How do we measure the size of the Moon and of the Sun?
Can you give ideas on how one would measure the apparent diameter of the sun or the moon?
It is impossible for the human eye to get a direct measurement of the size of the Moon, the Sun, or any other celestial body. The main reason is that when we look at the sky, we totally lack depth perception. This means that when you look at the sky, all the stars and planets appear to be at the same distance from us. We refer to this as the celestial sphere: a gigantic sphere of which the Earth is the center and onto which the stars appear to be. (The ancient astronomers had the same problem, they believed that all the stars were fixed on such a sphere and thus were all at the same distance from us. We now know that it is absolutely not the case and that it is only the result of our poor vision.)
Therefore, the only thing we can measure when we look at the sky are angular sizes and angular distances. If you divide the whole celestial sphere in 360degrees just as you would do for a circle, you can talk about the angular size of objects or their angular distance (the angle that appear to separate the two objects on the celestial sphere). When we calculate these angles for the Sun and the Moon, we surprisingly find almost the same result : 1/2 a degree. (this is just a coincidence, and fortunately for us it is the reason why we can get really nice solar eclipses).
There is an easy way to approximate angular distances when you look at the night sky. Hold your arm fully extended in front of you. Close your fist and look at it superimposed with the objects you are trying to measure the angular distance between. From one edge of your fist to the other is about 10 degrees. One knucle is about 2.5degrees, and if you open your hand, the full span of your hand from the tip of your thumb to the tip of your little finger is around 20 degrees on the sky.
Now astronomers get to measure angular sizes in a more accurate way, and with that they can get the actual sizes of the objects. To do that we have to take into account the distance to the objects we are measuring. An example of that is that even though the Sun and the Moon have the same angular size, the Sun is in fact much larger than the Moon. They just appear the same size because the Sun is much farther. So from accurate measurements of the distance to the Sun and to the Moon, and measuring their angular sizes, we can get good estimates of their actual sizes. The values we get are that the radius of the Sun is 696,000 km, and the radius of the Moon is 1740 km.
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