Why is there a need for the concept of Gravitational Field?

  A few students have been coming to ask me this,"Why is there a need for the concept of gravitational field? What is its significance?" They have been quite happy to accept Newton's Law of Gravitation and could not see a need for the concept of field.  So I will try my best to discuss this to my best understanding.
  When the concept of gravitational force was discovered, there was a great disbelief by many scientists of that age and one of the key question faced by the scientists then was "How could 2 objects without touching each other have an effect (force of attraction) on each other?"
  I always jokingly tell my students that this is because they have never seen Chinese kungfu and experience qi gong, or watched those martial arts Chinese serials....but back to the point.....
  To overcome this obstacle for understanding, the concept of field was then created.  Any object which possessed mass (let us call it a source mass) would be able to exert a field around itself (its like having invisible arms of influence).  Under normal circumstances, we would not be able to see the field.  However we know that a field is there when we place another (test mass) in this field as we can see that this test mass will experience a force.
  For physics, we like to quantify properties.  So we would like to quantify this field by the source mass.  Now, we would expect that the larger the value of source mass, its gravitational field should be larger.  (compare that of Earth and Sun) The further we are from the source mass, the less influence the source mass should have on the test mass. The gravitational field can only be "seen" by the test mass, but yet is a property of the source mass, hence, we measure that force that is on the test mass by the field, but divide that force by the test mass so that we have a quantity that becomes independent of the test mass
 
  The gravitational field strength at a point in the field, g = (Force on a test mass placed at the point)/(test mass)

If the source of the field is a point mass M, then we can further write g = GM/r^2
, where M is the mass of the source mass, and r is the distance from the source mass.  This is consistent with our argument above.

Hence, a gravitational field is just a region of space in which a mass when placed in it will experience a force and the force experience by the mass m placed is equal to the product of the field strength at that point and the mass of the test mass placed there.