Earth-centered inertial

To show a location about Earth using the ECI system, Cartesian coordinates are used. The x–y plane coincides with the equatorial plane of Earth. The x-axis is permanently fixed in a direction relative to the celestial sphere, which does not rotate as Earth does. The z-axis lies at a 90° angle to the equatorial plane and extends through the North Pole. Due to forces that the Sun and Moon exert, Earth's equatorial plane moves with respect to the celestial sphere. Earth rotates while the ECI coordinate system does not.

Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars.[1] "I" in "ECI" stands for inertial (i.e. "not accelerating"), in contrast to the "Earth-centered – Earth-fixed" (ECEF) frames, which remains fixed with respect to Earth's surface in its rotation, and then rotates with respect to stars.

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:

To represent the positions and velocities of terrestrial objects, it is convenient to use ECEF coordinates or latitude, longitude, and altitude.

In a nutshell:

  • ECI: inertial, not rotating, with respect to the stars; useful to describe motion of celestial bodies and spacecraft.
  • ECEF: not inertial, 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. 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 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.[2]

  1. ^ Ashby, Neil (2004). "The Sagnac effect in the Global Positioning System". In Guido Rizzi, Matteo Luca Ruggiero (ed.). Relativity in rotating frames: relativistic physics in rotating reference frames. Springer. p. 11. ISBN 1-4020-1805-3.
  2. ^ Tapley, Byron D; Schutz, Bob E; Born, George H (2004). Statistical Orbit Determination. Elsevier Academic Press. pp. 61–63. ISBN 978-0-12-683630-1.