Earth Centered Inertial Coordinate System

Earth-centered inertial (ECI) coordinate frames have their origins at the

center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

and are fixed with respect to the stars. "I" in "ECI" stands for

inertial In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...

(i.e. "not

accelerating In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by th ...

"), in contrast to the "Earth-centered - Earth-fixed" (

ECEF The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, ...

) frames, which remains fixed with respect to Earth's surface in its rotation, and then rotates with respect to stars. For

objects Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...

space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...

, the

equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...

that describe

orbital motion In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...

are simpler in a non-rotating frame such as ECI. The ECI frame is also useful for specifying the direction toward

celestial objects An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...

: To represent the positions and

velocities Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

of terrestrial objects, it is convenient to use ECEF coordinates or

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

longitude Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...

, and

altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...

. In a nutshell: * ECI:

, not

rotating Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...

, with respect to the stars; useful to describe motion of celestial bodies and spacecraft. * ECEF: not

, accelerated, rotating w.r.t stars; useful to describe motion of objects on Earth surface. The extent to which an ECI frame is actually inertial is limited by the non-uniformity of the surrounding

gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...

. For example, the Moon's gravitational influence on a high-Earth orbiting satellite is significantly different than its influence on Earth, so observers in an ECI frame would have to account for this

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

difference in their laws of motion. The closer the observed object is to the ECI-origin, the less significant the effect of the gravitational disparity is.

Coordinate system definitions

It is convenient to define the orientation of an ECI frame using the Earth's orbit plane and the orientation of the Earth's rotational axis in space. The Earth's orbit plane is called the

ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic again ...

, and it does not coincide with the Earth's equatorial plane. The angle between the Earth's equatorial plane and the ecliptic, ''ε'', is called the

obliquity In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbit ...

of the ecliptic and ''ε'' ≈ 23.4°. An

equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...

occurs when the earth is at a position in its orbit such that a vector from the earth toward the sun points to where the ecliptic intersects the celestial equator. The equinox which occurs near the first day of spring (with respect to the North hemisphere) is called the vernal equinox. The vernal equinox can be used as a principal direction for ECI frames. The Sun lies in the direction of the vernal equinox around 21 March. The fundamental plane for ECI frames is usually either the equatorial plane or the ecliptic. The location of an object in space can be defined in terms of

right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth. When paired w ...

and

declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the ...

which are measured from the vernal equinox and the

celestial equator 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 projectio ...

. Right ascension and declination are

spherical coordinates In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measu ...

analogous to

longitude and latitude The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various ...

, respectively. Locations of objects in space can also be represented using

Cartesian coordinates A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...

in an ECI frame. The gravitational attraction of the Sun and Moon on the Earth's equatorial bulge cause the rotational axis of the Earth to precess in space similar to the action of a top. This is called

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...

Nutation Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame ...

is the smaller amplitude shorter-period (< 18.6 years) wobble that is superposed on the precessional motion of the

Celestial pole The north and south celestial poles are the two points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently dire ...

. It is due to shorter-period fluctuations in the strength of the torque exerted on Earth's equatorial bulge by the sun, moon, and planets. When the short-term periodic oscillations of this motion are averaged out, they are considered "mean" as opposed to "true" values. Thus, the vernal equinox, the equatorial plane of the Earth, and the ecliptic plane vary according to date and are specified for a particular

epoch In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided by ...

. Models representing the ever-changing orientation of the Earth in space are available from the

International Earth Rotation and Reference Systems Service The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Pa ...

. Examples include: *J2000: One commonly used ECI frame is defined with the Earth's Mean Equator and Mean Equinox (MEME) at 12:00

Terrestrial Time Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. For example, the Astronomical Almanac uses T ...

on 1 January 2000. It can be referred to as ''J2K'', ''J2000'' or ''EME2000.'' The x-axis is aligned with the mean equinox. The z-axis is aligned with the

Earth's rotation axis In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbit ...

(or equivalently, the

celestial North Pole The north and south celestial poles are the two points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently dire ...

) as it was at that time. The y-axis is rotated by 90° East about the celestial equator.Tapley, Schutz, and Born, "Statistical Orbit Determination," Elsevier Academic Press, 2004, pp. 29–32. *M50: This frame is similar to J2000, but is defined with the mean equator and equinox at 12:00 on 1 January 1950. *GCRF: Geocentric Celestial Reference Frame is the Earth-centered counterpart of the

International Celestial Reference Frame The International Celestial Reference System (ICRS) is the current standard celestial reference system adopted by the International Astronomical Union (IAU). Its origin is at the barycenter of the Solar System, with axes that are intended to "sho ...

. *MOD: a Mean of Date (MOD) frame is defined using the mean equator and equinox on a particular date. *TEME: the ECI frame used for the

NORAD North American Aerospace Defense Command (NORAD ), known until March 1981 as the North American Air Defense Command, is a combined organization of the United States and Canada that provides aerospace warning, air sovereignty, and protection ...

two-line elements A two-line element set (TLE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the ''epoch''. Using a suitable prediction formula, the state (position and velocity) at any point in the pas ...

is sometimes called ''true equator, mean equinox'' (TEME) although it does not use the conventional mean equinox.

References

{{DEFAULTSORT:Earth-Centered Inertial Astronomical coordinate systems

Coordinate system definitions

See also

References