Earth-centered inertial

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 exactly inertial since the Earth center of mass 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.

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, 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 of the ecliptic and ε ≈ 23.4°.

An equinox 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 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.

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