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Encyclopedia > Circular orbit

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. Astrodynamics is the study and creation of orbits, especially those of artificial satellites. ... Celestial mechanics is a term for the application of physics, historically Newtonian mechanics, to astronomical objects such as stars and planets. ... In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. ... (This page refers to eccitricity in astrodynamics. ...

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Under standard assumptions the orbital velocity () of a body traveling along circular orbit can be computed as: 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. ... 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. ...

where:

Conclusion: In classical geometry, a radius of a circle or sphere is any line segment with one endpoint on the circle (i. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... 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 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...

• Velocity is constant along the path.

## Orbital period

Under standard assumptions the orbital period () of a body traveling along circular orbit can be computed as: 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. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ...

where:

Conclusions: 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 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...

• The orbital period is the same as that for an elliptic orbit with the semi-major axis () equal to orbit radius.

In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. ... In geometry, the semi-major axis (also semimajor axis) a applies to ellipses and hyperbolas. ...

## Energy

Under standard assumptions, specific orbital energy () is negative and the orbital energy conservation equation for this orbit takes the form: 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 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. ... In astrodynamics vis-viva equation (also referred to as orbital energy conservation equation) is one of the fundamental and useful equations that govern the motion of orbiting bodies. ...

where:

The virial theorem applies even without taking a time-average: 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. ... In classical geometry, a radius of a circle or sphere is any line segment with one endpoint on the circle (i. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... 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 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... The virial theorem states that the average kinetic energy of a system of particles whose motions are bounded is given by where ri and Fi are the position and force vectors on the i th particle respectively. ...

• the potential energy of the system is equal to twice the total energy
• the kinetic energy of the system is equal to minus the total energy

Thus the escape velocity from any distance is √2 times the speed in a circular orbit at that distance: the kinetic energy is twice as much, hence the total energy is zero. In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion, at that position, needs to have to move away indefinitely from the source of the field, as opposed to falling back or staying in an orbit within a...

## Equation of motion

Under standard assumptions, the orbital equation becomes: 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 astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ...

where:

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 specific relative angular momentum () of orbiting body () relative to central body () is the relative angular momentum of per unit mass. ... 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, 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...

## Delta-v to reach a circular orbit

Maneuvering into a large circular orbit, e.g. a geostationary orbit, requires a larger delta-v than an escape orbit, although the latter implies getting arbitrarily far away and having more energy than needed for the orbital speed of the circular orbit. It is also a matter of maneuvering into the orbit. See also Hohmann transfer orbit. A geostationary orbit (abbreviated GEO) is a circular orbit in the Earths equatorial plane, any point on which revolves about the Earth in the same direction and with the same period as the Earths rotation. ... General In general physics delta-v is simply the change in velocity. ... An escape orbit (also known as C3 = 0 orbit) is the high-energy parabolic orbit around the central body. ... 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. ... In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that moves a spacecraft from one orbit to another using a fairly low delta-v. ... Results from FactBites:

 SPACE.com -- Newfound Planet in Circular Orbit Around Another Star (666 words) But the newest discovery is among the minority found in a relatively circular orbit, adding to the likelihood that Earth-like planets could exist. It wasn't clear whether their odd orbits would turn out to be the norm or not, said Chris McCarthy, a researcher at the Carnegie Institution of Washington who participated in the latest find. The percentage of planets in these more "normal" circular orbits will likely grow as methods are refined and more planets are found farther from their stars, McCarthy said.
 Orbit (astronomy and physics) - MSN Encarta (940 words) The size of the orbit is given by the periapsis distance (SP) and the elongation of the orbit is given by the eccentricity (e). The three orbital elements that describe an orbit's orientation are the inclination (i), the longitude of the ascending node (Ω), and the argument of the periapsis (ω). The argument of the periapsis measures the angular displacement in the plane of the orbit between the ascending node and the line that passes through the center of the orbit (C) and the periapsis (P).
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