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The International Celestial Reference System (ICRS) defines coordinate axes that are closely aligned with those of the J2000 (aka EME2000) reference frame. The International Celestial Reference Frame (ICRF) and later versions of it (ICRF1, etc.) are realizations of the ICRS. For brevity, we'll simply refer to ``the ICRF'' below.

The rotational offset between the J2000 frame and the ICRS has magnitude of under 0.1 arcseconds.

-Reference Frames

I have found several references which show that there is a small difference between EME2000 and ICRS. I've also found several references which show that EME2000 is defined based on the orientation of the earth while ICRS is defined by extragalactic objects. However, I have not found any document describing why there is a difference between the two frames. What is the reason for why these frames were not constructed to be coincident with each other?

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The older coordinate systems were a bit more complicated. For example, the principal X axis is defined to be the vernal equinox direction at the epoch, not at the time of equinox. Its exact value depends on the exact time, and precise measurements of the Earth's orientation and its orbit. At that level of precision you can't treat the Earth as a rigid ball orbiting the Sun. It's a wobbly dynamic thing, in mutual orbit with the Moon.

The discrepancy between the ICRF and the EME2000 frame is unfortunate, but it's generally tricky to swap from one system to another without introducing any glitches. ;) And really, it's not a big discrepancy, relative to the errors in many old star coordinates that were produced before the modern era of computers and space telescopes.

Here's some relevant info from the JPL Horizons manual:

The ICRF was constructed to closely align with the older FK5/J2000 dynamic reference frame – within the uncertainties of that system – while replacing dynamical definitions based on intersecting and moving planes with ones based on the more precisely determined and fixed radio source positions.
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the ICRF is thought to differ from the previous FK5/J2000 dynamical system by at most 0.02 arcseconds.

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    $\begingroup$ That's very helpful. Your quote is also particularly helpful. Mine stated with authority that the difference was no more than X. Yours says "... is thought to differ..." which gives a very different feel. $\endgroup$
    – Cort Ammon
    Dec 1, 2023 at 4:02
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The idea that the J2000 reference frame is tied to the vernal equinox is true only in theory. Actually observing the equinox is impossible, it can only be inferred through measurements and computations done on them, all of which will have errors that build up, and are valid only for an instant in time.

In practice, the J2000 reference frame is defined by FK5, which were defined by actual observations of ~1500 stars at optical wavelengths. To determine the RA/Dec of some other object, they would be compared to stars of FK5 rather than the equinox. So, even if the orientation or orbit of the Earth turned out to be way off, the coordinates still would not change.

The ICRS at optical wavelengths was originally defined by the HIPPARCOS catalog. As detailed in Linking the FK5 to the ICRF, when you take the positions and proper motions of FK5 and propagate them to the epoch of the HIPPARCOS catalog, there is a systematic rotation between the two frames (on top of the random error).

In short, it is these errors that prevent the two systems from being equated exactly.

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