# Acceleration due to gravity of the earth

Acceleration (the rate of change of velocity) is caused by a net force on an object. On Earth, one force we can always count on is the ever present force of gravity pulling down on any object that has mass. If gravity is the only force acting on an object, then we find the object will accelerate at a rate of 9.8m/s^{2} down toward the center of the Earth

### Acceleration due to Gravity Formula

Force acting on a body due to gravity is : f = mg

Where, f = force acting on the body,

g = acceleration due to gravity and,

m = mass of the body.

As per universal law of gravitation, f = GmM/(r+h)^{2}

Where, f = force between two bodies,

G = universal gravitational constant (6.67×10^{-11} Nm^{2}/kg^{2})

m = mass of the object,

M = mass of the earth,

r = radius of the earth.

h = height of the body from the earth surface.

Since height (h) is too small compared to the radius of the eart, therefore we can re-frame the equation as follows:

f = GmM/r^{2}

Equating both the expressions,

mg = GmM/r^{2}

Hence, the formula of acceleration due to gravity is g = GM/r^{2}

When any object is moved then its speed is changed which is called velocity while the change in velocity is acceleration. When it is changed continues then it is in accelerating condition which is called the rate of acceleration. It is equal to the ratio of change in velocity with respect to time between the given paths. The vector quantity acceleration is used to show the increasing or decreasing speed or changing direction of object

### Variation of g with Height

Acceleration due to gravity varies with the height from the surface of the earth and can be calculated as follows:

gh = g(1+(h/R))^{−2}

Where, g = Acceleration due to gravity at the surface.

gh = Acceleration due to gravity at the height h.

R = The radius of the earth.