# Why is acceleration due to gravity constant?

##### 2 Answers

Mass of the falling body cancels out because the force of gravity is **directly** proportional to the mass and the acceleration caused by that force is **inversely** proportional to the mass.

#### Explanation:

The force of gravity on a body of mass

The only data used in the calculation of

where

#G# is the universal constant of gravitation, value:#6.673*10^-11 (N*m^2)/"kg"^2#

#M_e# is the mass of the Earth: value#5.983*10^24 kg#

#R_e# is the radius of the Earth: value#6.37*10^6 m#

Newton"s 2nd Law tells us that trhe acceleration of that body of mass

Since

I hope this helps,

Steve

As per Law of Universal Gravitation the force of attraction

#vecF_G =G (M_e*m)/r^2 hatr# .......(1)

Comparing modulii with the equation for Newton's Second Law of Motion

#vecF=mveca# ......(2)

we get acceleration due to gravity, which is also called gravity, as

#a=G(M_e)/r^2# ......(3)

from above we see that when the body is located on the surface of the earth gravity is

#a=G(M_e)/R_e^2# ......(4)

where#R_e# is radius of the earth.

As earth is not a perfect sphere, value of gravity

We also know that **average radius** of earth is **average value** of

Therefore, for practical purposes we take acceleration due to gravity as a constant.