B Star trails and the Earth's movemement

[Bandersnatch]

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.

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).

 

[hamischism]

No, it is an apparent motion because Earth rotates - and the camera rotates with it.

Yes, the camera rotates as it moves laterally with the earth. This combined motion makes a spiral. Yet only we only see circles.

 

[hamischism]

We know. But it isn't the motion through space that causes the photo to have streaks, it is the changing direction the camera is facing that causes the photo to have streaks. The speed of the motion through space is reeeeeeeeallly slooooooooow.

Relatively speaking, the motion through space (orbiting the sun) compared with the rotation is really fast. 67 times faster.

I should see star streaks that curl over into a spiral at a ratio of 1:67 ie really long spirals.

 

[hamischism]

May these pictures be of some help (hopefully)

I agree with all those diagrams and calculations, but they have nothing to do with what I am talking about. I already asked you not to further complicate this discussion.

We're talking about a very simple scenario here. The camera is a point in space. For example, the camera is looking directly at Polaris from the north pole. Now forget about the earth, and describe the path the camera takes, as a point of observation in space.

It is:

a) Rotating, which is revealed in circular star trail streaks.
b) Moving sideways at 67 times this rotational speed.

So it's not JUST a rotating point of observation. It is a spiraling point of observation.

If you were to look at each star trail, you'd be able to relate the length of the trail to the distance that the point of observation has traveled over 10 hours. If it were 5 hour period, the streaks would be half the length.

The arcing motion of the camera's path is revealed in the star trails, but the path the camera took was not an arc. It moved in a spiral motion - not a rotational motion.

If I had to recreate this scenario in Autocad, how would I possibly end up with what we see in real life star-trails? It would be an impossible model. If the Earth spins on the spot, looking at distant objects, I will get circles. If the Earth spins and moves laterally, spiraling streaks. You can't have it both ways.

 

[Bandersnatch]

a) Rotating, which is revealed in circular star trail streaks.
b) Moving sideways at 67 times this rotational speed.

How do you calculate this? Show your work.
Seriously, this is the crux of the problem. Don't forget units.

 

[mfb]

Yes, the camera rotates as it moves laterally with the earth.

That part is completely irrelevant. All the change in position of the camera is irrelevant over a few hours.

The change in camera orientation is the important point. It is something you can literally see within a few seconds with your eyes, right where you are. And you keep ignoring it.

 

[UsableThought]

If the stars are too far away, then why do we see any motion from our fixed point at all? And because we see motion, why is it only the rotation and not the much faster lateral orbit motion?

If I had to recreate this scenario in Autocad, how would I possibly end up with what we see in real life star-trails? It would be an impossible model. If the Earth spins on the spot, looking at distant objects, I will get circles. If the Earth spins and moves laterally, spiraling streaks. You can't have it both ways.

@hamischism, just to pile on to the answers already given - How do you explain that Polaris has for centuries been relied on as the "North Star" for marine navigation? If your talk of "spirals" were valid, sailors would not be able to treat Polaris as a fixed point. But they do. To quote Wikipedia:

Because Polaris lies nearly in a direct line with the axis of the Earth's rotation "above" the North Pole—the north celestial pole—Polaris stands almost motionless in the sky, and all the stars of the northern sky appear to rotate around it. Therefore, it makes an excellent fixed point from which to draw measurements for celestial navigation and for astrometry.

Something else strikes me as odd. You have admitted we don't see spirals; but when people attempt to explain why, you reject their answers & insist that we ought to be seeing spirals. Eh?

 

[Doc Al]

b) Moving sideways at 67 times this rotational speed.

Ignore the Earth's rotation for a moment. Please calculate the apparent angular velocity of Polaris that you'd expect due to the lateral motion. (Then compare that to the Earth's angular velocity.)

 

[hamischism]

@hamischism, just to pile on to the answers already given - which for some reason you can't grasp, I don't know why: How is it that Polaris has functioned for centuries as the North Star for navigation? Why have sailors never once complained about seeing "spirals"?

To quote Wikipedia:

Ever tried making a time-lapse sequence from a boat? It's a blurry mess.

 

[UsableThought]

Ever tried making a time-lapse sequence from a boat? It's a blurry mess.

What on Earth does that have to do with anything I said, or with the point of this thread?

 

[hamischism]

Ignore the Earth's rotation for a moment. Please calculate the apparent angular velocity of Polaris that you'd expect due to the lateral motion. (Then compare that to the Earth's angular velocity.)

I get what you're talking about, but please forget about polaris for a second. I shouldn't have mentioned that star, because it would be the only star whose motion could be plausible - if Earth's axis is always pointed directly at it.

 

[Doc Al]

I get what you're talking about, but please forget about polaris for a second. I shouldn't have mentioned that star, because it would be the only star whose motion could be plausible - if Earth's axis is always pointed directly at it.

Pick any star you like! How about Sirius.

 

[hamischism]

That part is completely irrelevant. All the change in position of the camera is irrelevant over a few hours.

The change in camera orientation is the important point. It is something you can literally see within a few seconds with your eyes, right where you are.

We might need to go 3D on this one to make sure we're on the same page. I just don't see how this will work in any modeling software. We will see star circles with the Earth spinning on the spot, or spirals with the Earth moving laterally and spinning.

 

[Drakkith]

After 3 pages and 43 posts I think it's time to close this thread. Hamischism, please re-read the answers in this thread several times and perform some of the recommended math. It should become apparent what is happening.

Thank you everyone for your contributions.

Thread locked.