conservation ofangular momentum, or equivalently,Kepler'ssecond law. This states that as a body moves around its orbit during a fixed amount of time, the line from the barycenter to the body sweeps a constant area of the orbital plane, regardless of which part of its orbit the body traces during that period of time.^[2]

This law implies that the body moves slower near itsapoapsis than near itsperiapsis, because at the smaller distance along the arc it needs to move faster to cover the same area.^[1]

Mean orbital speed

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For orbits with smalleccentricity, the length of the orbit is close to that of a circular one, and the mean orbital speed can be approximated either from observations of theorbital period and thesemimajor axis of its orbit, or from knowledge of themasses of the two bodies and the semimajor axis.^[3]

v\approx {2\pi a \over T}\approx {\sqrt {\mu  \over a}}

wherev is the orbital velocity,a is thelength of thesemimajor axis,T is the orbital period, andμ =GM is thestandard gravitational parameter. This is an approximation that only holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero.

When one of the bodies is not of considerably lesser mass see:Gravitational two-body problem

So, when one of the masses is almost negligible compared to the other mass, as the case forEarth andSun, one can approximate the orbit velocity $v_{o}$ as:^[1]

v_{o}\approx {\sqrt {\frac {GM}{r}}}

or:

v_{o}\approx {\frac {v_{e}}{\sqrt {2}}}

WhereM is the (greater) mass around which this negligible mass or body is orbiting, andv_e is theescape velocity at a distance from the center of the primary body equal to the radius of the orbit.

For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases withorbital eccentricitye, and is anellipse. This can be used to obtain a more accurate estimate of the average orbital speed:^[4]

v_{o}={\frac {2\pi a}{T}}\left[1-{\frac {1}{4}}e^{2}-{\frac {3}{64}}e^{4}-{\frac {5}{256}}e^{6}-{\frac {175}{16384}}e^{8}-\cdots \right]

The mean orbital speed decreases with eccentricity.

Instantaneous orbital speed

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For the instantaneous orbital speed of a body at any given point in its trajectory, both the mean distance and the instantaneous distance are taken into account:

v={\sqrt {\mu \left({2 \over r}-{1 \over a}\right)}}

whereμ is thestandard gravitational parameter of the orbited body,r is the distance at which the speed is to be calculated, anda is the length of the semi-major axis of the elliptical orbit. This expression is called thevis-viva equation.^[1]

For the Earth atperihelion, the value is:

{\sqrt {1.327\times 10^{20}~{\text{m}}^{3}{\text{s}}^{-2}\cdot \left({2 \over 1.471\times 10^{11}~{\text{m}}}-{1 \over 1.496\times 10^{11}~{\text{m}}}\right)}}\approx 30,300~{\text{m}}/{\text{s}}

which is slightly faster than Earth's average orbital speed of 29,800 m/s (67,000 mph), as expected fromKepler's 2nd Law.

Tangential velocities at altitude

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Orbit	Center-to-center distance	Altitude above the Earth's surface	Speed	Orbital period	Specific orbital energy
Earth's own rotation at surface on the equator (for comparison; not an orbit)	6,378 km	0 km	465.1 m/s (1,674 km/h or 1,040 mph)	23 h 56 min 4.09 sec	−62.6 MJ/kg
Orbiting at Earth's surface (equator) theoretical	6,378 km	0 km	7.9 km/s (28,440 km/h or 17,672 mph)	1 h 24 min 18 sec	−31.2 MJ/kg
Low Earth orbit	6,600 – 8,400 km	200 – 2,000 km	Circular orbit: 7.7–6.9 km/s (27,720–24,840 km/h or 17,224–15,435 mph) respectively Elliptic: 10.07–8.7 km/s respectively	1 h 29 min – 2 h 8 min	−29.8 MJ/kg
Molniya orbit	6,900 – 46,300 km	500 – 39,900 km	1.5–10.0 km/s (5,400–36,000 km/h or 3,335–22,370 mph) respectively	11 h 58 min	−4.7 MJ/kg
Geostationary	42,000 km	35,786 km	3.1 km/s (11,600 km/h or 6,935 mph)	23 h 56 min 4.09 sec	−4.6 MJ/kg
Orbit of the Moon	363,000 – 406,000 km	357,000 – 399,000 km	0.97–1.08 km/s (3,492–3,888 km/h or 2,170–2,416 mph) respectively	27.27 days	−0.5 MJ/kg

The lower axis gives orbital speeds of some orbits.

Planets

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The closer an object is to the Sun the faster it needs to move to maintain the orbit. Objects move fastest at perihelion (closest approach to the Sun) and slowest at aphelion (furthest distance from the Sun). Since planets in the Solar System are in nearly circular orbits their individual orbital velocities do not vary much. Being closest to the Sun and having the most eccentric orbit, Mercury's orbital speed varies from about 59 km/s at perihelion to 39 km/s at aphelion.^[5]

Orbital velocities of the Planets^[6]
Planet	Orbital velocity
Mercury	47.9 km/s (29.8 mi/s)
Venus	35.0 km/s (21.7 mi/s)
Earth	29.8 km/s (18.5 mi/s)
Mars	24.1 km/s (15.0 mi/s)
Jupiter	13.1 km/s (8.1 mi/s)
Saturn	9.7 km/s (6.0 mi/s)
Uranus	6.8 km/s (4.2 mi/s)
Neptune	5.4 km/s (3.4 mi/s)

Halley's Comet on aneccentric orbit that reaches beyondNeptune will be moving 54.6 km/s when 0.586 AU (87,700 thousand km) from the Sun, 41.5 km/s when 1 AU from the Sun (passing Earth's orbit), and roughly 1 km/s at aphelion 35 AU (5.2 billion km) from the Sun.^[7] Objects passing Earth's orbit going faster than 42.1 km/s have achievedescape velocity and will be ejected from the Solar System if not slowed down by agravitational interaction with a planet.

Velocities of better-known numbered objects that have perihelion close to the Sun
Object	Velocity at perihelion	Velocity at 1 AU (passing Earth's orbit)
322P/SOHO	181 km/s @ 0.0537 AU	37.7 km/s
96P/Machholz	118 km/s @ 0.124 AU	38.5 km/s
3200 Phaethon	109 km/s @ 0.140 AU	32.7 km/s
1566 Icarus	93.1 km/s @ 0.187 AU	30.9 km/s
66391 Moshup	86.5 km/s @ 0.200 AU	19.8 km/s
1P/Halley	54.6 km/s @ 0.586 AU	41.5 km/s

References

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^^a ^b ^c ^d ^eLissauer, Jack J.; de Pater, Imke (2019).Fundamental Planetary Sciences: physics, chemistry, and habitability. New York, NY, US: Cambridge University Press. pp. 29–31.ISBN 9781108411981.
^Gamow, George (2002) [1962].Gravity. New York, NY, US: Anchor Books, Doubleday & Co. pp. 66.ISBN 0-486-42563-0....the motion of planets along their elliptical orbits proceeds in such a way that an imaginary line connecting the Sun with the planet sweeps over equal areas of the planetary orbit in equal intervals of time.
^Wertz, James R.; Larson, Wiley J., eds. (2010).Space mission analysis and design (3rd ed.). Hawthorne, CA, US: Microcosm. p. 135.ISBN 978-1881883-10-4.
^Stöcker, Horst; Harris, John W. (1998).Handbook of Mathematics and Computational Science. Springer. pp. 386.ISBN 0-387-94746-9.
^"Horizons Batch for Mercury aphelion (2021-Jun-10) to perihelion (2021-Jul-24)".JPL Horizons (VmagSn is velocity with respect to Sun.). Jet Propulsion Laboratory. Retrieved26 August 2021.
^"Which Planet Orbits our Sun the Fastest?".
^v = 42.1219√1/r − 0.5/a, wherer is the distance from the Sun, anda is the major semi-axis.

Gravitationalorbits

Types

General	Box Circular Elliptical /Highly elliptical Horseshoe Hyperbolic trajectory Inclined /Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous semi sub Transfer orbit
Geocentric	Geosynchronous Geostationary Geostationary transfer Graveyard High Earth Low Earth Medium Earth Molniya Near-equatorial Orbit of the Moon Polar Sun-synchronous Transatmospheric Tundra Very low Earth
About other points	Mars Areocentric Areosynchronous Areostationary Lagrange points Distant retrograde Halo Lissajous Libration Lunar Sun Heliocentric Earth's orbit Mars cycler Heliosynchronous Other Lunar cycler

Parameters

Shape Size	e Eccentricity a Semi-major axis b Semi-minor axis Q, q Apsides
Orientation	i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis
Position	M Mean anomaly ν,θ,f True anomaly E Eccentric anomaly L Mean longitude l True longitude
Variation	T Orbital period n Mean motion v Orbital speed t₀ Epoch