Sun Days

Summary

As we have seen in the planetarium, the sky appears to revolve once per day. We can use the sky's rotation to tell time. The questions below are all related to timekeeping and rotations.

Assignment

Assume that the Earth is round and that it rotates around its axis every day. Also, assume that the moon moves in a circular orbit around the Earth every four weeks and that the Earth orbits the Sun once per year. (By the way, we all claim to know these facts, but I challenge you to prove them experimentally!) Assume the Sun is very far away.

Feel free to use figures (sketches or graphs) to make your answers clearer and shorter.

1. (1/2 page maximum including figures) The definition of a day is ambiguous. Let's say that we use object A in the sky to keep time. To define the length of a day we would start a stopwatch when object A crosses the meridian - your longitude line projected onto the sky. The length of a day is the reading on the stopwatch the next time object A crosses the meridian.

The solar day is measured with respect to the Sun, and is 24h 00m in length on average. The sidereal day is measured with respect to the stars, and is 23h 56m. The lunar day is measured with respect to the moon, and is about 24h 48m long.

Explain why the length of the day depends on whether you use a star, the Sun, or the Moon to measure it. Also account qualitatively for the fact that the lunar day is the longest, the sidereal day is the shortest, and the solar day is in between. If it helps to do so, pretend that all stars are visible in the daytime (this would be true if the Earth didn't have an atmosphere). Then you can treat the stars as a reference system against which the locations of the Sun and Moon can be monitored.

2. (2 pages maximum including figures) Outside the lab room, on the southwest wall facing the Burke-Gilman trail, you will find a sundial. (The sundial was designed in 1994 by Prof. Woody Sullivan of the Astronomy Dept. for the new building.) Sketch the sundial and turn the sketch in. Note the time when you observed the sundial.

If the sun is out, then be sure to include the shadow of the gnomon (stick) and its ball in your sketch. (If the Sun isn't out then guess where their shadows would fall and draw this.) Also indicate the expected direction of the shadow's motion over the next few hours.

Be sure to carefully read the explanatory plaque below the sundial. Then answer these questions:
1. From an astronomical point of view, how does this (and every other) sundial work?
2. Why can't this particular sundial be used very early in the morning?
EXTRA CREDIT (A few sentences only)
3. It is easy to read the season of the year using the sundial - but only if you know whether the current date lies between Dec. 21 and June 21, or between June 21 and Dec. 21. Why?

3. (1 page maximum including figures) Explain how you could use the noon shadow of a stick of known length to measure your latitude on March or September 21 (that is, at the spring and autumnal equinox).