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Each particle produces a gravitational field around it which exerts the gravitational force on each of the other particles present within this region. The portion around a point mass in which each other point mass experience a gravitational force, is called the gravitational field i.e. The intensity of gravitational field at point is the gravitational force exerted on a unit mass kept at that point.
The force performing on a particle of mass m placed at a distance r from the centre of earth is given by
1.png) ..... (i)
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.png)
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Where M is the mass of earth
The gravitational field strength (also called gravitational intensity) is given by
2.png)
..... (ii)
The field intensity is always directed towards the centre of earth. Once the field strength is known the gravitational force on any particle of mass m, that is, its weight is given by
W = mg ..... (iii)
The magnitude of field strength on the surface of earth is given by
I0 = GM/R2 ..... (iv)
Where R is the radius of earth
Dimensional formula of gravitational field intensity: 3.png)
Difference between gravitational field strength (I) and the acceleration due to gravity (g): Consider a particle of mass m at latitude q on the earth as shown in the figure. The gravitational force mg is directed to the centre and serves two functions:
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1. It causes the particle to fall with acceleration of gravity g, and
2. It produces the centripetal acceleration ac.
From the second law of motion -
5.png)
or 6.png)
The vectors 9.png) and 10.png) are parallel only at the poles and at the equator.
Thus, vertical that passes through the centre of the earth.
At the pole ac = 0 and same 7.png) ...... (i)
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4.png)
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At the equator ac = v2/R = 3.4 cm/s2
And thus, 8.png)
Combining these two results, we get, gP - gc = (IP - Ic) + 3.4 cm/s2
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