Numerical value of acceleration due to gravity on Earth
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Gravitational Constant (G) = 6.6734x10-11 Nm2/kg2
Mass of the Earth (M
e) = 6x10
24 kg
Radius of the Earth (Re) = 6.4x106 m
The value of acceleration due to gravity on Earth is 9.8m/s
2. This means that when a body falls freely towards the Earth its velocity increases at the rate of 9.8m/s during its motion. Similarly when an object is projected vertically upwards its velocity decreases at the rate of 9.8m/s and eventually the velocity becomes zero. The height at which the velocity of an object moving against gravity becomes zero is described as the maximum height attained by the object. When the velocity becomes zero the object starts falling down, with an acceleration as if released from that height.
Variation of g with latitude and altitude
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The expression for acceleration due to gravity is
From this expression it is very clear that acceleration due to gravity is inversely proportional to the square of the distance between the centre of the Earth and the object. That is, if the object is on the surface of the Earth it is dependent on the radius of the Earth. But as Earth is not a perfect sphere (slightly bulging out at the equator) its radius decreases as we move from the equator to the poles. At the equator at sea level its value is about 9.78m/s
2 and at the poles it is 9.83 m/s
2. Its mean value is taken as 9.8m/s
2 for all calculations.
Similarly the value of g decreases as we go up to the top of a mountain or higher up in the air.
Distance of the object from the centre of the Earth
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The value of g inside the Earth is directly proportional to the distance from the centre of the Earth. Hence, g decreases as we go down into the Earth till it becomes zero at the centre of the Earth.
Centre of Gravity
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We know that the earth attracts every particle towards the centre. A body can be considered to be made up of number particles. As the size of the body is small when compared to that of the earth, the gravitational pull acting on these particles can be regarded to be parallel to each other as shown in the figure.
A single force passing through a fixed point called the center of gravity of the body can replace these parallel forces acting vertically in the downward direction. The resultant force is equal to the weight of the body.
Thus center of gravity is the point through which the weight of the body acts irrespective of the position of the body.
For bodies which are of regular shape and which have uniform density, the center of gravity lies at the geometrical center of the body.
Application of Newton's law of gravitation
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One of the important applications of Newton's law is to estimate masses of binary stars. A binary star is a system of two stars orbiting round their common center of mass.
Any irregularity in the motion of a star indicates that it might be another star or a planet going round the stars. This regularity in the motion of a star is called a wobble.
