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I'm completely confused about the difference between geocentric equatorial coordinate systems, ECI, and ECEF. David Vallado, in his book 'Fundamentals of Astrodynamics and Applications,' mentions that the ECI frame is commonly confused with the geocentric coordinate system. In the Body-Fixed Coordinate System section, he also states that he will use ECEF as a synonym for such system. Later in another section, he treats both as geocentric coordinate systems. However, in Curtis Howard's book 'Orbital Mechanics for Engineering Students,' the difference is never mentioned, and ECI and ECEF are treated as if they belong to the geocentric coordinate system.

So the question is, are ECI and ECEF frames and not coordinate systems, and do they belong to the geocentric equatorial systems since both have their origins at the center of the Earth? If I want to explain, would it be like this:

Under the geocentric equatorial coordinate systems, the ECI and ECEF frames can be found?

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    $\begingroup$ All three are centered on the Earth. But ECI is fixed relative to the distant stars, ECEF is fixed relative to the Earth's surface, and geocentric doesn't specify a fixed orientation. So ECI and ECEF are both types of geocentric coordinate systems. $\endgroup$ Dec 11, 2023 at 17:04
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    $\begingroup$ I'd sooner say that ECI and ECEF are really properties that coordinate systems can have (or some set of coordinate systems) and not unique coordinate systems themselves. They require further definition (i.e. where the principal axes point to) to be used rigorously. $\endgroup$
    – Erin Anne
    Dec 11, 2023 at 18:04
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    $\begingroup$ I agree with @ErinAnne. ECI is a type of coordinate system, and J2000 is a specific ECI that includes the further definitions that they refer to. The wikipedia page is useful to distinguish these terms: en.wikipedia.org/wiki/Earth-centered_inertial $\endgroup$
    – mdc
    Dec 11, 2023 at 18:33
  • $\begingroup$ Also, it might help to know that the International Terrestrial Reference Frame (ITRF) is a specific realization of an ECEF frame, and the Geocentric Celestial Reference Frame (GCRF) is a specific realization of an ECI frame. $\endgroup$ Dec 13, 2023 at 16:00

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ECI and ECEF are really terms that characterize a coordinate system or a reference frame. I think of them as more like adjectives than nouns.

ECI simply means that its origin is at the Earth's center and it's not rotating along with the Earth and ECEF means that its origin is at the Earth's center and it is rotating with the earth.

The distinction is important, for example, if you are calculating rocket trajectories. On the pad, the rocket is stationary in an ECEF coordinate system but moving in an ECI coordinate system. If you want to use orbital mechanics to help you calculate its trajectory in flight, you will need to do that in ECI (meaning "do that in an ECI coordinate system"), but if you then want to plot the rocket's position versus time relative to the Earth's surface in a rendering, you'll need to convert all of the position-versus-time values in the trajectory back to ECEF (meaning "back to the ECEF coordinate system").

People will often use the terms ECI and ECEF as nouns when really, strictly speaking, they should be used as adjectives. The use of these terms as nouns is a kind of jargon - it will confuse people who are not familiar with it.

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