Derivation of Relation Between G and g

Relation between G and g

Difference between G and g

Newton’s Law states that the force F between two masses m₁ and m₂ is given by:

F = Gm₁m₂/r²

where:

F is the gravitational force between the masses,

G is the gravitational constant,

m₁and m₂ are the masses of the objects,

r is the distance between the centers of the two masses.

Let us consider m₁ as the mass of the Earth (M), m₂ as the mass of an object (m), and r as the radius of the Earth (R).

The force F acting on the object due to Earth’s gravity = object’s weight = mg where g is the acceleration due to gravity. So,

mg = GMm/ r²

Eliminating m on both sides. To find g, we rearrange the equation:

g = GM/r²

This equation shows that g, the acceleration due to gravity at the surface of the Earth, depends on G, the mass of the Earth (M), and the square of the radius of the Earth (R).

What is the Relation between G and g?

G is the gravitational constant that helps us calculate the force between two masses. On the other hand, g measures how fast objects fall due to gravity. The relation between G and g is given as g = GM/r². In this article, we will learn about the relationship between G and g in detail.

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