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 barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the d ...

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

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 an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...

(i.e. "not

accelerating In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnit ...

"), 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 in

space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...

, 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. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...

that describe

orbital motion In celestial mechanics, an orbit (also known as orbital revolution) 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 obj ...

are simpler in a non-rotating frame such as ECI. The ECI frame is also useful for specifying the direction toward celestial objects: To represent the positions and velocities of terrestrial objects, it is convenient to use ECEF coordinates or

latitude In geography, latitude is a geographic coordinate system, geographic 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 t ...

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 lett ...

, and

altitude Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum (geodesy), datum and a point or object. The exact definition and reference datum varies according to the context (e.g., aviation, geometr ...

. In a nutshell: * ECI:

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

, accelerated, rotating with respect to the 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 or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...

. 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 (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...

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 Earth's orbit, Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making. Fr ...

, 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 orbital ...

of the ecliptic and ''ε'' ≈ 23.4°. An

equinox A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, arou ...

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 equinox (celestial coordinates), March equinox to the (hour circle of the) point in questio ...

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. The declination angle is measured north (positive) or ...

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. By extension, it is also a plane of reference in the equatorial coordinate system. Due to Earth's axial tilt, the celestial ...

. Right ascension and declination are

spherical coordinates In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are * the radial distance along the line connecting the point to a fixed point ...

analogous to

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

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

Cartesian coordinates In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular o ...

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 o ...

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 fra ...

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 axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at ...

. 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 b ...

. 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 P ...

. 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 ...

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

(or equivalently, the celestial North Pole) as it was at that time. The y-axis is rotated by 90° East about the celestial equator. *M50: This frame is similar to J2000, but is defined with the mean equator and equinox at the beginning of the Besselian year 1950, which is B1950.0 = JDE 2433282.423357 = 1950 January 0.9235 TT = 1949 December 31 22:09:50.4 TT.David G. Edwards, "Attitude and Pointing Flight Procedures Handbook," Rev A, January 1985, NASA Document JSC-10511, page 1-10. *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 ; , CDAAN), 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 pr ...

two-line elements 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