Orbital Speed

Information about 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.

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.

Thus, under standard assumptions the orbital speed ( $\text{[math]}$ ) is:

in general: $\text{[math]}$
elliptic orbit: $\text{[math]}$
parabolic trajectory: $\text{[math]}$
hyperbolic trajectory: $\text{[math]}$

where:

$\text{[math]}$ is the standard gravitational parameter
$\text{[math]}$ is the distance between the orbiting body and the central body
$\text{[math]}$ is the specific orbital energy
$\text{[math]}$ is the semi-major axis

Note:

Velocity does not explicitly depend on eccentricity but is determined by length of semi-major axis ( $\text{[math]}$ ),

Radial trajectories

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.

Transverse orbital speed

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. This means that the body moves faster near its periapsis than near its apoapsis, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time."

Mean orbital speed

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.

$\text{[math]}$

where $\text{[math]}$ is the orbital velocity, $\text{[math]}$ is the length of the semimajor axis, $\text{[math]}$ is the orbital period, and $\text{[math]}$ 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.

Taking into account the mass of the orbiting body,

$\text{[math]}$

where $\text{[math]}$ is now the mass of the body under consideration, $\text{[math]}$ is the mass of the body being orbited, $\text{[math]}$ is specifically the distance between the two bodies (which is the sum of the distances from each to the center of mass), and $\text{[math]}$ 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.

For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with eccentricity $\text{[math]}$ , and is given at ellipse. This can be used to obtain a more accurate estimate of the average orbital speed:

$\text{[math]}$ ^[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

References

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

planet, as defined by the International Astronomical Union (IAU), is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, not massive enough to cause thermonuclear fusion in its core, and has cleared its neighbouring region of
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A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. Such objects are often called moons. Technically, the term could also refer to a planet orbiting a star, or even to a star orbiting a galactic center, but these
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satellite is an object which has been placed into orbit by human endeavor. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon.
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multiple star consists of three or more stars which appear from the Earth to be close to one another. This closeness may be merely apparent, in which case the multiple star is optical
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ORBit is a CORBA compliant Object Request Broker (ORB). The current version is called ORBit2 and is compliant with CORBA version 2.4. It is developed under the GPL license and is used as middleware for the GNOME project.
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Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
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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.
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kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.
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Potential energy can be thought of as energy stored within a physical system. This energy can be released or converted into other forms of energy, including kinetic energy.
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A1: and are the only objects in the universe and thus influence of other objects is disregarded,

A2: The mass of the orbiting body () is far smaller than central body (), i.e.
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elliptic orbit can be computed from the Vis-viva equation as:

where:

is standard gravitational parameter,
is radial distance of orbiting body from central body,
is length of semi-major axis.

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In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit.
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In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body.
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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

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In astrodynamics, an orbiting body () is a body that orbits central body (). Under standard assumptions in astrodynamics:

it is less massive than the central body by several orders of magnitude (i.e. ).

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semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
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orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape. Eccentricity may be interpreted as a measure of how much this shape deviates from a circle.
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semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

Ellipse

An escape orbit (also known as C3 = 0 orbit) is a high-energy parabolic orbit around the central body. A body in this orbit has at each position the escape velocity with respect to this central body, for this position.
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A capture orbit is a reverse escape orbit. It is a parabolic orbit with as special case a straight line in the direction of the center of the central body. If it intersects the central body or its atmosphere the object will crash into the central body or there will be atmospheric
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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. As such, it plays a fundamental role in setting the timescale for a wide variety of astrophysical processes --
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angular momentum of an object rotating about some reference point is the measure of the extent to which the object will continue to rotate about that point unless acted upon by an external torque.
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Johannes Kepler

A 1610 portrait of Johannes Kepler by an unknown artist
Born November 27 1571
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Kepler's laws of planetary motion are three mathematical laws that describe the motion of planets in the Solar System. German mathematician and astronomer Johannes Kepler (1571–1630) discovered them.
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The orbital period is the time taken for a planet (or another object) to make one complete orbit.

When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.
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semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

Ellipse

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Orbital Speed

Information about Orbital Speed

Radial trajectories

Transverse orbital speed

Mean orbital speed

Earth orbits

See also

References

Ellipse

Ellipse

Ellipse