# Is this an ECI frame?

I am reading a document on satellite attitude control and the Kalman Filter and it mentions that the satellite is tumbling through free space in a reference frame that has the Sun vector of constant orientation at $\left[\begin{array}{c}-1 \\0\\0\end{array}\right]$ and the Earth's magnetic field at $\left[\begin{array}{c}0\\0\\-1\end{array}\right]$.
My question is, is this the same as the ECI (Earth Centred Interial) reference frame?

Apologies if this is the wrong place to be asking.

• It sounds like a hypothetical frame, in other words a frame that's made ip just for the purposes of an example, in order to simplify something. If those three directions are supposed to be orthogonal, the Earth's field wouldn't in general be perpendicular to the spacecraft-sun direction except along mathematically defined curves that would not also be natural orbits. So, and answer will likely be something along the lines of "in general, no." – uhoh Mar 30 '17 at 13:10
• An ECI frame wouldn't have a constant Sun vector. – Organic Marble Mar 30 '17 at 13:50
• @OrganicMarble I am not that familiar with orbital frames, hence the question, hence not knowing that, and hence wanting a name, if one exists, of such a frame mentioned in the question. – MrPhooky Mar 30 '17 at 15:36
• I'm certainly no expert on them (hence my comment instead of an answer). But in the ECI frames I'm familiar with, since they are fixed in relation to the distant stars, the Sun appears to move about the Earth. This article might get you started: en.wikipedia.org/wiki/Earth-centered_inertial – Organic Marble Mar 30 '17 at 15:45
• It is a hypothetical frame, its certainly not ECI as Organic Marble explained. If anything, this can be a satellite centered frame like RSW, NTW, PQW etc. – VolkanOzcan Mar 30 '17 at 20:49

## 1 Answer

It is likely that uhoh is correct, and the frame is just made to provide an example. However, such a frame could exist.

Sun Synchronous Orbits are orbits where the satellite is always within LOS of the sun. What happens is the orbital precession is equal to the time it takes for the Earth to complete one orbit around the sun. If a satellite were in such an orbit, one could define a rotating reference frame where one axis was always pointed away from the sun and another was always pointed zenith (away from Earth).

It is unlikely this is what the author meant, especially if the satellite is "tumbling through free space", as you said. In any case, it's definitely not ECI.

• The question says "Earth's magnetic field" which is what makes this so very unlikely to be possible. – uhoh Apr 26 '17 at 17:52
• Oh I wasn't paying attention to that, good point. The spacecraft could rotate according to the magnetic field, but if the field is ever not 90 degrees from the sun axis, then this reference frame would not be a true orthogonal frame. I'm not very familiar with the magnetic field direction, but I don't believe it would allow for a 90 degree constant. – Arthur Dent Apr 26 '17 at 18:16