g vs. G: What's the difference?

g vs. G: What's the difference?

Topics Covered: Universal Gravitation, acceleration due to gravity, g, G

In physics, we encounter various letters that stand for different physical concepts. For example, a stands for acceleration and F stands for force. Then what about g? or G? Most of us know that both little g and big G have to deal with something related to gravity, but are not completely sure about their difference. Well, if that’s you, don’t worry! We’ve got that covered in this blog!

Let’s start with big G. G stands for Newton’s universal gravitational constant. Long, long time ago in the 1600s, a young scientist named Isaac Newton (sounds familiar, huh?) discovered that Gravity is universal. In other words, the force that pulls an apple to the ground is the same force that holds the Moon to the Earth!

Newton’s discovery was revolutionary, and he decided to call this new, universal gravity “Universal Gravitation” (well, duhh..). According to Newton’s law of Universal Gravitation, EVERY object in the universe that has mass attracts EVERY OTHER mass in the universe, no matter where they are. This means, while you are reading this, no matter where you are, I am attracting you and you are attracting me, because I have mass and you have mass (or hopefully you do).

Ok, you might be wondering, then why am I not getting pulled to you if the force of attraction exists between you and me? Well, according to Newton’s law of gravitation, Force of gravity = G* m1*m2/r2, where m1 and m2 represent the masses of two objects (in kg), r represents the distance between two objects’ center of mass (in meter), and finally, G represents Newton’s universal constant of gravitation, which he defined as G = 6.67 x 10-11. This is an extremely small number!

To help you understand, I will give you an example. Let’s say we are in the same room, I’m 50 kg, you are 60 kg, and we are 5 m apart from each other. According to Newton’s law of gravitation, the force of gravity that you exert on me (and I exert on you) is G * 50 * 60 / 52 = (6.67 x 10-11 * 50 * 60) / 25 = 8.0 x 10-9 N ! Now I hope it makes sense why we are not getting pulled to each other even if we are in the same room.

Now let’s move on to little g, which stands for average acceleration due to gravity at Earth’s surface. To understand where g comes from, we need to go back to Newton’s law of universal gravitation. Remember, force of gravity is still a force, so our familiar equation (Newton’s second law) F = ma still applies here. Now, if we want to measure the acceleration that is caused by Earth’s gravity, we set two equations equal to each other. And I’ll let the picture explain.

The value we got for acceleration a, we write that constant as value g, and that’s where g comes from! To summarize, G is Newton’s constant of universal gravitation that is true everywhere in the universe, whereas g is the average acceleration due to gravity that only applies at the surface of the Earth, not universal!