Why do satellite solar arrays misalign from each other?

Question

Searching for an answer to the title's question, I came across a post (How accurately can solar panels be continuously oriented toward the sun on a typical satellite?), in which someone said that "Twice a year, the solar arrays of a geostationary satellite with one degree of rotational freedom will be misaligned from optimal by at least 23.5 degrees."

1. What is a degree of rotational freedom?
2. How did he get to the value of 23.5 degrees?

And finally:

3. AFIK, solar arrays also unalign from each other (for instance, the North SA "moving" faster than the South SA). Why does it happen?

Answer 1

The detailed questions:

1. in this context "one degree of rotational freedom" simply means that the solar arrays have one drive motor and thus rotate about one axis. Contrast this with a solar array that has two drive motors, one mounted upon the other, this has two degrees of rotational freedom.

2. an easy to understand example would be a geostationary satellite. It orbits in the Earth's equatorial plane. Normally the satellite body points to Earth so, in inertial terms, the body is rotating once per day. The solar arrays stick out North and South and have one drive motor each and thus can track the sun whilst the satellite body rotates. However, the sun's relative path is not in the Earth's equatorial plane. Seen from the satellite's orbit the sun is sometimes in the Northern hemisphere and sometimes in the Southern hemisphere. At these times the sun is 23.5 degrees away, out of plane, compared to the equatorial plane. i.e. this angle is not measured in terms of the axis around which the solar arrays rotate.

I couldn't immediately find a diagram that showed the satellite's orbit and the direction of the solar arrays, you'll have to meet me halfway on that. In this diagram the sun's relative position compared to the equator is that it crosses the equatorial plane at the equinoxes and is 23.5 deg away at the solstices.

3. The answer quoted in the OP that mentions misalignment is still just talking about the 23.5 deg at para 2 above. I don't think David Hammen meant to infer that the solar arrays are misaligned with respect to one another and rotating at different rates. For what its worth, despite my comment just now, something vaguely similar can actually happen deliberately: a satellite operator could choose to orient the solar panels slightly differently for attitude control reasons, however in such a case both arrays are still rotating once per 24 hours, but slightly offset to one another.