Video
Measuring the Moon's Distance Using Trigonometry
Overview:
Imagine you're an astronomer, looking up at the Moon on a clear night. How can you measure how far it is from Earth? Well, you can use a clever method called trigonometry! 🌕✨
In this activity, you’ll learn how to measure the apparent size of the Moon and use trigonometry to calculate its distance from Earth. With just a ruler or your smartphone camera, you can estimate the Moon’s distance!
Heat Lab
Scientific Background:
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Apparent Size
The Moon doesn't look the same size from Earth all the time. It changes a little bit depending on how far it is from Earth. This is called the apparent size of the Moon.
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Trigonometry
We can use trigonometry to relate the Moon’s apparent size (how big it looks) and its actual size (its real diameter of 3,474.8 km). By measuring the Moon’s apparent size with a ruler and knowing the focal length of your camera, we can calculate the distance to the Moon!
Formula
The distance d to the Moon:
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Where:
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θ is the angular diameter in degrees.
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D is the actual diameter of the Moon (3,474.8 km).
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d is the distance to the Moon, which we want to calculate.
To get the angular diameter in degrees from the image:
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Where:
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Dapparent is the measured apparent diameter of the Moon (in cm or mm).
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f is the focal length of the camera (in mm).
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57.29 is the factor to convert radians to degrees.
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How It Works: Step 1: Measure the Apparent Size Take a photo of the Moon using your smartphone, or measure it with a ruler. Record the apparent size of the Moon (in cm). Step 2: Find the Focal Length Use your smartphone’s camera focal length (found in your camera settings or online), or if you’re using a telescope, use its focal length. Step 3: Use Trigonometry Apply the formula to calculate the distance to the Moon. You will use the focal length and the apparent size to estimate the distance. Step 4: Compare with the Real Distance
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Credits
This activity is built with the following tools and resources:
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OpenAI API: Powered Ved, and learning feedback.
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ChatGPT: Utilised for designing and coding the Lab functionalities, including adaptive tutoring and lab simulations.
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NASA (National Aeronautics and Space Administration). "Moon Distance and Size." NASA, link.
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