mean anomaly

Information about mean anomaly

In the study of orbital dynamics the mean anomaly of an orbiting body is the angle the body would have traveled about the center of the orbit's auxiliary circle. Unlike other measures of anomaly, the mean anomaly grows linearly with time. Because of the linear growth with time, the mean anomaly makes calculating the time of flight between two points on the orbit very easy. The mean anomalies for the two points are calculated and their difference is found. Knowing this, the ratio of this difference relative to the entire $\text{[math]}$ encompassing one orbit is simply equal to ratio of the time of flight to the period of one whole orbit (i.e. $\text{[math]}$ ).

When measured in radians the mean anomaly has a value of $\text{[math]}$ at the initial crossing of the orbit's point of periapsis, and a multiple of $\text{[math]}$ at any later crossing of the point periapsis. In the diagram below, the mean anomaly of point $\text{[math]}$ on the obit around $\text{[math]}$ is given by angle $\text{[math]}$ (the angle $\text{[math]}$ ).

The point y is defined such that the circular sector area z-c-y is equal to the elliptic sector area z-s-p, scaled up by the ratio of the major to minor axes of the ellipse. Or, in other words, the circular sector area z-c-y is equal to the area x-s-z.

Calculation

In astrodynamics mean anomaly $\text{[math]}$ can be calculated as follows:

$\text{[math]}$

where:

$\text{[math]}$ is the mean anomaly at time $\text{[math]}$ ,
$\text{[math]}$ is the start time,
$\text{[math]}$ is the time of interest, and
$\text{[math]}$ is the mean motion.

Alternatively:

$\text{[math]}$

where:

$\text{[math]}$ is orbit's eccentric anomaly,
$\text{[math]}$ is orbit's eccentricity.

• • [ e] Orbits
Orbit types	Box orbit • Circular orbit • Ecliptic orbit • Elliptic orbit • Highly Elliptical Orbit • Graveyard orbit • Hyperbolic trajectory • Inclined orbit • Osculating orbit • Parabolic trajectory • Capture orbit • Escape orbit • Semi-synchronous orbit • Subsynchronous orbit • Synchronous orbit • Parking orbit
Earth-centered orbits	Geosynchronous orbit • Geostationary orbit • Sun-synchronous orbit • Low Earth orbit • Medium Earth Orbit • Molniya orbit • Near equatorial orbit • Orbit of the Moon • Polar orbit • Tundra orbit
Other orbits	Areosynchronous orbit • Areostationary orbit • Halo orbit • Lissajous orbit • Lunar orbit • Heliocentric orbit • Heliosynchronous orbit
Orbital elements	Inclination ( $\text{[math]}$ ) • Longitude of the ascending node ( $\text{[math]}$ ) • Eccentricity ( $\text{[math]}$ ) • Argument of periapsis ( $\text{[math]}$ ) • Semi-major axis ( $\text{[math]}$ ) • Mean anomaly at epoch ( $\text{[math]}$ )
Other orbital parameters	True anomaly ( $\text{[math]}$ ) • Semi-minor axis ( $\text{[math]}$ ) • Linear eccentricity ( $\text{[math]}$ ) • Eccentric anomaly ( $\text{[math]}$ ) • Mean longitude ( $\text{[math]}$ ) • True longitude ( $\text{[math]}$ ) • Orbital period ( $\text{[math]}$ )
Orbital maneuvers	Bi-elliptic transfer • Geostationary transfer orbit • Gravitational slingshot • Hohmann transfer orbit • Orbital inclination change • Orbit phasing • Space rendezvous
Other orbital mechanics topics	Apsis • Celestial coordinate system • Delta-v budget • Epoch • Ephemeris • Equatorial coordinate system • Gravity turn • Ground track • Interplanetary Transport Network • Kepler's laws of planetary motion • Lagrangian point • List of orbits • n-body problem • Orbit equation • Orbital state vectors • Perturbation • Retrograde and direct motion • Specific orbital energy • Specific relative angular momentum • The Oberth effect

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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angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept
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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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radian, in mathematics, is a unit of plane angle, equal to 180/π degrees, or about 57.2958 degrees. It is represented by the symbol "rad" or, more rarely, by the superscript c (for "circular measure"). For example, an angle of 1.2 radians would be written as "1.
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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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In geometry, the semi-minor axis (also semiminor axis) is a line segment associated with most conic sections (that is, with ellipses and hyperbolas). One end of the segment is the center of the conic section, and it is at right angles with the semi-major axis.
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ellipse (from the Greek ἔλλειψις, literally absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
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Orbital mechanics or astrodynamics is the study of the motion of rockets and other spacecraft. The motion of these objects is determined by Newton's laws of motion and the law of universal gravitation.
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Mean Motion, , is a measure of how fast a satellite progresses around its orbit. Unless the orbit is circular, the Mean Motion is only an average value, and does not represent the instantaneous angular rate.
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The eccentric anomaly is the angle between the direction of periapsis and the current position of an object on its orbit, projected onto the ellipse's circumscribing circle perpendicularly to the major axis, measured at the centre of the ellipse.
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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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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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In astronomy, the true anomaly (, also written ) is the angle between the direction z-s of periapsis and the current position p of an object on its orbit, measured at the focus s of the ellipse (the point around which the object orbits).
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In stellar dynamics a box orbit refers to a particular type of orbit which can be seen in triaxial systems, that is, systems which do not possess a symmetry around any of its axes.
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For other meanings of the term "orbit", see orbit (disambiguation)

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
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A non-inclined orbit is an orbit which is contained in the plane of reference. It therefore has inclination equal to zero. If the plane of reference is the equator, these orbits are called equatorial; if the plane of reference is the ecliptic, they are called ecliptic.
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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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Highly Elliptical Orbit (HEO) is an elliptic orbit characterized by a relatively low-altitude perigee and an extremely high-altitude apogee. These extremely elongated orbits can have the advantage of long dwell times at a point in the sky during the approach to and descent from
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A graveyard orbit, also called a supersynchronous orbit, junk orbit or disposal orbit, is an orbit significantly above synchronous orbit where spacecraft are intentionally placed at the end of their operational life.
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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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A satellite is said to occupy an inclined orbit around the Earth if the orbit exhibits an angle other than zero degrees with the equatorial plane. This angle is called the orbit's inclination.
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In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space is the gravitational Keplerian orbit about a central body that it would have if other perturbations were not present.
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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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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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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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Semi-Synchronous Orbit (SSO): An orbit with approximately a 12-hour period. A circular SSO is at an altitude of approximately 20,200 km.^[1]

References

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A subsynchronous orbit refers to the orbit of a satellite that is nearer the planet than it would be if it were in synchronous orbit, i.e. the orbital period is less than the sidereal day of the planet.
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mean anomaly

Information about mean anomaly

Calculation

See also

Ellipse

See also

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