Cindy Skinner, age 13, of Chesterfield, Indiana, for her question:

What is the limit of twilight?

Soft twilight subdues the world before the sun rises above the eastern horizon and again after it sinks out of sight in the west. The dim twilight phase may begin or end when the sun is 18 degrees below the curved horizon of the globe. This distance is about 36 times the width of the full moon. The period of twilight is limited by the sun's position in relation to this point below the horizon. This is a highly complex problem of angles that vary with latitude and change with the seasons. The shortest periods of morning and evening twilight occur in the tropics. The longest occur in the polar regions    and here there are only two twilight periods during the year.

At the equator the sun sinks below the horizon most quickly. Here the short twilight is limited to about 22 minutes. At latitude 40 degrees north of the equator, near Muncie, Indiana, the sun's path slants over the sky and below the horizon. Here the limit of twilight is about 37 minutes. At the poles, there is a whole month of twilight before the sun rises to stay above the horizon through the summer months. There is another month of twilight after it sets before the lone winter night begins.