To find the approximate distance from Moon to the Earth, measure the angle between the Moon and the vertical as shown in the figure 6 hours after you observed the moon just above the horizon. For 6 hours, you will rotate for 90°. Since the size of the Earth is very small compared to the distance to the Moon, we may neglect the differences between angles θ and θ':
So, we a have a right triangle with a base of known length (Earth's radius or 6375 km), we have angle theta, and it's very easy to find the hypotenuse, which represents the distance between the planet and its satellite:
It is better of you use a large protractor that allows measuring fractions of a degree.
Now, it's time to find the size of the moon. Just measure how many degrees the Moon takes whenever you wish.
Using the same reasoning, the radius of the Moon is
The possible errors that can arise: wrong angle measurement, also, we have a systematic error because the suggested method for finding the distance must use θ', not θ.
How they can be minimized: using θ' instead of θ (and doing appropriate calculations of course) and by using a more precise protractor.
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