Artemis was not the moon goddess, she was the moon itself

Artemis

 Artemis was the moon. Telling that she was the goddess of the moon simply means that she was symbolizing the moon. So, she was the moon itself. In the beginning, antique greeks had simply worshipped the natural things. Animals, sun, moon, volcanoes etc. But in around 800 BJ, two wise men (or a group of wise men symbolized by them) Homeros and Hesiodos wrote two books each and told some stories to people. After that, the educated guys began to call the moon Artemis and the sun Apollo. Ordinary people didn't get involved so much with the writings of Homeros and Hesiodos.
This is what makes Artemis and Apollo archers. Their arrows were the lights of the moon and the sun.
And this is what make them brothers. They are close like the moon and the sun.
And this is what they make them the kids of Zeus. Because Zeus is the sky.
Sky has two kids: the sun and the moon. And they send lights to people. Now it makes more sense, right?

Read Felicien Challaye's great book of "the History of Religions" to learn more about the issue.



Apollo