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answers:
Zheia say: The Moon formed from the accretion of matter and it happened to drift towards Earth, ending up in orbit around it.
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YKhan say: The Big Bang happened 13.8 billion years ago. During this event all of the protons, neutrons, and electrons that exist in this universe, and ever will exist were created (short-form story). Think of the protons & neutrons as the Lego building blocks of the universe, from these Legos we build all of the atoms. The Big Bang was only energetic enough to build a few simple Lego structures, hydrogen and helium, and basically nothing else more complicated than that. From nothing else but this hydrogen and helium, the first generation of stars were born, and the first generation of galaxies, including our own galaxy.
Fast forward approximately 10 billion years, and a cloud of gas is starting to condense after a supernova explosion compressed it and seeded it full of heavy atoms. Supernova explosions are where all of the more complicated Lego atoms are made, everything above helium, all of the way to Uranium. It's out of these mixtures of heavy atoms and hydrogen & helium that the current generation of stars, planets, and everything else in the universe are made. Our star, the Sun formed out of one of these gas clouds. Our entire solar system came from this same gas cloud. The Sun formed first, and then all of the planets formed after that, with the heaviest ones being the earliest formers, such as Jupiter. Earth was formed somewhere in the middle of all of this. This was happening 4.5 billion years ago. At that time in the solar system there were all kinds of planets, more than there are now. A whole bunch of them collided and formed bigger planets. Then some of the bigger planets started to collide too. In this case a young Earth, collided with a Mars-sized object called Theia (in Greek mythology, Theia is the mother of the moon-godess Selene). When Earth and Theia collided, most of Theia got absorbed into the Earth, but some portion of the Earth and Theia mixed and entered into orbit around the new Earth. This debris coalesced into the Moon.