May these pictures be of some help (hopefully):
Situation A1 shows camera being stationary on the north pole. The planet is not moving through space w/r to other stars (not orbiting the Sun, not traveling through the Galaxy). In this idealised situation, the planet can only rotate (period: 24h), and there is just one star to look at.
Situation A2 is the same setup, but 6 hours later, with the planet having rotated by 90⁰. The camera has not moved (displacement = 0km). All it has done is change orientation. The resultant star trail is a fourth of a circle (90⁰ of arc). One again - despite there being no motion other than orientation changes, star trails still appear.
(t=elapsed time; ε=angular displacement; d=linear displacement)
In situation B1 we place the camera on the equator. The planet is still not moving. The camera is made to rotate in the opposite direction to the planet's rotation, so as to compensate (analogous to the setup in the video linked to by mfb in post #22).
In B2, the planet has rotated by 90⁰, but its rotation was compensated by the camera, for net rotation =0⁰. This eliminated most of the apparent motion of the star (the regular star trails). However, since the camera is no longer on one of the poles, rotation of the planet has carried it away from the initial position, so that after 6 hours it is displaced by the planet's radius - as counted in the plane of the planetary cross-section (i.e., as seen from the star; I don't want to get into detail why like this, and not e.g. 1/4th equatorial circumference; it has to do with small angle approximation).
The displacement causes parallax to appear.
To reiterate - this situation shows that motion across the planet surface does not cause star trails to appear, providing you compensate for orientation changes.
Situations C1 and C2 show combination of the rotational star trails with parallactic displacement. As in all pictures, parallax is exaggerated.
Situations D1 and D2 additionally include the motion of the planet, traveling with some velocity V to the right, which causes additional parallax to appear.
In all these pictures, parallax is negligibly tiny as compared to the apparent motion due to rotation (changes in orientation). In other words, motion through space, be it rectilinear or spiral-like, has very little bearing on star trails, and is not their primary cause.
Lastly, look at this snapshot from the Vsauce video you linked to earlier, to which I added some arrows:
It illustrates components of motion causing parallax
- 1, displacement due to motion of the Sun through the galaxy
- 2, displacement due to orbital motion
- 3, displacement due to being carried by Earth's surface during a day - with magnitude depending on latitude, with 0 at the poles and maximum at the equator
Blue arrows illustrate changing orientation of the camera/observer during approx 6 hours (90 degrees of arc), and arrow 4 shows rotational component of motion, which approximates the star trail visible as a result.
It cannot be stressed enough, only component no.4 causes star trails - the other components cause parallax.
hamischism said:
If this were to be modeled in 3D software
Try one of the interactive planetarium software available (for free) on the Net. E.g. Celestia. You can fly to any modeled object, land at any spot, look in any direction, advance time as you see fit, or even mod an artificial solar system with the parameters you desire (e.g. a planet with no rotation, just the orbital motion - see if you'll find any star trails there).