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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-
$g=\frac{GMm}{{R}^{2}m}$
Thus, we infer the g formula in physics as -
$g=\frac{GM}{{R}^{2}}$
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