How is acceleration due to gravity calculated?

Question

Isabella Alvarez · Accepted Answer

Here you go

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 = GMm/R^2# where G is the Universal gravitational constant 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. #GMm/R^2 = ma# #GM/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 #ms^-1# 'a' is our acceleration due to gravity exerted by earth. Please Note: HAPPY LEARNING!!

Nora Arzate · Answer

undefined Acceleration due to gravity is calculated using the formula:

$$ g = \frac{F}{m} $$

where $ g $ is the acceleration due to gravity, $ F $ is the force of gravity, and $ m $ is the mass of the object. In most cases, on the surface of the Earth, the force of gravity is approximately $ 9.8 \, \text{m/s}^2 $.