Mechanics

# Value of Acceleration due to gravity

Acceleration of a freely falling body is called gravitational acceleration or acceleration due to gravity. The value of gravitational acceleration is 10 ms-². Acceleration due do gravity formula is calculated by using Newton’s law of gravitation.

## Acceleration due to gravity formula

The value of acceleration due to gravity is 10 m/second-second which is calculated by using formula given below.

The above formula shows that the value of acceleration due to gravity g depends on the radius of the earth at its surface. The value of g is inversely proportional to the square of the radius of the earth. But it does not remain constant. It decreases with altitude. Altitude is the height of an object or place above sea level. The value of g is greater at sea level than at the hills.

Consider a body of mass m at an altitude as shown in the figure. The distance of the body from the center of the earth becomes R +h.

The formula of g (gravitational acceleration) is:

According to the above relation, we come to know that at a height equal to one earth radius above the surface of the earth,g becomes one-fourth of its value on the earth. Similarly, at a distance of two earth’s radius above the earth’s surface, the value of g becomes one-ninth of its value on the earth. Value of g on the surface of a celestial object depends on its mass and its radius.

The value of g on some of the objects is given below in the table:

 Object g(ms-2) Sun 274.2 Mercury 3.7 Venus 8.87 Moon 1.62 Mars 3.73 Jupiter 25.94

## Value of g at the center of the earth

The value of g at the center of earth is zero.