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It was hypothesized that around 13.8 billion years ago, and expansion happened, which released energy, matter, light, and time. After the big bang theory, the universe was formed.
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This is approximately when Earth formed.
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This is approximately when the Moon formed.
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The Hadean Eon is characterized by the accretion of dust and gases to the stabilization of Earth's core. Convection currents occurred in the mantle raised molten to the surface and descended cooling rock into magmatic seas. Heavier elements descended and formed the core, lighter elements rose and incorporated into the growing crust.
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The Earth's surface started cooling down after it formed. It happened around 4-3.8 billion years ago.
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About 4.5 to 3.8 years ago, it was believed that when failed planets and small asteroids slammed and crashed into larger planets' surface in the solar system
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The Earth's inner core formed 1 billion and 1.5 billion years ago. We don't know when the outer core formed, assuming before the inner core.