Understanding Gravity: The Moon's Orbit in Our Solar System Explained

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This is a simple question: Why does the moon or orbit the Earth or the planets in our solar system orbit the sun?

The moon is held in its elliptical orbit by Earth's gravity. Why doesn't the moon simply crash into the earth, or the Earth into the sun, of the sun to the center of the galaxy? Is the force of gravity pulling the moon to the Earth in equilibrium with the forces pulling it away from the earth? Is that what keeps the moon from crashing into the Earth or floating out into space?
 
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The moon has enough inertia and velocity to keep it in a stable orbit around earth. The moon is trying to escape but gravity is trying to pull it toward it so the two forces are in equilibrium.
 

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