Why then is it possible for solar systems to form? Shouldn't the same law forbid it?
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Please explain your line of reasoning, or are you just trying to pick an online fight? The reason a molecular cloud starts to flatten out when it starts rotating faster is because there is insufficent mass in the cloud so it flattens out to conserve angular momentum as the protosustar starts to condense. The conservation of angular momentum is not violated in any way. Trying to intentionally provoke an online argument is harassment, and that's a violation of the community guidelines.
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The point here is that the Earth-moon system has a certain amount of rotational momentum, whch cannot be created or destroyed, but can be transferred. The moon raises tides on the Earth. These attempt to follow the moon as the Earth rotates, but are stopped by the continents across their path: Europe and Africa in the Atlantic, Australia in the Indian, and the Americas in the Pacific. The tides running up against the continents causes friction, which slows the earth's spin down; the day is slowly getting longer. The rotational momentum is transferred to teh moon's orbit because it is dragging on the Earth through the tides, and is therefore gaining the momentum, and very slowly orbiting farther out. When the moon was created in the Big Splash, the day was about ten hours long and the moon was only about 22,000 miles out. It covered about 64 times more sky than it does today, and the tides were huge.
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The moon is slowly moving away from Earth because of tidal drag extracting energy from the moon's orbital energy.