What is the relationship between G and g in physics?

There are differences between Gravitation (G) and Gravity (g) are as follow:

Gravitation (G)	Gravity (g)
1. Gravitation is the force of attraction acting between any two bodies of the universe.	1. Gravity is the earth's gravitational pull on the body, lying near the surface of the earth.
2. It requires two masses.	2. It requires only one mass.
3. It is a weak force.	3. It is a strong force.
4. G is the Universal Gravitational Constant.	4. g is the acceleration due to gravity.
5. The force, $F=G\frac{M1\times M2}{{R}^{2}}$ (G = gravitational constant).	5. The force, $F=m\times g$ (g = acceleration due to gravity).
6. The value of G remains constant everywhere. (G = 6.673×10^-11Nm²/kg²)	6. The value of g varies from one place to another on the Earth.

There is no connection between acceleration due to gravity (g) and universal gravitation constant (G), as the value of G is constant. Also, they are not dependent on each other.

However, a formula exists to express the relation between g and G in physics.

$g=\frac{GM}{{R}^{2}}$

Where,

g = the acceleration due to the gravity of any massive body measured in m/s².

G = the universal gravitational constant measured in Nm²/kg².

R = the radius of the massive body measured in km.

M = the mass of the massive body measured in Kg.

The relationship can be derived as-

According to the universal law of gravity,

$F=\frac{GMm}{{R}^{2}}$ ---------------> (i)

From Newton’s second law of motion, we can write –

$g=\frac{F}{m}$ ---------------> (ii) Substituting equation (i) in (ii) we get-