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So, this is called a two-body problem.
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So, this is one example where you realize, "Hey, center of mass,
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if I follow it, it cannot be moving
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and therefore the actual motion of planets
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is more complicated than we thought."
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Okay, then, there is a whole slew of problems one can do,
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where the center of mass is not moving.
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So, I'll just give you a couple of examples; then, I will stop,
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but I won't do the numbers.
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Here is one example.
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That is a carriage
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that contains a horse,