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What is meant by relative strength of gravitational force?  Is any particle responsible for this force?

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Well, when you speak of the relative strength of gravitational force, you are talking about the force of gravity that exists between two objects.  All that is necessary for a force of gravitation (gravity) to exist between two objects is for the objects to have mass and have some defined distance between them.  Sir Isaac Newton is the author of the law of universal gravitation.  Before Newtons time, people could not explain how gravity worked, they simply understood things "fell" towards the Earth when dropped.  According to legend, Newton was sitting under an apple tree one day when an apple fell and hit him on the head.  That got him to theorizing why things fall towards the Earth.

To my knowledge, there is no one individual particle that causes this.  Newton stated the force of gravity between two objects was equal to the product of the two masses divided by the distance between the two objects.  The force of gravity at sea level has been ascertained to be 9.8 meters per second per second.

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