In your own words, define the gravitational field at a point, in analogy to the definition of the electric field, and find a vector expression for the gravitational field in terms of the gravitational force acting on a test mass.

(Gm/r'²)×r"

Explanation: The gravitational field is simply a region or a space that has the ability to exert a gravitational force on any object placed within it vicinity or surrounding.

The ratio of the gravitational force to it mass is known as the strength of the gravitational field.

Let m1 create a gravitational field and m is the test mass placed within with vicinity of m1.

The position vector of m1 is (r1) and the position vector of m is (r).

Mass m experiences a gravitational force from m1 which is defined by Newton's law of gravitation.

F =G×m1×m/r² where G = gravitational constant.

But strength of gravitational field = F/m1

Hence strength of gravitational field = (G×m1×m/r²)/m1

Strength of gravitational field =(G×m1×m/r²) ×1/m1

Strength of gravitational field = Gm/r'²

Where r' is the distance between m1 and m

r' = |r1-r| ( modulus of difference in position vector or m1 and m)

In vector form, we have to consider the unit vector of the 2 vectors r".

Where r" = (r1 - r)/r'

Hence the gravitation field in vector form is given below as

(Gm/r'²)×r"

explanation:

newton's third law, for every action there is an equal and opposite reaction.