Newtonian gravitation

Gravity is an archetypal example of a long-range force. The field strength in this case is defined as the force per unit mass that acts on a particle at any given point in the field. This is a sensible definition: It tells us how strong the gravity force field is by telling us the force that it exerts on an object of unit mass.

Gravitational field strength is a vector denoted by the symbol g. So, the definition tells us that

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You will recognize this as being equivalent to the familiar formula for the gravitational force on an object of mass m:

So, the gravitational field strength is a vector with magnitude equal to the acceleration ...

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