Spring 2001

Space & Time workshop Astronomy & Cosmologies

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GOALS: SPACE:  To learn to find your way around the stars using your hands and binoculars as measuring tools. TIME:  To understand the difference between sidereal time and the solar day. EQUIPMENT: SPACE:  hands, binoculars TIME:  landmark in class or outdoors ACTIVITIES: Space: Calibrate your hands Binoculars field of view Time: Watch the Sun Model the Sun's motion Compare it to the motion of stars

You can describe the size and position of star patterns surprisingly precisely without special equipment, using your own hands as measuring tools.

1) First, recall how many degrees are in a circle. How many degrees from horizon to horizon in the sky?

2) Hold your fist before your face and notice how much sky it covers. As you stretch your arm away from your face, your fist covers a smaller patch of sky. With an arm fully extended, the angular size of the patch you see your fist cover is nearly the same for everyone. People with smaller hands tend to have shorter arms, so their fist covers the same angle as a large fist held further away by a longer arm.

Measure the sky, fist to fist. Count how many fists it takes to span the horizon. How close is your estimate? (Could you be off by one fist? more? Make the best estimate you can.)

3) Knowing how many degrees are in the horizon, calculate how many degrees your fist spans, at arm's length. How close is your estimate? (Could you be off by one degree? more?)

4) Devise a method to find out how many degrees wide your thumb is, at arm's length. How close is your estimate? Compare your result with classmates' angles.

5) Find the Big Dipper, and estimate its angular size. How wide is the dipper part of the Dipper? How deep is the dipper?

6) Now measure how many degrees your binocular field spans. How precise is this estimate? If Orion is still up, use your binoculars to try to estimate the angular separation between stars in the sword scabbard.

The sun and stars appear to move around the Earth. Why? Because the Earth spins on its axis - and because the Earth orbits the Sun. These motions happen on different timescales, and have different spatial effects. This workshop should help you envision their combined effect in detail.

0) First, watch the sun move across the sky. Note its position relative to some landmark on the horizon at the start of class, and how it moves as throughout the hour.

1) Once you have a sense of how the Sun is moving, forget everything you know about Earth and how it turns and moves. Forget you are standing on the Earth. Imagine your head is the Earth. As you turn your face, the Sun can rise and set out of the corner of your eyes.

How do you have to turn your head to make the Sun set? If you turned around in a full circle, could you make it rise properly (or nearly so?)

2) Make note of how you turned your head to make the Sun rise and set, traveling east to west. Does the Earth spin on east to west on its axis (looking down on the North Pole), or west to east? Watch the Sun move across a morning sky this week, and try the experiment again.

3) Now choose a nearby landmark to represent the Sun, and abstract your understanding a little further. Your head is still the Earth. Spin your Earth-head to make the Sun-landmark rise and set.

4) Okay, that's a day. Now for year: the Earth orbits around the Sun, traveling east to west. Walk that way all around your Sun-landmark. That's a year. Estimate how far you need to walk to represent one day worth of orbit around the sun.

5) Now to see how these motions combine. First choose reference point, a distant landmark far beyond your Sun, to serve as a fixed star. Orient yourself so your Sun-landmark is between your distant-star landmark and your Earth-head. Now spin once (in the proper direction) for a day, while you take a step forward (orbiting around the sun).

Watch the distant star. As you spin on your axis and orbit your Sun, which returns directly before you first, the Sun or the star?

The time it takes you to return to face the sun, after about one spin and a day's worth of travel along your orbit, is exactly 24 hours. The time it takes you to return to face the star is called the sidereal time (star time). Is this more or less than 24 hours? The difference is only about 4 seconds, each day.