Relation Between G and g

The acceleration on an object due to the gravity of any massive body is represented by g (small g). The force of attraction between any two unit masses separated by unit distance is called universal gravitational constant denoted by G(capital g). The relation between G and g is not proportional. That means they are independent entities.

G and g

In physics, G and g can be related mathematically as –

\(g=\frac{GM}{R^{2}}\)

Where,

  • g is the acceleration due to gravity of any massive body measured in m/s2.
  • G is the universal gravitational constant measured in Nm2/kg2.
  • R is the radius of the massive body measured in km.
  • M is the mass of the massive body measured in Kg

G and g relation

Although there exists a formula to express the relation between g and G in physics. there is no correlation between acceleration due to gravity and universal gravitation constant, as the value of G is constant. The value of G is constant at any point in this universe. G and g are not dependent on each other.

What is G and g?

The G and g are distinct entities in physics. Below is the table of the difference between G and g.

Symbol

Definition

Nature of Value

Unit

Acceleration due to gravity

g

The acceleration experienced by a body under free fall due to the gravitational force of the massive body

Changes from place to place.

Acceleration due to gravity of earth is 9.8m/s2

m/s2

Universal Gravitational Constant

G

The force of attraction between two objects with unit mass separated by unit distance at any part of this universe.

Constant at any point in this universe.

G = 6.673×10-11Nm2/kg2

Nm2/kg2

g Formula

According to the universal law of gravity ,

\(F=\frac{GMm}{R^{2}}\) ————(1)

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

\(g=\frac{F}{m}\) ———–(2)

Substituting equation (1) in (2) we get-

\(g=\frac{GMm}{R^{2}m}\)

Thus, we arrive at the g formula in physics as –

\(\Rightarrow g=\frac{GM}{R^{2}}\)

Hope you understood the relation and conversion between G and g along with formula, definition, difference and their values.

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