Sizing Up Sol!

Category: modeling

Learning Objectives:
Student will be able to:

1. Make accurate measurements and correctly calculate a proportion.
2. Use mathematical calculations to infer conditions on different planets.

Materials:

• Meter stick
• Metric ruler
• Eight to ten 3 x 5 or heavier cards marked off with grid of 1 centimeter x 1 centimeter squares
• Eight to ten 3 x 5 cards with a 1/2 centimeter x 1/2 centimeter square hole cut from the center
• Medium nail or large darning needle
• Light source such as a single bare bulb in a table lamp
• Single edged razor blade and different shaped punches to make different shaped holes for the extension exercise (optional)
• Plain 3 x 5 cards, 2 per meter stick
• Tape
• Notebook paper

Safety:

• Never look directly at the sun.
• Be careful using sharp objects.

Sequence:
Students can work in teams that range from 3 or 4 students up to the whole class.

Duration:
One fourty-five minute class period.

Introduction: "Ancient people thought the sun was smaller than the Earth. How do we know it isn't? [discuss] Once astronomers agreed that the sun is in the center of the solar system, they began to estimate how far away it is. Early estimates used geometry and parallax. More recently they have used radar to accurately measure the distance to the sun. Now that we know how far away it is, we can measure its size."

Activity One: Have students predict the size of the sun in kilometers given that the Earth's diameter is 40,000 kilometers. Pass out a metric ruler, a meter stick, and 2 cards to each team or individual. Have students measure and calculate the size of the sun.

Student Instructions:

1. Write down your prediction of the diameter of the sun. The Earth is 40,000 kilometers in diameter.
2. Punch a clean round hole in the center of one card.
• Caution: be careful using sharp objects.
3. Tape the punched card at the 0 centimeter mark on the meter stick so that it stands up perpendicular to the stick.
4. Tape the other card so that it stands up parallel to the first card like a screen at the 100 centimeter mark.
5. Take your meter stick to a sunny area and point the punched card toward the sun. Caution: never look directly at the sun, not even through the pinhole. Hint: when the shadow of the punched card falls on the other card your meter stick is lined up.
6. Carefully measure and record the diameter of the circular image of the sun to the nearest 1/10 of a millimeter.
7. Calculate the size of the sun using the formula:
   Diameter of sun= [distance of sun x diameter of image]/[ distance of hole to surface]
   
   Therefore,
   Diameter of sun = [1.5 x 108 km x (your measurement) x 10-6 km]/[ 1.0 x 10-3 km] or, Sun Diameter (in kilometers) = (your measurement) x 150,000
   Record your results.
8. How does your calculated size of the sun compare with your prediction?

Activity two: Students work in teams of 3 or 4. Set up the light source near the middle of the room and dim the room lights as much as possible. Caution: Bare bulbs get hot. Pass out a card with grid and a card with 1/2 centimeter square hole to each team.

Student Instructions:

1. Hold up the card with the hole so that light from the source comes through it. It will work best if you are about 1 or 2 meters from the light. Hold your grid card so the square of light falls on it. Adjust the distance between cards until the square of light just covers 1 grid square (1 square centimeter). Measure and record the distance between cards.
2. Don't move the card with the hole, but move the grid card further back until the light covers 4 square centimeters (2 squares x 2 squares). Again measure and record the distance.
3. Continue the process for 9 squares (3 x 3), 16 squares (4 x 4), 25 squares (5 x 5) and so on until the light is too faint or you run out of grid space.
4. Analyze your results. Look for a pattern in the distances you have measured. A certain fixed amount of light is coming through the hole in the first card. When you double the distance that light has to travel before landing on a surface, how much larger is the area it spreads over? What is the relationship between distance light travels and area it spreads over?
5. Remember how the light got dimmer and harder to measure as you moved away. Suppose an ant were on your grid card looking at the light. When the light spread out over twice the area how much dimmer would it look to the ant?
6. Apply the ideas from your analysis to how bright the sun would look to a person on each of the planets. Astronomers measure the distance from the sun to each planet in astronomical units. One astronomical unit is the distance from the sun to the Earth. Complete the chart below:

Planet	Average distance from sun in astronomical units.	Brightness of sun compared to brightness we see from Earth.
Mercury	0.39
Venus	0.72
Earth	1.00
Mars	1.52
Jupiter	5.20
Saturn	9.54
Uranus	19.18
Neptune	30.06
Pluto	39.44

Extension Activity: To help students see that the image of the sun that they measured is not an image of the hole in the card, they can try different shaped holes.

Student Instructions:

1. Remove the card with the hole from your meter stick. Fold the card and cut out tiny wedges to make different shaped holes. Remember to be careful with sharp objects. The holes should no more than 5 millimeters.
2. Return to the sunny area. Slide the card with holes along the meter stick from a few centimeters up to one meter from the card that is still attached to project different images. Notice the change in the images.
3. Analyze your results. Can you see any systematic changes? Does the size of the hole relate to the distance where the image becomes round? How do you explain the change in the shape of the image?

Evaluation: Based on individual answers and participation with team. Was the calculated size of the sun between 1.2 and 1.4 million kilometers? Was the chart completed accurately?