"rottingroom" got in with illustrations while I was composing my typically long-winded reply. Brief glance looks like his illustration shows very well the point about the horizon appearing well below level if you are observing from a very high mountain.
According to your logic, the Sun would rise and set at the same place...Have you ever observed such a fantastic phenomena?
Can you entertain me by explaining why you think that? If rotation causes sunrise and sunset then it follows that sunrise should occur at the opposite side of the horizon from sunset. Given some variance depending on the time of year.
According to your logic, the Sun apparently goes up and down, because (due to tilt and rotation) an observer on the Earth changes an angle of observation. Right?
Yes.
Now, doesn't Sun's apparent motion across the sky (heading in arc from East to West) depend on changing an angles of observation, also?
Yes.
You even admit that there is a Zigging and Zagging of the Sun, only we cannot see it!
If by "Zigging and Zagging" you mean parallax, then, yes. It's quite small and difficult to detect, but it's there.
According to your logic, if we climbed up on the top of a hypothetical 1000 km high mountain, significant change of the perspective of the Sun would occur,
Where did anyone say that?
so that we could easily observe such a dramatic change of angles (up & down), but if we travelled 1000 km towards the East or towards the West, we wouldn't be able to notice any change of the perspective of the Sun, because (according to you and Alpha2Omega) going West/East makes no difference at all, but in the same time going Up/Down makes huge difference in producing apparent motions of the Sun.
Aha! It looks like the term "up and down" is ambiguous. By "up and down" I'm referring to
the Sun's Zenith angle (angle between "straight up" and the Sun) changing, not your height above datum changing.[nb]Zenith angle is easier to use here than elevation angle (the angle the Sun is above or below the local level), but they're simply complements of each other (one is 90° minus the other).[/nb]
Do note that climbing the hypothetical 1,000 km mountain would cause your sightline to the horizon to be lower since the horizon is nearby[nb]The horizon would be 30° below level from 1,000 km above the surface of a sphere with 6378 km radius[/nb]. Parallax against the distant stars would be affected only slightly - about 16% due to the lengthened baseline - so the Zenith angle would not be affected noticeably. Returning to the
Parallax at the Equator analysis a few days ago, we expect about 18 arcseconds of solar parallax at the equator at perihelion, based on a radius of 6,378.1 km (baseline 12,756.2 km) and distance to sun of 147,098,290 km. If we're atop a 1,000-km high mountain on the equator, this will increase the baseline by 2,000 km, so the parallax will increase from about 18 arcseconds to about 21 arcseconds. This would still be hard to detect without very specialized equipment.
Did either of us say moving east and west wouldn't affect the Sun's position in the sky? It certainly would. Moving north or south would also have a similar effect. The change in position in the sky would be by an angle equal to the angular change in position on earth.
Parallax against the background stars due to the changed position on earth would be negligible, though - maybe that's what you were referring to.
Would you be so kind to explain to our precious audience, what EXACTLY determines such a huge difference regarding "up & down" apparent motion of the Sun, and "Left & Right" apparent motion of the Sun?
"Precious". Love the editorializing!
"Left and right" (meaning parallax in this context, I presume) is dependent on the length of the baseline (sum of the diameter of earth (12,750 km or so) plus height above datum times cosine of the latitude) and the distance to the Sun (150,000,000 km give or take).
"Up and down" (meaning the Zenith angle) is the angle between a line from the center of rotation (center of the Earth) through the observer[nb]This establishes the local vertical (and, thus, the Zenith).[/nb] and a line from the observer in the direction of the Sun.
The lengths of these lines do not matter; only the angle between them. The upshot is that the distances involved cause a very small parallax effect, and the angular position of the Sun relative to zenith is absolutely dominated by rotation, which is independent of the distances.