With all the other forces we have discussed this semester – the normal force, friction forces, tension forces, spring forces – the interaction between the two objects has required them to be in contact.  However, two masses will feel a gravitational force even if they are not in contact.  So, if the masses aren’t in contact with each other, how does the interaction between them occur?  The gravitational force occurs because each mass sets up a gravitational field in the space around it, which is felt by the other mass once it is placed in the field.  This is perhaps easier to understand if we bring the masses together one at a time.  Initially, there is just empty space.  But when we bring in the first mass, it creates a gravitational field in the space around itself.  This gravitational field is a measure of how the mass influences the space.  The field points towards the mass and becomes stronger the closer you get to the mass.  When you bring in the second mass, it recognizes the presence of the gravitational field of the first mass.  The second mass responds to the gravitational field of the first mass through the gravitational force.  `\vec{F}_{g}=m\vec{g}` describes how the gravitational force felt by the second mass relates to the gravitational field of the first mass when placed in the field.  In some sense, the gravitational field is how the first mass announces its presence to the second mass, letting the second mass know how it needs to react to the first based on where it is located within the field.