[fpknidxn] Observing Uranus with a rotating camera

Consider viewing a rotating and orbiting planet from the point of view of the sun.  On an equinox, you will see its whole surface over the course of its day, though the polar regions will be at a very oblique angle (assuming orthographic projection).

If the planet has a 90 degree axial tilt like Uranus, then on each solstice one polar region will face the sun directly.  Over the course of the year, every point on the planet experiences the sun roughly directly overhead.

The overhead sun traces a spiraling path on each hemisphere, circling around the poles, close to but not quite parallel to circles of latitide.

Constantly rotate your camera so that the planet gets viewed at every possible orientation, varying which direction is at the top of the photograph. The goal is to see every possible orientation of a 3D object in a smooth animation.  Previously.

I think more time will be spent near the poles.  This could be mitigated by artificially making the orbital speed faster near the solstices.

Also at the poles, the rotating camera and rotating planet will directly add or subtract each other (gimbal lock).

The planetary rotation period, orbital period, and camera rotation period should not be rational multiples of each other.

Incidentally, a surveillance satellite in polar orbit also eventually sees every point on the planet directly underneath it, but via a very different path: close to but not quite parallel with lines of longitude.  Perhaps this is the same as the above situation but with a planet with a day much longer than its year.  The surveillance satellite also oversamples near the poles.

Both of these seem to be simultaneous rotations of a sphere around 3 vaguely orthogonal axes, though I haven't thought through which axes move around due to rotation happening around another axis.  There are some awkward spots, but it's nice that it sort of works.

Consider dealing with the problem of oversampling near the poles by having the poles precess as they do in real life.  This is a vague idea, not sure how or if it will work.