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Gravitational Field

Earth and the Moon pull on each other. This is action at a distance, because Earth and Moon interact with each other even though they are not in contact. We can look at this in a different way: We can regard the Moon as interacting with the gravitational field of the Earth. The properties of the space surrounding any massive body can be considered to be altered in such a way that another massive body in this region experiences a force. The field concept plays an in between role in our thinking about the forces between different masses. A gravitational field is an example of a force field, for any body with mass experiences a force in the field space.

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Force Between Point Masses

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We know that there are four basic forces in nature. The force between two bodies by virtue of its masses is called as gravitational force. Newton proposed a law about the gravitational force between two point masses. Point mass is not the mass of the smaller size rather it is a concept. The mass of any shape and size is called as a point mass, if it is studied from a distance larger than the size of the body. Newton's law of universal gravitation is stated as follows: A point mass will attract another point mass in any part of the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically, F = $\frac{Gm_{1}m_{2}}{r^{2}}$

Where, F is the gravitational force
           $m_{1}$ is the mass of particle 1
           $m_{2}$ is the mass of particle 2
           r is the distance between particle 1 and 2
           G is the universal gravitational constant

This law is applicable only between point masses. Every spherical object with constant density can be considered as a point mass at the centre of the sphere. Non spherical objects with varying density cannot be treated so simply. The gravitational force is derived using calculus.

Field of a Point Mass

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Consider now the region of gravitational influence around a point mass or a uniform sphere. Since the strength and direction of the gravitational attraction is different in different locations, the force experienced by a point mass in this case changes in both magnitude and direction as its location is changed. Again the gravitational influence due to the source mass may be thought of as existing at every point in space although this influence becomes apparent only when a mass is located at the point. These regions of gravitational influence are examples of force fields. The idea of a force field proves to be a very useful concept, particularly where action at a distance is involved, that is when the influence is experienced at points distant from the source of the force even though there is no material medium through which the force can be transmitted.

Field near to the Surface of the Earth

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The gravitational field strength g near the surface of the Earth is given by:

g = $\frac{GM}{R^{2}}$
Where R, M are the radius and mass of the Earth.

The gravitational field strength g near the surface of the Earth is approximately constant. The gravitational field strength g near the surface of the Earth is also known as the acceleration of free fall.

Gravitational Potential

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Gravitational potential is defined as the work must be done to move a mass against a gravitational field. Consider mass M causes a gravitational field. Mass m has been moved through this field, from an infinite distance (where the gravitational force is zero) to point P. The gravitational potential V (at point P) is defined as follows:
V = $\frac{W}{m}$

Where W is the work done in moving a mass m from infinity to point P.

  • Like energy, gravitational potential is a scalar.
  • At infinity, the gravitational potential is zero.
  • Elsewhere, the gravitational potential is negative. This is because gravity is a force of attraction. Work is done by the mass as it is pulled from infinity to P, so negative work is done on it.

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