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Measuring the Diameter of the Sun
Lesson 1 of 3
Objective: Students will be able to calculate the diameter of the Sun using ratios.
This lesson is based on California's Middle School Integrated Model of NGSS.
NGSS Performance Expectation (PE): (MSESS13) Analyze and interpret data to determine scale properties of objects in the solar system.
Science and Engineering Practice 2: Developing and using models.
Disciplinary Core Ideas (DCI): ESS1.B: Earth and the Solar System  The solar system consists of the sun and a collection of objects, including planets, their moons, and asteroids that are held in orbit around the sun by its gravitational pull on them.
Crosscutting Concepts (CCC): Systems and System Models  Models can be used to represent systems and their interactions.
This lesson was inspired by "TakeHome Physics: 65 HighImpact, LowCost Labs" by Michael Horton and published by NSTA Press.
Students will use an index card with a hole punched in it to project an image of the Sun on their paper. A simple ratio comparing the a) distance from the index card, b) the size of the projected image, and c) the known distance to the Sun in order to calculate d) the actual diameter of the Sun. Measurements and conversion skills are necessary in order to perform this activity. Your students will be able to see the projected image of the Sun as a scale model compared to the actual size of the Sun and make inferences about it's overall mass compared to the planets in our Solar System (MSEES13).
Setup
Materials Needed
 3 x 5 Index Card with a single hole punch
 Meter stick (1m)
 Centimeter ruler (30cm)
Directions
 Pass out index cards with a single hole punch in it.
 Go outside and position the Index Card so that the Sun shines through the hole and projects an image of the Sun onto your lab sheet. Angle the Index card and your lab sheet so that the projection is as near to a perfect circle as possible.
 Using a meter stick position the index card exactly 1 meter from your lab sheet.
 Trace the projected Sun on your lab sheet.
 Using your centimeter ruler carefully record the diameter of the projected Sun and record in box A. Be sure to convert your measurements to meters.
 If you positioned the index card exactly 1 meter from your lab sheet, record that measurement in box B.
 Using the following ratio calculate the diameter of the Sun.
 Multiply the 'Diameter of the projected Sun' by the actual 'Distance to the Sun' and divide that value by the 'Distance from the index card to the projected Sun' to determine the 'Diameter of the real Sun'.
Needed Fact: The Sun is on average 150,000,000,000 meters from the Earth.
DATA
A:

= 

B:

150,000,000,000 m 
Student Activity
Pass out a copy of Measuring the Diameter of the Sun Lab to each student. Allow them to work outside on a sunny day. Explain that they will need to face the Sun as perpendicular as possible, otherwise they may alter their Sun sketch.
In this lab I have my students place the index card 1 meter from their paper. I prefer the simplicity of dividing by 1. The further you can place the index card from the projected image the more accurate this technique becomes.
Measuring the Diameter of The Sun
At the conclusion of this activity I have my students calculate their percentage of error. To do this you would subtract the published diameter of the Sun from their calculated value and divide by the published diameter and multiply this answer by 100 to get a percentage of error.
Student Work Sample
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Extension
If you would like to provide your students with background knowledge about the Sun I have included The Sun Is Our Local Star, a Powerpoint presentation that includes details about the layers of the Sun along with stunning NASA photos.
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