what do we call the gravitational frorce between the earth and the object
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Gravitational force between the Earth's gravity or weight of the object.
••••Note in weight of an object:
This is often expressed in the formula W = mg, where W is the weight, m the mass of the object, and g gravitational acceleration. ... "The weight W of a body is equal to the magnitude Fg of the gravitational force on the body." The gravitational acceleration varies from place to place.
In SI base units: kg⋅m⋅s-²
SI unit: newton (N)
Other units: pound-force (lbf)
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