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In gravitationally bound systems, the **orbital speed** of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.

- Radial trajectories
- Transverse orbital speed
- Mean orbital speed
- Instantaneous orbital speed
- Tangential velocities at altitude
- Planets
- See also
- References

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 at periapsis (perigee, perihelion, etc.), while the minimum speed for objects in closed orbits occurs at apoapsis (apogee, aphelion, etc.). In ideal two-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's specific orbital energy, sometimes called "total energy". Specific orbital energy is constant and independent of position.^{ [1] }

In the following, it is thought 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 to *E*_{k} − *E*_{p}. (kinetic energy − 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 the specific orbital energy is positive the orbit is unbound, or open, and will follow a hyperbola with the larger body the focus of the hyperbola. Objects in open orbits do not return; once past periapsis their distance from the focus increases without bound. See radial hyperbolic trajectory
- If the total energy is zero, (
*E*_{k}=*E*_{p}): the orbit is a parabola with focus at the other body. See radial 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 an ellipse with one focus at the other body. See radial elliptic trajectory, free-fall time. Planets have bound orbits around the Sun.

The transverse orbital speed is inversely proportional to the distance to the central body because of the law of conservation of angular momentum, or equivalently, Kepler's second 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 its apoapsis than near its periapsis, because at the smaller distance along the arc it needs to move faster to cover the same area.^{ [1] }

For **orbits with small eccentricity **, 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 the orbital period and the semimajor axis of its orbit, or from knowledge of the masses of the two bodies and the semimajor axis.^{ [3] }

where *v* is the orbital velocity, *a* is the length of the semimajor axis, *T* is the orbital period, and *μ* = *GM* is the standard 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 for Earth and Sun, one can approximate the orbit velocity as:^{ [1] }

or assuming *r* equal to the radius of the orbit^{[ citation needed ]}

Where *M* is the (greater) mass around which this negligible mass or body is orbiting, and *v _{e}* is the escape velocity.

For an **object in an eccentric orbit** orbiting a much larger body, the length of the orbit decreases with orbital eccentricity *e*, and is an ellipse. This can be used to obtain a more accurate estimate of the average orbital speed:^{ [4] }

The mean orbital speed decreases with eccentricity.

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:

where *μ* is the standard gravitational parameter of the orbited body, *r* is the distance at which the speed is to be calculated, and *a* is the length of the semi-major axis of the elliptical orbit. This expression is called the vis-viva equation.^{ [1] }

For the Earth at perihelion, the value is:

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

Orbit | Center-to-center distance | Altitude above the Earth's surface | Speed | Orbital period | Specific orbital energy |
---|---|---|---|---|---|

Earth's own rotation at surface (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: 6.9–7.8 km/s (24,840–28,080 km/h or 14,430–17,450 mph) respectively
- Elliptic orbit: 6.5–8.2 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 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] }

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 an eccentric orbit that reaches beyond Neptune 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 achieved escape velocity and will be ejected from the Solar System if not slowed down by a gravitational interaction with a planet.

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 |

In celestial mechanics, the **Lagrange points** are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem.

In celestial mechanics, an **orbit** is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

In celestial mechanics, **escape velocity** or **escape speed** is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically stated as an ideal speed, ignoring atmospheric friction. Although the term "escape velocity" is common, it is more accurately described as a speed than a velocity because it is independent of direction. The escape speed is independent of the mass of the escaping object, but increases with the mass of the primary body; it decreases with the distance from the primary body, thus taking into account how far the object has already traveled. Its calculation at a given distance means that no acceleration is further needed for the object to escape: it will slow down as it travels—due to the massive body's gravity—but it will never quite slow to a stop. On the other hand, an object already at escape speed needs slowing for it to be captured by the gravitational influence of the body.

An **apsis** is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, for orbits about the Sun the apsides are called aphelion (farthest) and perihelion (nearest).

The **orbital period** is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. It may also refer to the time it takes a satellite orbiting a planet or moon to complete one orbit.

In astronautics, the **Hohmann transfer orbit** is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or another solar planet or asteroid. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target.

**Orbital mechanics** or **astrodynamics** is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.

The **Hill sphere** of an astronomical body is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sphere of its own. Any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. One simple view of the extent of the Solar System is the Hill sphere of the Sun with respect to local stars and the galactic nucleus.

**Earth's orbit** is an ellipse with the Earth-Sun barycenter as one focus and a current eccentricity of 0.0167. Since this value is close to zero, the center of the orbit is relatively close to the center of the Sun. Earth orbits the Sun at an average distance of 149.60 million km in a counterclockwise direction as viewed from above the Northern Hemisphere. One complete orbit takes 365.249 days, during which time Earth has traveled 940 million km.

In astrodynamics or celestial mechanics a **parabolic trajectory** is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an **escape orbit**, otherwise a **capture orbit**. It is also sometimes referred to as a **C _{3} = 0 orbit** (see Characteristic energy).

In astrodynamics or celestial mechanics, a **hyperbolic trajectory** or **hyperbolic orbit** is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one.

In astrodynamics, the **characteristic energy** is a measure of the excess specific energy over that required to just barely escape from a massive body. The units are length^{2} time^{−2}, i.e. velocity squared, or energy per mass.

In astrodynamics or celestial mechanics, an **elliptic orbit** or **elliptical orbit** is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1. In a wider sense, it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.

A **circular orbit** is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle.

In astrodynamics, an **orbit equation** defines the path of orbiting body around central body relative to , without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance, has an orbit that is a conic section with the central body located at one of the two foci, or *the* focus.

In astrodynamics, the **orbital eccentricity** of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy.

**Spacecraft flight dynamics** is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.

The **two-body problem in general relativity** is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun. Solutions are also used to describe the motion of binary stars around each other, and estimate their gradual loss of energy through gravitational radiation.

In geometry, the **major axis** of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The **semi-major axis** is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The **semi-minor axis** of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle.

**C/1980 E1** is a non-periodic comet discovered by Edward L. G. Bowell on 11 February 1980 and which came closest to the Sun (perihelion) in March 1982. It is leaving the Solar System on a hyperbolic trajectory due to a close approach to Jupiter. In the 42 years since its discovery only two objects with higher eccentricities have been identified, 1I/ʻOumuamua (1.2) and 2I/Borisov (3.35).

- 1 2 3 4 5 Lissauer, Jack J.; de Pater, Imke (2019).
*Fundamental Planetary Sciences: physics, chemistry, and habitability*. New York, NY, USA: Cambridge University Press. pp. 29–31. ISBN 9781108411981. - ↑ Gamow, George (1962).
*Gravity*. New York, NY, USA: 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, USA: 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. Retrieved 26 August 2021. - ↑ "Which Planet Orbits our Sun the Fastest?".
- ↑
*v*= 42.1219 √1/*r*− 0.5/*a*, where*r*is the distance from the Sun, and*a*is the major semi-axis.

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