Description

This simulation shows the shadow cast by a gnomon (vertical stick) at any time of day, on any day of the year, from any location on Earth. The view on the left shows the (red) gnomon sticking up from a green horizon plane. A magenta arrow points due North. When the (orange) sun is above the horizon a sunbeam points from the sun, through the tip of the gnomon, to a point on the horizon. The gnomon's shadow stretches from the base of the gnomon to this point.

The view on the right shows the Earth (blue) and the gnomon's horizon plane (green). A magenta arrow points due North. The (red) gnomon sticks up from the center of the horizon disk. A an orange sunbeam passes through the tip of the gnomon. Over the course of a day this sunbeam rotates (or the Earth rotates while the sunbeam stays still), thus forming a cone whose vertiex lies at the tip of the gnomon. The intersection of this cone and the horizon plane shows the path followed by the end of the shadow (which thus must be a conic section).

Buttons allow the user to play, pause, step, or reset, or erase the simulation. The user can adjust the latitude of the gnomon, the time of day, and the day of the year. Contols let the user use either the true sun or the mean sun, a vertical gnomon or a sundial tilted to align with Earth's axis, display shadows at each hour mark, or trace the path of the shadow's end. In addition, the user can easily set the date to an equinox or solstice.

Two plots are shown. To generate a plot of the sun's altitude as a function of time for a single day, simply play the simulation or else move the time slider. To generate a plot of the sun's altitude as function of day (for a fixed time of day), move the day slider.