Earth Centered Inertial
Encyclopedia
Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of the Earth. ECI frames are called inertial in contrast to the Earth-centered, Earth-fixed (ECEF
) frames which rotate in inertial space
in order to remain fixed with respect to the surface of the Earth. 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
.
ECI coordinate frames are not truly inertial since the Earth itself is accelerating as it travels in its orbit about the Sun. In many cases, it may be assumed that the ECI frame is inertial without adverse effect. However, when computing the gravitational influence of a third body such as the Moon on the dynamics of a spacecraft, the acceleration of the ECI frame must be considered. For example, when computing the acceleration of an Earth-orbiting spacecraft due to the gravitational influence of the Moon, the acceleration of the Earth itself due to the Moon's gravity must be subtracted.
, and it does not coincide with the Earth's equatorial plane. The angle between the Earth's equatorial plane and the ecliptic,
, is called the obliquity of the ecliptic
and
.
The intersection of the ecliptic and Earth's equatorial plane can be used as a principal direction for ECI frames and is called the vernal equinox. The Sun lies in the direction of the vernal equinox around March 21. 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
and declination
which are measured from the vernal equinox and the celestial equator
. Right ascension and declination are spherical coordinates
analogous to longitude and latitude
, respectively. Locations of objects in space can also be represented using Cartesian coordinates
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
. Nutation
is the smaller amplitude shorter-period (< 18.6 years) wobble that is superposed on the precessional motion of the Celestial pole
. 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
. Models representing the ever-changing orientation of the Earth in space are available from the International Earth Rotation and Reference Systems Service
.
on 1 January 2000. It can be referred to as J2000 or EME2000. The x-axis is aligned with the mean equinox. The z-axis is aligned with the Earth's spin axis or celestial North Pole
. The y-axis is rotated by 90° East about the celestial equator.
.
two-line elements is sometimes called true equator, mean equinox (TEME) although it does not use the conventional mean equinox.
ECEF
ECEF stands for Earth-Centered, Earth-Fixed, and is a Cartesian coordinate system, and is sometimes known as a "conventional terrestrial" system. It represents positions as an X, Y, and Z coordinate. The point is defined as the center of mass of the earth, hence the name Earth-Centered...
) frames which rotate in inertial space
Inertial space
In physics, the expression inertial space refers to the background reference that is provided by the phenomenon of inertia.Inertia is opposition to change of velocity, that is: change of velocity with respect to the background, the background that all physical objects are embedded in....
in order to remain fixed with respect to the surface of the Earth. 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
Equation of motion
Equations of motion are equations that describe the behavior of a system in terms of its motion as a function of time...
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
Astronomical object
Astronomical objects or celestial objects are naturally occurring physical entities, associations or structures that current science has demonstrated to exist in the observable universe. The term astronomical object is sometimes used interchangeably with astronomical body...
.
ECI coordinate frames are not truly inertial since the Earth itself is accelerating as it travels in its orbit about the Sun. In many cases, it may be assumed that the ECI frame is inertial without adverse effect. However, when computing the gravitational influence of a third body such as the Moon on the dynamics of a spacecraft, the acceleration of the ECI frame must be considered. For example, when computing the acceleration of an Earth-orbiting spacecraft due to the gravitational influence of the Moon, the acceleration of the Earth itself due to the Moon's gravity must be subtracted.
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 eclipticEcliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
, and it does not coincide with the Earth's equatorial plane. The angle between the Earth's equatorial plane and the ecliptic,
, is called the obliquity of the eclipticEcliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
and
.The intersection of the ecliptic and Earth's equatorial plane can be used as a principal direction for ECI frames and is called the vernal equinox. The Sun lies in the direction of the vernal equinox around March 21. The fundamental plane
Fundamental plane
The fundamental plane may refer to:* Fundamental plane , which divides a spherical coordinate system* Fundamental plane , which shows an empirical relationship among mean surface brightness, velocity dispersion and effective radius of an elliptical galaxy...
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
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...
and declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
which are measured from the vernal equinox and the celestial equator
Celestial equator
The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space...
. Right ascension and declination are spherical coordinates
Spherical coordinate system
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 inclination angle measured from a fixed zenith direction, and the azimuth angle of...
analogous to longitude and latitude
Geographic coordinate system
A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...
, respectively. Locations of objects in space can also be represented using Cartesian coordinates
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
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
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
. Nutation
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 behavior of a mechanism...
is the smaller amplitude shorter-period (< 18.6 years) wobble that is superposed on the precessional motion of the Celestial pole
Celestial pole
The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere...
. 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
Epoch (astronomy)
In astronomy, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as celestial coordinates, or elliptical orbital elements of a celestial body, where these are subject to perturbations and vary with time...
. Models representing the ever-changing orientation of the Earth in space are available from the International Earth Rotation and Reference Systems Service
International Earth Rotation and Reference Systems Service
The International Earth Rotation and Reference Systems Service , formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter and International Celestial Reference System ...
.
J2000
One commonly used ECI frame is defined with the Earth's Mean Equator and Equinox at 12:00 Terrestrial TimeTerrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
on 1 January 2000. It can be referred to as J2000 or EME2000. The x-axis is aligned with the mean equinox. The z-axis is aligned with the Earth's spin axis or celestial North Pole
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...
. 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 12:00 on 1 January 1950.GCRF
Geocentric Celestial Reference Frame (GCRF) is the Earth-centered counterpart of the International Celestial Reference FrameInternational Celestial Reference Frame
The International Celestial Reference Frame is a quasi-inertial reference frame centered at the barycenter of the Solar System, defined by the measured positions of 212 extragalactic sources . Although relativity implies that there is no true inertial frame, the extragalactic sources used to...
.
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 NORADNorth American Aerospace Defense Command
North American Aerospace Defense Command is a joint organization of Canada and the United States that provides aerospace warning, air sovereignty, and defense for the two countries. Headquarters NORAD is located at Peterson AFB, Colorado Springs, Colorado...
two-line elements is sometimes called true equator, mean equinox (TEME) although it does not use the conventional mean equinox.