Why do the sun and the moon appear the same size?

Answer

The sun is about 150 million kilometers away, and has a diameter of about 1.4 million kilometers. If you want to calculate the angular size of the sun, you do it like this: tangent(1.4 million/150 million)=~0.5°. The moon has a much smaller diameter of about 3500 kilometers. It is also much closer to Earth: at about 400,000 kilometers. If you calculate the angular size in the same way, you get ~0.5° again. So the sun and moon appear the same size from Earth. This also ensures that total solar eclipses are possible: the moon neatly covers the sun.

The moon slowly moves away from us: about 4 centimeters per year. From this we can surmise that the moon used to be much closer to the earth; the angular size of the moon will therefore also have been larger. The source I found states that the moon was 20 to 30 thousand kilometers after its origin. So much closer than it currently stands!

Is Earth the only planet where the moon-sun ratio is just right? Probably not: Jupiter, Saturn, Uranus and Neptune have very many moons. So it is certainly possible that a moon is the same size as the sun.

I’ve also included a photo of shadows of Jupiter’s moons on their planet. The angular size of the moons in this case is much larger than that of the sun. A very long solar eclipse can be seen in the place of the black spots…

Feel free to let us know if something is not clear!