I know that mass increases gravity and that less mass decreases gravity. But is there a minimum gravity amount that won't let meteors or astroids have gravity because of their littler masses?
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6What do you mean "have gravity"? As far as we know, every mass exerts gravity, no matter how big or small it is. – ACuriousMind Nov 14 '15 at 21:45
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1The Earth, and the rest of the solar system, was initially formed from gas and dust under the influence of gravity. – RedGrittyBrick Nov 14 '15 at 21:50
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You may be interested in this question about the smallest object whose gravitational pull was demonstrated – Floris Nov 15 '15 at 03:21
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If Earth was split into thousands of astroid-size chucks, would any of them have gravity?
Yes.
In 1797–98, Henry Cavendish proved that gravitational attraction forces exist even between some metal spheres (0.73 kg and 158 kg) he made to test if the gravity law of Newton is really universal and valid even for terrestrial objects not only for celestial bodies. See the Cavendish experiment.

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