# Orbital plane (astronomy)

Last updated An orbital plane as viewed relative to a plane of reference. An orbital plane can also be seen in relative to conic sections, in which the orbital path is defined as the intersection between a plane and a cone. Parabolic (1) and hyperbolic (3) orbits are escape orbits, whereas elliptical and circular orbits (2) are captive.

The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example would be the positions of the centers of a massive body (host) and of an orbiting celestial body at two different times/points of its orbit. In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point, a line and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry. In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the central mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. The notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects. Until the 17th century, lines were defined as the "[…] first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width. […] The straight line is that which is equally extended between its points."

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The orbital plane is defined in relation to a reference plane by two parameters: inclination (i) and longitude of the ascending node (Ω).

Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics. The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a reference direction, called the origin of longitude, to the direction of the ascending node, measured in a reference plane. The ascending node is the point where the orbit of the object passes through the plane of reference, as seen in the adjacent image. Commonly used reference planes and origins of longitude include:

By definition, the reference plane for the Solar System is usually considered to be Earth's orbital plane, which defines the ecliptic, the circular path on the celestial sphere that the Sun appears to follow over the course of a year. The Solar System is the gravitationally bound planetary system of the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun directly, the largest are the eight planets, with the remainder being smaller objects, such as the five dwarf planets and small Solar System bodies. Of the objects that orbit the Sun indirectly—the moons—two are larger than the smallest planet, Mercury. Earth orbits the Sun at an average distance of 149.60 million km, and one complete orbit takes 365.256 days, during which time Earth has traveled 940 million km. Earth's orbit has an eccentricity of 0.0167. Since the Sun constitutes 99.76% of the mass of the Sun–Earth system, the center of the orbit is extremely close to the center of the Sun. The ecliptic is the mean plane of the apparent path in the Earth's sky that the Sun follows over the course of one year; it is the basis of the ecliptic coordinate system. This plane of reference is coplanar with Earth's orbit around the Sun. The ecliptic is not normally noticeable from Earth's surface because the planet's rotation carries the observer through the daily cycles of sunrise and sunset, which obscure the Sun's apparent motion against the background of stars during the year.

In other cases, for instance a moon or artificial satellite orbiting another planet, it is convenient to define the inclination of the Moon's orbit as the angle between its orbital plane and the planet's equatorial plane. A natural satellite or moon is, in the most common usage, an astronomical body that orbits a planet or minor planet. In the context of spaceflight, a satellite is an artificial object which has been intentionally placed into orbit. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as Earth's Moon. The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic. The inclination has varied from about 22.0° to 24.5° over the past 5 million years.

## Artificial satellites around the Earth

For launch vehicles and artificial satellites, the orbital plane is a defining parameter of an orbit; as in general, it will take a very large amount of propellant to change the orbital plane of an object. Other parameters, such as the orbital period, the eccentricity of the orbit and the phase of the orbit are more easily changed by propulsion systems.

A propellant or propellent is a chemical substance used in the production of energy or pressurized gas that is subsequently used to create movement of a fluid or to generate propulsion of a vehicle, projectile, or other object. Common propellants are energetic materials and consist of a fuel like gasoline, jet fuel, rocket fuel, and an oxidizer. Propellants are burned or otherwise decomposed to produce the propellant gas. Other propellants are simply liquids that can readily be vaporized.

The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy.

Orbital planes of satellites are perturbed by the non-spherical nature of the Earth's gravity. This causes the orbital plane of the satellite's orbit to slowly rotate around the Earth, depending on the angle the plane makes with the Earth's equator. For planes that are at a critical angle this can mean that the plane will track the Sun around the Earth, forming a Sun-synchronous orbit. The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, or 109 times that of Earth, and its mass is about 330,000 times that of Earth. It accounts for about 99.86% of the total mass of the Solar System. Roughly three quarters of the Sun's mass consists of hydrogen (~73%); the rest is mostly helium (~25%), with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron. A Sun-synchronous orbit is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time. More technically, it is an orbit arranged so that it precesses through one complete revolution each year, so it always maintains the same relationship with the Sun.

A launch vehicle's launch window is usually determined by the times when the target orbital plane intersects the launch site.

## Related Research Articles Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. Apsis denotes either of the two extreme points—ie, the farthest or nearest point—in the orbit of a planetary body about its primary body. The plural term, "apsides", usually implies both apsis points ; apsides can also refer to the distance of the extreme range of an object orbiting a host body. For example, the apsides of Earth's orbit of the Sun are two: the apsis for Earth's farthest point from the Sun, dubbed the aphelion; and the apsis for Earth's nearest point, the perihelion. .

Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics to astronomical objects, such as stars and planets, to produce ephemeris data.

A geocentric orbit or Earth orbit involves any object orbiting Planet Earth, such as the Moon or artificial satellites. In 1997 NASA estimated there were approximately 2,465 artificial satellite payloads orbiting the Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center. Over 16,291 previously launched objects have decayed into the Earth's atmosphere. In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined. In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude at which the periapsis would occur if the body's orbit inclination were zero. It is usually denoted ϖ.

In celestial mechanics, the plane of reference is the plane used to define orbital elements (positions). The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longitude of the ascending node.

Spacecraft flight dynamics is the science of space vehicle performance, stability, and control. It requires analysis of the six degrees of freedom of the vehicle's flight, which are similar to those of aircraft: translation in three dimensional axes; and its orientation about the vehicle's center of mass in these axes, known as pitch, roll and yaw, with respect to a defined frame of reference. Spherical astronomy or positional astronomy is the branch of astronomy that is used to determine the location of objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of spherical geometry and the measurements of astrometry.

Cassini's laws provide a compact description of the motion of the Moon. They were established in 1693 by Giovanni Domenico Cassini, a prominent scientist of his time. A ground track or ground trace is the path on the surface of a planet directly below an aircraft or satellite. In the case of a satellite, it is the projection of the satellite's orbit onto the surface of the Earth.

The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets, as well as natural satellites and minor-planet moons. Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and do not rotate with respect to the stars. ECI frames are called inertial, in contrast to the Earth-centered, Earth-fixed (ECEF) frames, which remain fixed with respect to Earth's surface in its rotation. It is convenient to represent the positions and velocities of terrestrial objects in ECEF coordinates or with latitude, longitude, and altitude. However, for objects in space, the equations of motion that describe orbital motion are simpler in a non-rotating frame such as ECI. The ECI frame is also useful for specifying the direction toward celestial objects. The beta angle is a measurement that is used most notably in orbital spaceflight. The beta angle determines the percentage of time that a satellite in low Earth orbit (LEO) spends in direct sunlight, absorbing solar energy. The term is defined as the angle between the orbital plane of the satellite and the vector to the Sun. The beta angle is the smaller of the two angles between the Sun vector and the plane of the object's orbit. The beta angle does not define a unique orbital plane; all satellites in orbit with a given beta angle at a given altitude have the same exposure to the Sun, even though they may be orbiting in completely different planes around Earth. Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is the central object. It may also describe other motions such as precession or nutation of the object's rotational axis. Prograde or direct motion is motion in the same direction as the primary rotates. Rotation is determined by an inertial frame of reference, such as distant fixed stars. However, retrograde and prograde can also refer to an object other than the primary if so described.

This glossary of astronomy is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy features an extensive vocabulary and a significant amount of jargon.

• Fundamentals of Astrodynamics', (1971) Roger R. Bates, Donald D. Mueller, Jerry E. White, Dover Publications, Inc, New York, p.21