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Does the force of gravitation exist between two objects on the earth

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Absolutely. There is a force of gravitation between every two specks of mass. There is a gravitational force between the lint in your pocket and the tissue that the mayor of your city dropped into the trash 5 minutes ago. Everything attracts everything else by gravity. But the forces are so weak that we don't notice them compared to the force of the Earth.
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User Thomas Ducrot
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