Force is basically due to the interaction between two particles. Depending upon the type of interaction we can have two kinds of forces: Contact forces and Non-contact forces.

**Gravitational
field**

Force
is basically due to the interaction between two particles. Depending upon the
type of interaction we can have two kinds of forces: Contact forces and
Non-contact forces (Figure 6.8).

Contact
forces are the forces applied where one object is in physical contact with the
other. The movement of the object is caused by the physical force exerted
through the contact between the object and the agent which exerts force.

Consider the case of Earth orbiting around the Sun.

Though the Sun and the Earth
are not physically in contact with each other, there exists an interaction
between them. This is because of the fact that the Earth experiences the
gravitational force of the Sun. This gravitational force is a non-contact
force.

It sounds mysterious that the Sun attracts the Earth despite
being very far from it and without touching it. For contact forces like push or
pull, we can calculate the strength of the force since we can feel or see. But
how do we calculate the strength of non-contact force at different distances?
To understand and calculate the strength of non-contact forces, the concept of
‘field’ is introduced.

The
gravitational force on a particle of mass ‘m_{2}’ due to a particle of
mass ‘m_{1}’ is

Where
rˆ is a unit vector that points from *m*_{1} to *m*_{2} along the line joining the masses *m*_{1} and *m*_{2}.

The
gravitational field intensity (here after called as gravitational field) at a point which is at a distance *r* from *m*_{1} is defined as the gravitational force experienced by
unit mass placed at that point. It is given by the ratio /m_{2} (where m_{2} is the mass of the object m_{2} on
which acts)

Using = /m2 in equation (6.14) we get,* *is a vector quantity that points towards the* *mass *m*_{1} and is independent of mass *m*_{2}, Here *m*_{2}* *is taken to be of unit magnitude . The
unit* rˆ *is along the line between *m*_{1} and the point in question.
The field is
due to the mass *m*_{1}.

In
general, the gravitational field intensity due to a mass M at a distance r is
given by

Now
in the region of this gravitational field, a mass ‘m’ is placed at a point P
(Figure 6.9). Mass ‘m’ interacts with the field and experiences an attractive force
due to M as shown in Figure 6.9. The gravitational force experienced by ‘m’ due
to ‘M’ is given by

Now
we can equate this with Newton’s second law

In other words, equation (6.18) implies that the gravitational field at a point is equivalent to the acceleration experienced by a particle at that point. However, it is to be noted that and are separate physical quantities that have the same magnitude and direction. The gravitational field is the property of the source and acceleration is the effect experienced by the test mass (unit mass) which is placed in the gravitational field . The non-contact interaction between two masses can now be explained using the concept of “Gravitational field”.

**Points to be noted:**

i)
The strength of the gravitational field decreases as we move away from the mass
M as depicted in the Figure 6.10. The magnitude of decreases as the distance r increases.

Figure 6.10 shows that the strength of the gravitational field at points P, Q, and R is given by . It can be understood by comparing the length of the vectors at points P, Q, and R.

ii) The “field” concept was introduced as a mathematical tool to calculate gravitational interaction. Later it was found that field is a real physical quantity and it carries energy and momentum in space. The concept of field is inevitable in understanding the behavior of charges.

iii)
The unit of gravitational field is Newton per kilogram (N/kg) or m s^{-2}.

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11th Physics : UNIT 6 : Gravitation : Gravitational field |

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