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# Measure the Solar Diameter

Edward Gomez
Goals
• Students will have an appreciation of the relative and actual size of the Sun.
• Students will have an appreciation of how fast the Sun moves across the sky.
Learning Objectives
• Students will be able to describe perspective which makes the Sun appear smaller in the sky than it is in reality.
• Students will be able to describe why the Sun appears to move across the sky when in fact its apparent motion is produced by Earth’s rotation.
• Students will be able to convert between different time units, angles and calculate an accurate diameter for the Sun.
Background
• Understanding of the concept of angles and angular distance
• Understanding of the concept of velocity
• Appreciation that the sun's movement is apparent, and caused by the Earth's rotation, and
• Awareness of the dangers of looking directly at the Sun.
Full Description

#### Setup:

1. Cut a small hole (something between a pinhole and 5mm diameter hole) in the centre of the piece of thick paper.
2. Tape this piece of paper to the front of your mirror, so that you can only see the mirror through the small hole you made.
3. Attach the mirror to the tripod, so that the paper faces upward.
4. If you don’t have a tripod, put the plasticine/playdough on the floor and embed the block on it so that the mirror is at about a 40 degree angle (facing the Sun).
5. Stand your screen up and make sure it cannot move during the experiment: if it does move, you will have to start all over again.

#### Method:

1. Angle the mirror so the Sun is reflected onto the screen.
2. The projected image of the Sun must be circular, so angle your mirror and screen until it is.
3. Trace around the image of the Sun on the screen.
5. Wait until the Sun has moved to just outside the circle you drew.
6. Note the time on the stopwatch and reset.
7. Repeat steps 2–5 a few times (repeat 3–4 times for more accurate results).
8. Take the mean average of all your timings (in seconds).

#### Discussion and Results:

In this activity, you have been measuring how long it takes the Sun to move a distance equal to its own diameter across the sky. The Sun will take 24 hours to travel 360 degrees all the way around the sky and return to the same position it was in on the previous day. The speed it travels at is:

360 degrees/24hours:
= 360 deg/(24x60) minutes
= 0.25 deg per minute
= 0.00416 degrees per second or 1/240 degs per second

Calculate the size of the Sun as an angle: Average duration (in seconds) × 1/240 (degrees per second) = _ _ _ degrees

Congratulations! You have calculated the angular size of the Sun.

#### Calculate the physical size of the Sun

You can use your value for the angular size of the Sun to calculate the physical size of the Sun.

Your number for angular size converted into radians × distance from Earth to the Sun = size of the Sun

Angular size × (pi/180) × 92 955 887.6 miles = _ _ _ miles OR

Angular size × (pi/180) × 149 598 000 km = _ ______km

Congratulations! You have measured and calculated the diameter of the Sun in miles/kilometers!

Evaluation
• Make sure each of the objectives is reached.
• Ask students to describe what is happening as Sun moves across sky by using a ball and globe (representing the Sun and Earth).
• Ask students to explain their measurements in terms of the ball and globe model.
Curriculum
Country Level Subject Exam Board Section
UK GCSE Physics AQA Science A Not in current curriculum
UK GCSE Physics Edexcel P1.3.4
UK GCSE Physics OCR A P7.1: 1-4
UK GCSE Physics OCR B Not in current curriculum
UK GCSE Physics WJEC Not in current curriculum
UK GCSE Astrophysics Edexcel Unit 1.1.3: a, b
UK KS3 Physics - Space Physics: Our Sun as a Star