by Chris Peterson » Mon Sep 19, 2022 4:13 pm
johnnydeep wrote: ↑Mon Sep 19, 2022 3:49 pm
Thanks for trying. Apparently, the only case I am capable of understanding is if the Earth had a perfectly circular orbit, a 0 degree axis tilt, and was tidally locked so that one side faced the Sun at all times (such that the rotation rate matched the yearly orbital period). In that case, the position of the Sun in the sky would never change at all for any observer anywhere on the Earth, and the "analemma" would be a single point.
Now, let's see, if the orbit was allowed to be a proper Newtonian ellipse (all other aforementioned hypotheticals remaining in effect), would the analemma still be a point? Yes, right?
Maybe you can slowly devolve your "perfect" system.
If the Earth had no axial tilt with respect to its orbital plane, and an orbital eccentricity of zero (i.e. a circular orbit), the analemma would be a point. The Sun would appear in the same spot each day at a give time. (Noon is easiest to understand, with the Sun right on the meridian and its altitude determined only by the latitude of the observer.)
Now lets give the Earth some axial tilt. This basically just introduces seasons, so the Sun is higher or lower in the sky depending on which part of our annual orbit we're on. So now the analemma has become a line perpendicular to the horizon. The Sun is still always on the meridian at noon, but its altitude depends both upon the observer's latitude and the position in our orbit.
Now lets make our orbit a little eccentric. That means our orbital speed isn't uniform. Per Kepler's Second Law our orbital speed will be greater when we're closer to the Sun. So this makes the Sun a little before or a little after the meridian at noon, depending on where we are in our orbit. If we had no axial tilt, the analemma would again be a line, but in this case parallel to the horizon. With both tilt and eccentricity, we have deviation vertically and horizontally, which is why real world analemmas look like closed roundish or figure-eight paths.
[quote=johnnydeep post_id=325932 time=1663602582 user_id=132061]
Thanks for trying. Apparently, the only case I am capable of understanding is if the Earth had a perfectly circular orbit, a 0 degree axis tilt, and was tidally locked so that one side faced the Sun at all times (such that the rotation rate matched the yearly orbital period). In that case, the position of the Sun in the sky would never change at all for any observer anywhere on the Earth, and the "analemma" would be a single point.
Now, let's see, if the orbit was allowed to be a proper Newtonian ellipse (all other aforementioned hypotheticals remaining in effect), would the analemma still be a point? Yes, right?
[/quote]
Maybe you can slowly devolve your "perfect" system.
If the Earth had no axial tilt with respect to its orbital plane, and an orbital eccentricity of zero (i.e. a circular orbit), the analemma would be a point. The Sun would appear in the same spot each day at a give time. (Noon is easiest to understand, with the Sun right on the meridian and its altitude determined only by the latitude of the observer.)
Now lets give the Earth some axial tilt. This basically just introduces seasons, so the Sun is higher or lower in the sky depending on which part of our annual orbit we're on. So now the analemma has become a line perpendicular to the horizon. The Sun is still always on the meridian at noon, but its altitude depends both upon the observer's latitude and the position in our orbit.
Now lets make our orbit a little eccentric. That means our orbital speed isn't uniform. Per Kepler's Second Law our orbital speed will be greater when we're closer to the Sun. So this makes the Sun a little before or a little after the meridian at noon, depending on where we are in our orbit. If we had no axial tilt, the analemma would again be a line, but in this case parallel to the horizon. With both tilt and eccentricity, we have deviation vertically and horizontally, which is why real world analemmas look like closed roundish or figure-eight paths.