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The name "gravity" comes from the Latin word, gravitas. In the Europe of Newton's time, Latin was the language used by the learned, and many books on academic and scientific subjects were written in Latin so that they could be read by people in all the European countries regardless of the reader's own native language. English is coming to play a similar role in the world today. Gravitas simply meant "heaviness" or "weight," and heavy bodies were usually said at this time to possess the property of gravity. Their heaviness, or weight, was what made them fall down. Newton had new things to say about heaviness, and a new way of talking about it. By saying that gravity should be understood as a force that's exerted between heavy bodies that had what Newton called mass, Newton was saying that weight shouldn't any longer be regarded as simply a property possessed by a "heavy body", but that a body that seems to be heavy is in fact being attracted by another body with mass, in this case, the earth. So it tends to push downwards towards the center of the earth, against anything (such as your hand) that gets in the way to prevent it from falling. When you weigh something, you're measuring how difficult it is to prevent the heavy body from moving downward.
So after Newton's work became accepted, scientific people talked about heaviness. They thought of it as a quantity that resulted from a relationship between bodies instead of just a property of a single body, such as a bag of sugar or a rock. After Newton, heaviness reflected a force acting between two (or more) bodies. If there were only one body with mass in the entire universe, it wouldn't have any weight at all, because there would be no other bodies to exert a gravitational force on it (and at the same time to have its gravitational force exerted on them). This lonely body in an empty universe still has mass, but the mass doesn't exhibit gravity, or heaviness, although the parts of this body would still gravitationally attract one other.
Newton didn't really "discover" gravity, because everyone knew that the world was full of "heavy" bodies. But he explained what heaviness (gravitas) was in a new way. This new way also allowed him to describe celestial bodies, like planets and moons, as exerting gravitational forces on each other, as indicated by their orbital motions. An orbiting planet doesn't fly away from the sun, on this view, because there is a gravitational force between the planet and the sun that continually pulls it back. Planets and the sun were, in effect, heavy.
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