SpaceTime

Space:

Calibrate your hands
Binoculars field of view

Time:

Watch the Sun
Model the Sun's motion
Compare it to the motion of stars

Spatial measurements: You can describe the size and position of star patterns relatively 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 uncertain is this 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 uncertain is this estimate? Could you be off by one degree? more? ____

What is the fractional uncertainty in the angular size of your fist? uncertainty / size = ____/____ = fractional uncertainty. Multiply this by 100 and you have the percent uncertainty: ____.

OPTIONAL: Repeat the activities above for your outstretched hand, from thumb to little finger. Hand = _____ degrees +/- _____ (uncertainty)

4) Devise a method to find out how many degrees wide your pointer finger is, at arm's length. ____ What is the uncertainty in this estimage? ____ Compare your result with classmates.

5) Find the Big Dipper. The two stars at the head of the dipper point toward the North star; these are sometimes called the Pointer Stars. Estimate the angular separation between the pointer stars. ____ How many times this distance does it take to reach the North Star? ____

6) Now measure how many degrees your binocular field spans. _____ How uncertain is this estimate? ____

7) If Orion is still up, use your binoculars to try to estimate the angular separation between stars in the sword scabbard. ____

8) Find an interesting dim star in the sky, and direct a classmate to find it, by describing its distance from a bright star in angles. Then trade roles. Practice using your new skills to locate and describe objects in the sky.

9) If the Moon is up, estimate the angular size of the Moon_____.

10) Have you ever noticed that the Moon looks much bigger when it is on the horiaon? Why do you think that is so?

Compare the size of the Moon (using your calibrated finger) when it is on the horizon and at another time when it is high in the sky, and you can measure the difference. How much bigger do you predict it will be at the horizon?

You may be surprised to find that your Moon measurements are different from your predictions. Times like that are the best opportunities to take your understanding a step deeper.

Summarize your results in the table below. Add additional rows or columns if you have additional results. Note similarities and differences between your results and those of your teammates. Differences are not necessarily wrong!

angular size	closed fist	open hand	pointer finger	binocs	Dipper pointers	Orion sword	Moon
degrees
uncertainty

TIME: Hours and seconds

1) How many degrees in a complete revolution? ____ How many hours does it take Earth to turn once on its axis? _____

2) Combine these to find out how many degrees the Earth turns in one hour: _____degrees / ____ hours = ______ degrees/hour = angular speed

3) If there are twelve constellations of approximately equal size spanning the sky, how many degrees does each constellation span? _____ = angular size

4) Find how many hours it takes an average constellation to rise above the horizon. Since speed = distance/time, time = distance/speed, or time = size/speed = __________.

5) The Sun's apparent motion across the sky is due to the Earth turning on its axis, similar to the motion of the stars. Now that you have estimated the speed of this motion and calibrated your hand, you can combine that information to figure out when you need to stop traveling and start setting up camp, if you are outdoors without a watch. Say you need an hour to set up camp before darkness falls. How many hands high in the sky will the Sun be, when you need to stop traveling? (Can you think subtleties that may complicate this calculation?)

OPTIONAL: Sidereal time and the Solar day. 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.