Orbital speed - Citizendia

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. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is A natural satellite or moon is a Celestial body that Orbits a Planet or smaller body which is called the primary. This article is about artificial satellites For natural satellites also known as moons see Natural satellite. A multiple star consists of three or more Stars which appear from the Earth to be close to one another in the sky In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object 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. In Astrodynamics the specific Orbital energy \epsilon\\! (or vis-viva energy) of an Orbiting body traveling through Space The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system

Thus, under standard assumptions the orbital speed ( $v\,$ ) is:

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

where:

$\mu\,$ is the standard gravitational parameter
$r\,$ is the distance between the orbiting body and the central body
$\epsilon\,$ is the specific orbital energy
$a\,\!$ is the semi-major axis

Note:

Velocity does not explicitly depend on eccentricity but is determined by length of semi-major axis ( $a\,\!$ ). For most of the problems in Astrodynamics involving two bodies m_1\ and m_2\ standard assumptions are usually the following A1 In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 In Astrodynamics or Celestial mechanics a Parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 In Astrodynamics or Celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1 Small body orbiting a central body Under Standard assumptions in astrodynamics we have m where m \ is the mass In Astrodynamics, an Orbiting body (m_1\ is a body that Orbits Central body (m_2\ In Astrodynamics a central body (m_1\ is a body that is being orbited by an Orbiting body (m_2\ In Astrodynamics the specific Orbital energy \epsilon\\! (or vis-viva energy) of an Orbiting body traveling through Space In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae

1 Radial trajectories
2 Transverse orbital speed
3 Mean orbital speed
4 Earth orbits
5 See also
6 References

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. An escape orbit (also known as C 3 = 0 orbit is a high-energy Parabolic orbit around the central body 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 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. The free-fall time is the characteristic Time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse

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. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. 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. In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from 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. In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape The orbital period is the time taken for a given object to make one complete Orbit about another object In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object

$v_o \approx {2 \pi a \over T}$

$v_o \approx \sqrt{\mu \over a}$

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. Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae Small body orbiting a central body Under Standard assumptions in astrodynamics we have m where m \ is the mass 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,

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

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. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass This is still a simplified version; it doesn't allow for elliptical orbits, but it does at least allow for bodies of similar masses. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a

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. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a This can be used to obtain a more accurate estimate of the average orbital speed:

$v_o = \frac{2\pi a}{T}\left[1-\frac{1}{4}e^2-\frac{3}{64}e^4 -\frac{5}{256}e^6 -\frac{175}{16384}e^8 - \dots \right]$ ^[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. Distance is a numerical description of how far apart objects are The orbital period is the time taken for a given object to make one complete Orbit about another object In Astrodynamics the specific Orbital energy \epsilon\\! (or vis-viva energy) of an Orbiting body traveling through Space A sub-orbital spaceflight (or sub-orbital flight is a Spaceflight in which the Spacecraft reaches space, but its Trajectory intersects 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. A Low Earth Orbit (LEO is generally defined as an Orbit within the locus extending from the Earth’s surface up to an altitude of 2000 km 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. A Molniya orbit is a type of Highly elliptical orbit with an Inclination of 63 5 to 10. 0 km/s	11 h 58 min	54. 8 MJ/kg
GEO	42,000 km	35,786 km	3. A geostationary orbit (GEO is a Geosynchronous orbit directly above the Earth 's Equator (0° Latitude) with a period equal to the Earth's 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. The orbit of the Moon around the Earth is completed in approximately 27 97 to 1. 08 km/s	27. 3 days	61. 8 MJ/kg

References

^ H. In Astronautics and Aerospace engineering, the Hohmann transfer orbit is an Orbital maneuver using two engine impulses which under standard assumptions St̀eocker, J. Harris (1998). Handbook of Mathematics and Computational Science. Springer, p. 386. ISBN 0387947469.

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Contents

Radial trajectories

Transverse orbital speed

Mean orbital speed

Earth orbits

See also

References