# Why does Earth's North Pole RA flip by ~180 deg around AD2000 relative to SSB? (JPL Horizons data)

Using JPL's Horizons API I see that the Earth's North Pole RA flipped by ~180 degrees quite suddenly around AD 2000. It was pretty stable around 180deg for at least 1000 years prior, and then remains stable around 360 deg for at least 1000 years more.

Why is this? Is this an artifact to do with J2000 and ICRF ?

You can see this here - from AD 1000 to AD 3000

Is this an artifact to do with J2000 and ICRF?

It's an artifact of choosing to use right ascension and declination to describe the Earth's orientation. Right ascension is undefined at a declination of 90°, and is poorly defined at declinations near 90°. The heart of the problem is that the Earth's declination is defined to be 90° at 12 noon TT on 1 Jan 2000. That's exactly where right ascension is undefined. Near that point in time, there is barely any difference in orientation for even a 180° change in Earth's right ascension.

Satellite tracking antennae experience a similar problem when the satellite they are tracking is very close to directly overhead. Most tracking software algorithms avoid abruptly changing azimuth when the tracked satellite is directly overhead because if blindly applied, the tracking algorithm would have the antenna spin wildly. The antenna instead has to spin enough and smoothly enough so as to ensure the tracked satellite remains in view throughout the singularity and will remain in view after the singularity passes. A 180° rotation exactly at zenith is not needed. That 180° azimuth rotation is needed because that is the way tracking antennae work, but it can be done slowly. The spacecraft? It simply passed overhead. Azimuth and elevation work nicely away from the vertical, not so nicely near the vertical.

Another way to look at this is that using right ascension and declination to describe the orientation of the Earth's rotation axis is not the best choice. Yet another way to look at it: This is an incredibly bad choice because that choice passes through a singularity at noon TT on 1 Jan 2000. Nothing physical happened to the Earth at noon TT on 1 Jan 2000.

• If one instead uses quaternions to describe the Earth's orientation with respect to its orientation at noon TT 1 Jan 2000, what one will see is a nice smooth and smallish change due to precession and nutation that occurs across the noon TT 1 Jan 2000 boundary, the same as any other point in time. In other words, there is no boundary. Dec 27, 2022 at 7:31
• for more about those What are quaternions...?
– uhoh
Dec 27, 2022 at 12:49
• Thanks for this explanation @DavidHammen . I had suspected it was a problem with RA & DEC, but what threw me was that the data doesn't show DEC at 90 or RA crossing 0 on 1 Jan 2000. I presume this is the instability you mention? Dec 27, 2022 at 15:00
• @DavidHammen does the Horizons API offer any quaternion-based orientation data ? Dec 27, 2022 at 15:04
• @angst Regarding when the Horizons API offers quaternion based orientation data: The answer is that it does not. In addition, Horizons doesn't use an up-to-date model of the Earth's orientation. You can get a more up-to-date model from the Standards Of Fundamental Astronomy (SOFA), but that will require some programming. Dec 27, 2022 at 15:23