Gnonom
Description
We see two viewpoints here.
On the left, our viewpoint is from the Zenith, looking directly down. We can see the tip of the gnomon's shadow cast by the sun. The points Sunrise and Sunset indicate their respective positions along the horizon.
On the right, our viewpoint is from beyond the two-sphere universe. The path of the sun is shown for the days of the solstices and equinoxes.
Usage
Use the Latitude slider to adjust the horizon for the observer's location.
Use the Annual Motion Slider to select a path for the sun. Moving the slider to the left, shifts the sun's path to the south as it does in winter. Likewise, moving the slider to the right, shifts the sun's path to the north as it does in summer.
Clicking the Show Trace box will cause the sun to travel along its path from sunrise to sunset in the right view. On the left, we will see the trajectory of the sun's shadow traced out in red.
The Annual Motion Slider can be moved without clearing the trajectories. This allows users to show how the trajectory of the sun shadow changes throughout a year.
Adjusting the Latitude slider will clear all the trajectories.
Things to Try
Adjust the Latitude to your home. Show the trajectory for the sun's shadow at different parts of a year. At the point of the trajectory when the sun is crossing the meridian, in which direction does the shadow point? During which part of year is this shadow the longest? During which part of the year is it the shortest?
Try the above at a few different latitudes. Do the answers change?
For some latitudes, it is possible to choose a path for the sun where Maximum Altitude coincides with the Zenith. What latitudes are these?