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Encyclopedia > Orbital speed

The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. It can be used to refer to either the mean orbital speed, the average speed as it completes an orbit, or instantaneous orbital speed, the speed at a particular point in its orbit. This article is about the astronomical term. ... A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... For other uses, see Satellite (disambiguation). ... Artists impression of the orbits of HD 188753, a triple star system A multiple star consists of three or more stars which appear from the Earth to be close to one another. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it was concentrated. ... For other uses, see Mass (disambiguation). ...

The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy. In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy can be thought of as energy stored within a physical system. ...

Thus, under standard assumptions the orbital speed ($v,$) is: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ...

• in general: $v= sqrt{2left({muover{r}}+{epsilon}right)}$
• elliptic orbit: $v= sqrt{muleft({2over{r}}-{1over{a}}right)}$
• parabolic trajectory: $v=sqrt{muleft({2over{r}}right)}$
• hyperbolic trajectory: $v=sqrt{muleft({2over{r}}+{1over{a}}right)}$

where: Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. ... In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. ... In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. ...

Note: In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s-2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting... In astrodynamics, an orbiting body () is a body that orbits central body (). Under standard assumptions in astrodynamics: it is orders of magnitude lighter than central body (i. ... In astrodynamics a central body () is a body that is being orbited by orbiting body(). Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. ... In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...

• Velocity does not explicitly depend on eccentricity but is determined by length of semi-major axis ($a,!$),

11.2 km/s is the least orbiting speed. Meanwhile 42.2 km/s is the greatest orbitng speed. Mr. Mckay is worng and is never right about anything he says.....Get the teachers edition book. In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...

## Contents

In the case of radial motion:

• if the energy is non-negative: the motion is either for the whole trajectory away from the central body, or for the whole trajectory towards it. For the zero-energy case, see escape orbit and capture orbit.
• if the energy is negative: the motion can be first away from the central body, up to r=μ/|ε|, then falling back. This is the limit case of an orbit which is part of an ellipse with eccentricity tending to 1, and the other end of the ellipse tending to the center of the central body. See also free-fall time.

An escape orbit (also known as C3 = 0 orbit) is the high-energy parabolic orbit around the central body. ... A capture orbit is the high-energy parabolic orbit that allows the capture other than crashing directly to the central bodys surface (or atmospheric re_entry). ... The free-fall time is the characteristic time it would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse. ...

## Mean orbital speed

11.2 km/s is the least orbiting speed. Meanwhile 42.2 km/s is the greatest orbitng speed. Mr. Mckay is worng and is never right about anything he says.....Get the teachers edition book.

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. In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... In geometry, the semi-major axis (also semimajor axis) a applies to ellipses and hyperbolas. ... For other uses, see Mass (disambiguation). ...

$v_o approx {2 pi a over T}$
$v_o approx sqrt{mu over a}$

where $v_o,!$ is the orbital velocity, $a,!$ is the length of the semimajor axis, $T,!$ is the orbital period, and $mu,!$ is the standard gravitational parameter. Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero. For other uses of this word, see Length (disambiguation). ... In geometry, the semi-major axis (also semimajor axis) a applies to ellipses and hyperbolas. ... In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s-2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...

Taking into account the mass of the orbiting body,

$v_o approx sqrt{m_2^2 G over (m_1 + m_2) r}$

where $m_1,!$ is now the mass of the body under consideration, $m_2,!$ is the mass of the body being orbited, $r,!$ is specifically the distance between the two bodies (which is the sum of the distances from each to the center of mass), and $G,!$ is the gravitational constant. This is still a simplified version; it doesn't allow for elliptical orbits, but it does at least allow for bodies of similar masses. According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... For other uses, see Ellipse (disambiguation). ...

For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with eccentricity $e,!$, and is given at ellipse. This can be used to obtain a more accurate estimate of the average orbital speed: For other uses, see Ellipse (disambiguation). ...

$v_o = frac{2pi a}{T}left[1-frac{1}{4}e^2-frac{3}{64}e^4 -frac{5}{256}e^6 -frac{175}{16384}e^8 - dots right]$[1]

The mean orbital speed decreases with eccentricity.

## Earth orbits

orbit center-to-center
distance
altitude above
the Earth's surface
speed period/time in space specific orbital energy
minimum sub-orbital spaceflight (vertical) 6500 km 100 km 0.0 km/s just reaching space 1.0 MJ/kg
ICBM up to 7600 km up to 1200 km 6 to 7 km/s time in space: 25 min 27 MJ/kg
LEO 6,600 to 8,400 km 200 to 2000 km circular orbit: 6.9 to 7.8 km/s
elliptic orbit: 6.5 to 8.2 km/s
89 to 128 min 32.1 to 38.6 MJ/kg
Molniya orbit 6,900 to 46,300 km 500 to 39,900 km 1.5 to 10.0 km/s 11 h 58 min 54.8 MJ/kg
GEO 42,000 km 35,600 km 3.1 km/s 23 h 56 min 57.5 MJ/kg
Orbit of the Moon 363,000 to 406,000 km 357,000 to 399,000 km 0.97 to 1.08 km/s 27.3 days 61.8 MJ/kg

Geocentric orbit refers to the orbit of any object orbiting the Earth, such as the Moon or artificial satellites. ... Distance is a numerical description of how far apart objects are at any given moment in time. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ... A sub-orbital spaceflight (or sub-orbital flight) is a spaceflight that does not involve putting a vehicle into orbit. ... A Minuteman III missile soars after a test launch. ... A low Earth orbit (LEO) is an orbit in which objects such as satellites are below intermediate circular orbit (ICO) and far below geostationary orbit, but typically around 350 - 1400 km above the Earths surface. ... Molniya orbit is a class of a highly elliptic orbit with inclination of +/-63. ... Geostationary orbit A geostationary orbit (GEO) is a geosynchronous orbit directly above the Earths equator (0Â° latitude), with orbital eccentricity of zero. ... The orbit of the Moon around the Earth is completed in approximately 27. ...

• examples

In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that, under standard assumption, moves a spacecraft from one circular orbit to another using two engine impulses. ...

## References

1. ^ H. St̀eocker, J. Harris (1998). Handbook of Mathematics and Computational Science. Springer, p. 386. ISBN 0387947469.

Results from FactBites:

 Orbital speed - Wikipedia, the free encyclopedia (578 words) The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy. 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.
 Orbital spaceflight - Wikipedia, the free encyclopedia (697 words) The expression "orbital spaceflight" is mostly used to distinguish from sub-orbital spaceflights, which are flights where the spacecraft reaches space but does not have a high enough angular velocity to enter into orbit. The problem of deceleration from orbital speeds is solved through using atmospheric drag (aerobraking) to lose nearly all of the speed. On an orbital space flight initial deceleration is provided by the retrofiring of the craft's rocket engines, perturbing the orbit (by lowering perigee down into the atmosphere) onto a suborbital trajectory.
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