Orbital inclination

It is the angle between the orbital plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator. For planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun. This reference plane is most practical for Earth-based observers. Therefore, Earth's inclination is, by definition, zero. Inclination can instead be measured with respect to another plane, such as the Sun's equator or the invariable plane (the plane that represents the angular momentum of the Solar System, approximately the orbital plane of Jupiter).


ecliptical orbitsecliptic planeplane of the ecliptic
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 (and hence the Sun's apparent path around Earth). 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. The motions as described above are simplifications.

Orbital node

Nodeascending nodenodes
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes. Common planes of reference include the following: If a reference direction from one side of the plane of reference to the other is defined, the two nodes can be distinguished. For geocentric and heliocentric orbits, the ascending node (or north node) is where the orbiting object moves north through the plane of reference, and the descending node (or south node) is where it moves south through the plane.

Solar System

outer Solar Systeminner Solar Systemouter planets
The Sun's four largest orbiting bodies, the giant planets, account for 99% of the remaining mass, with Jupiter and Saturn together comprising more than 90%. The remaining objects of the Solar System (including the four terrestrial planets, the dwarf planets, moons, asteroids, and comets) together comprise less than 0.002% of the Solar System's total mass. Most large objects in orbit around the Sun lie near the plane of Earth's orbit, known as the ecliptic. The planets are very close to the ecliptic, whereas comets and Kuiper belt objects are frequently at significantly greater angles to it.


orbitsorbital motionplanetary motion
Longitude of the ascending node . Argument of periapsis . Eccentricity (e). Semimajor axis (a). Mean anomaly at epoch (M 0 ). Low Earth orbit (LEO): Geocentric orbits with altitudes up to 2,000 km (0–1,240 miles). Medium Earth orbit (MEO): Geocentric orbits ranging in altitude from 2,000 km (1,240 miles) to just below geosynchronous orbit at 35786 km. Also known as an intermediate circular orbit. These are "most commonly at 20200 km, or 20650 km, with an orbital period of 12 hours.". Both geosynchronous orbit (GSO) and geostationary orbit (GEO) are orbits around Earth matching Earth's sidereal rotation period.


Earth's surfaceterrestrialworld
The orbital and axial planes are not precisely aligned: Earth's axis is tilted some 23.44 degrees from the perpendicular to the Earth–Sun plane (the ecliptic), and the Earth–Moon plane is tilted up to ±5.1 degrees against the Earth–Sun plane. Without this tilt, there would be an eclipse every two weeks, alternating between lunar eclipses and solar eclipses. The Hill sphere, or the sphere of gravitational influence, of the Earth is about 1.5 e6km in radius. This is the maximum distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets.

Orbital elements

orbital parametersorbital elementKeplerian elements
Longitude of the ascending node —horizontally orients the ascending node of the ellipse (where the orbit passes upward through the reference plane, symbolized by ☊) with respect to the reference frame's vernal point (symbolized by ♈︎). This is measured in the reference plane, and is shown as the green angle Ω in the diagram. Argument of periapsis defines the orientation of the ellipse in the orbital plane, as an angle measured from the ascending node to the periapsis (the closest point the satellite object comes to the primary object around which it orbits, the blue angle ω in the diagram).

Binary star

spectroscopic binaryeclipsing binarybinary
All planets were found to be in S-type orbits around the primary star. In these three cases the secondary star was much dimmer than the primary and so was not previously detected. This discovery resulted in a recalculation of parameters for both the planet and the primary star. Science fiction has often featured planets of binary or ternary stars as a setting, for example George Lucas' Tatooine from Star Wars, and one notable story, "Nightfall", even takes this to a six-star system.

Orbital pole

ecliptic polenorth ecliptic poleecliptic north pole
For the remaining planets, the orbital pole in ecliptic coordinates is given by the longitude of the ascending node and inclination (i): l = ☊ - 90°, b = 90° - i. The ecliptic is the plane on which Earth orbits the Sun. The ecliptic poles are the two points where the ecliptic axis, the imaginary line perpendicular to the ecliptic, intersects the celestial sphere. The two ecliptic poles are mapped below.

Non-inclined orbit

equatorial orbitequatorialEcliptic orbit
A non-inclined orbit is an orbit coplanar with a plane of reference. The orbital inclination is 0° for prograde orbits, and π (180°) for retrograde ones. If the plane of reference is a massive spheroid body's equatorial plane, these orbits are called equatorial; if the plane of reference is the ecliptic plane, they are called ecliptic. As these orbits lack nodes, the ascending node is usually taken to lie in the reference direction (usually the vernal equinox), and thus the longitude of the ascending node is taken to be zero. Also, the argument of periapsis is undefined. Geostationary orbit is a geosynchronous example of an equatorial orbit. * List of orbits

First Point of Aries

sun passes into the constellation Aries
The First Point of Aries, also known as the Cusp of Aries, is the location of the vernal equinox, used as a reference point in celestial coordinate systems; in diagrams using such coordinate systems, it is often indicated with the symbol ♈︎. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the First Point of Libra, located exactly 180° from it. Due to precession of the equinoxes, currently, the position of the Sun on the March equinox is in Pisces, while that on the September equinox is in Virgo (as of J2000).

Semi-major and semi-minor axes

semi-major axissemimajor axissemi-major axes
The semi-major axis is sometimes used in astronomy as the primary-to-secondary distance when the mass ratio of the primary to the secondary is significantly large (M \gg m); thus, the orbital parameters of the planets are given in heliocentric terms. The difference between the primocentric and "absolute" orbits may best be illustrated by looking at the Earth–Moon system. The mass ratio in this case is 81.30059. The Earth–Moon characteristic distance, the semi-major axis of the geocentric lunar orbit, is 384,400 km. (Given the lunar orbit's eccentricity e = 0.0549, its semi-minor axis is 383,800 km. Thus the Moon's orbit is almost circular.)


autumnal equinoxautumn equinoxequinoxes
An equinox is commonly regarded as the instant of time when the plane (extended indefinitely in all directions) of Earth's equator passes through the center of the Sun. This occurs twice each year: around 20 March and 23 September. In other words, it is the moment at which the center of the visible Sun is directly above the equator. The word is derived from the Latin aequinoctium, from aequus (equal) and nox (genitive noctis) (night). On the day of an equinox, daytime and nighttime are of approximately equal duration all over the planet.

Celestial mechanics

celestialcelestial dynamicscelestial mechanician
A planet orbiting the Sun. A moon orbiting a planet. A spacecraft orbiting Earth, a moon, or a planet (in the latter cases the approximation only applies after arrival at that orbit). Astrometry is a part of astronomy that deals with measuring the positions of stars and other celestial bodies, their distances and movements. Astrodynamics is the study and creation of orbits, especially those of artificial satellites. Celestial navigation is a position fixing technique that was the first system devised to help sailors locate themselves on a featureless ocean. Dynamics of the celestial spheres concerns pre-Newtonian explanations of the causes of the motions of the stars and planets.


equatorial planeThe Equator
The equator of a rotating spheroid (such as a planet) is the parallel (circle of latitude) at which latitude is defined to be 0°. It is the imaginary line on the spheroid, equidistant from its poles, dividing it into northern and southern hemispheres. In other words, it is the intersection of the spheroid with the plane perpendicular to its axis of rotation and midway between its geographical poles. On Earth, the equator is about long, of which 78.8% lies across water and 21.3% over land. Indonesia is the country straddling the greatest length of the equatorial line across both land and sea.

Heliocentric orbit

Heliocentrictrans-Mars injectionsolar orbit
All planets, comets, and asteroids in the Solar System, and the Sun itself are in such orbits, as are many artificial probes and pieces of debris. The moons of planets in the Solar System, by contrast, are not in heliocentric orbits, as they orbit their respective planet (although the Moon has a convex orbit around the Sun). The barycenter of the Solar System, while always very near the Sun, moves through space as time passes, depending on where other large bodies in the Solar System, such as Jupiter and other large gas planets, are located at that time. A similar phenomenon allows the detection of exoplanets by way of the radial-velocity method.

Geocentric orbit

GeocentricEarth orbitEarth-orbit
;Equatorial plane: as used here, an imaginary plane extending from the equator on the Earth to the celestial sphere. ;Escape velocity: as used here, the minimum velocity an object without propulsion needs to have to move away indefinitely from the Earth. An object at this velocity will enter a parabolic trajectory; above this velocity it will enter a hyperbolic trajectory. ;Impulse: the integral of a force over the time during which it acts. Measured in (N·sec or lb * sec). ;Inclination: the angle between a reference plane and another plane or axis. In the sense discussed here the reference plane is the Earth's equatorial plane.


In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time. However, planetocentric longitude is always measured positively to the east, regardless of which way the planet rotates. East is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole.

Hour circle

The location of stars, planets, and other similarly distant objects is usually expressed in the following parameters, one for each of the three spatial dimensions: their declination, right ascension (epoch-fixed hour angle), and distance. These are as located at the vernal equinox for the epoch (e.g. J2000) stated. A meridian on the celestial sphere matches an hour circle at any time. The hour circle is a subtype whereby it is expressed in hours as opposed to degrees, radians, or other units of angle.

Orbital mechanics

astrodynamicsastrodynamicistorbital dynamics
For the case of orbital transfer between non-coplanar orbits, the change-of-plane thrust must be made at the point where the orbital planes intersect (the "node"). As the objective is to change the direction of the velocity vector by an angle equal to the angle between the planes, almost all of this thrust should be made when the spacecraft is at the node near the apoapse, when the magnitude of the velocity vector is at its lowest. However, a small fraction of the orbital inclination change can be made at the node near the periapse, by slightly angling the transfer orbit injection thrust in the direction of the desired inclination change.


NNordNorth Korea
However, the International Astronomical Union (IAU) defines the geographic north pole of a planet or any of its satellites in the Solar System as the planetary pole that is in the same celestial hemisphere, relative to the invariable plane of the Solar System, as Earth's north pole. This means some objects, such as Uranus, rotate in the retrograde direction: when seen from the IAU north, the spin is clockwise. Maps tend to be drawn for viewing with either true north or magnetic north at the top.

Perturbation (astronomy)

Most systems that involve multiple gravitational attractions present one primary body which is dominant in its effects (for example, a star, in the case of the star and its planet, or a planet, in the case of the planet and its satellite). The gravitational effects of the other bodies can be treated as perturbations of the hypothetical unperturbed motion of the planet or satellite around its primary body. In methods of general perturbations, general differential equations, either of motion or of change in the orbital elements, are solved analytically, usually by series expansions.

Argument of periapsis

argument of perihelionargument of perigeeargument of pericenter
An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis. However, especially in discussions of binary stars and exoplanets, the terms "longitude of periapsis" or "longitude of periastron" are often used synonymously with "argument of periapsis".

HD 189733 b

HD 189733bbHD189733b
The apparent longitude of ascending node of its orbit is 16 degrees +/- 8 away from north-south in our sky. It and HD 209458 b were the first two planets to be directly spectroscopically observed. The parent stars of these two planets are the brightest transiting-planet host stars, so these planets will continue to receive the most attention by astronomers. Like most hot Jupiters, this planet is thought to be tidally locked to its parent star, meaning it has a permanent day and night. The planet is not oblate, and has neither satellites with greater than 0.8 the radius of Earth nor a ring system like that of Saturn.

List of orbits

equatorialjovicentricorbital classifications
Inclined orbit: An orbit whose inclination in reference to the equatorial plane is not 0. Polar orbit: An orbit that passes above or nearly above both poles of the planet on each revolution. Therefore, it has an inclination of (or very close to) either 90 degrees or −90 degrees. Polar Sun-synchronous orbit (SSO): A nearly polar orbit that passes the equator at the same local solar time on every pass. Useful for image-taking satellites because shadows will be the same on every pass. Non-inclined orbit: An orbit whose inclination is equal to zero with respect to some plane of reference. Ecliptic orbit: A non-inclined orbit with respect to the ecliptic.