# How is acceleration due to gravity calculated?

May 2, 2018

Here you go

#### Explanation:

Calculating acceleration due to gravity is pretty easy actually. All you have to do is draw some high school level FBD of a body and equate some values and you'll get the acceleration due to gravity of any object kept on the surface or wherever you want to keep it.
In this answer I'll keep it short by just explaining how we can calculate acceleration due to gravity on the surface of the earth (I am just assuming earth because you didnt mention the planet and everyone is only curious about earth )
So here we go :

Force on any object exerted by the earth kept on the surface is equal to $F = G M \frac{m}{R} ^ 2$
where G is the Universal gravitational constant

$$                 M is the Mass of the Earth

R is the radius of the Earth

m is the mass of the object on the surface


And from our past experiences with physics we also know that Newton told us all that any force experienced by a body can be written as F=ma where 'm' is the mass of the body itself and 'a' is the acceleration it experiences due to that force.

So now we just equate both the forces because they are the same things written in two different mathematical way.

$G M \frac{m}{R} ^ 2 = m a$

$G \frac{M}{R} ^ 2 = a$

we know G = 6.67408 × 10-11 m3 kg-1 s-2
M = 5.972 × 10^24 kg
R = 6,371 km
Placing all the values in their respective places and equating them (MATHSSS!!!) we get the value of 'a'.
'a' comes out to be approx. 9.8 $m {s}^{-} 1$
'a' is our acceleration due to gravity exerted by earth.

• This is the case only when the object is kept at the poles and not at other positions. The value for acceleration due to gravity changes with change in both altitude and latitude. At the equator the value of R changes to 6,378 km and when we place this value in our equation we get the value of 'a' approx. = 9.78 $m {s}^{-} 1$ .