Earth's gravitational acceleration | Acceleration due to gravity

Earth’s gravitational acceleration

The earth exerts gravitational force on objects near it. According to Newton’s second law of motion, a force acting on a body results in its acceleration. Thus, the gravitational force due to the earth on a body results in its acceleration. This is called acceleration due to gravity and is denoted by ‘g’.

Acceleration is a vector quantity. As the gravitational force on any object due to the earth is directed towards the centre of the earth, the direction of the acceleration due to gravity is also directed towards the centre of the earth i.e. vertically downwards.

A. Change along the surface of the earth : Will the value of g be the same everywhere on the surface of the earth? The answer is no.

Earth

The reason is that the shape of the earth is not exactly spherical and so the distance of a point on the surface of the earth from its centre differs somewhat from place to place. Due to its rotation, the earth bulges at the equator and is flatter at the poles. Its radius is largest at the equator and smallest at the poles. The value of ' g 'is thus highest(9.832 m/s²) at the poles and decreases slowly with decreasing latitude. It is lowest (9.78 m/s²) at the equator.

B. Change with height : As we go above the earth’s surface, the value of r ( radius ) increases and the value of g ( gravity )decreases. However, the decrease is rather small for heights which are small in comparison to the earth’s radius. For example, remember that the radius of the earth is 6400 km. If an aeroplane is flying at a height 10 km above the surface of the earth, its distance from the earth’s surface changes from 6400 km to 6410 km and the change in the value of g due to it is negligible. On the other hand, when we consider an artificial satellite orbiting the earth, we have to take into account the change in the value of g due to the large change in the distance of the satellite from the centre of the earth. Some typical heights and the values of g at these heights are given in the following table.

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C. Change with depth : The value of g also changes if we go inside the earth. The value of r ( radius )in decreases and one would think that the value of g ( gravity ) should increase as per the formula. However, the part of the earth which contributes towards the gravitational force felt by the object also decreases. Which means that the value of M ( Mass ) also decreases. As a combined result of change in r and M, the value of g decreases as we go deep inside the earth.

Every planet and satellite has different mass and radius. Hence, , the values of g on their surfaces are different. On the moon it is about 1/6th of the value on the earth. As a result, using the same amount of force, we can jump 6 times higher on the moon as compared to that on the earth.

Remember this point 👇👇👇

1) Formula of acceleration due to gravity is

g = GM
R²

2) this are inversely proportional which means if value g increases then value of r decreases while r if increases then g decrease or G stand for universal gravitational constant and M stand for mass of any object and r for radius of planet

Earth's gravitational acceleration | Acceleration due to gravity | Gravitational force