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What is the Relation between G and g?

Last Updated : 23 Jul, 2025

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.

What is G?

G refers to the gravitational constant. It is a key part of the universal law of gravitation, which was first given by Sir Isaac Newton. This constant is used for calculating the attractive force between two masses.

The gravitational force between two bodies of masses m1 and m2 separated by distance r is given by

F = Gm1m2/r2

Here, G stands for the universal gravitational constant, which is a proportionality constant.

  • The value of G is 6.67408 x 10-11 m3 kg-1 s-2.
  • The dimensional formula of G is [M-1 L3 T-2].
  • The value of G is the same throughout the universe. It does not change from object to object.

What is g?

g refers to the acceleration due to gravity. This is the rate at which objects fall toward a celestial body, like Earth, when dropped.

  • This is a type of acceleration that is only caused by gravity.
  • Since smaller objects have very small gravitational force, this is usually reserved for massive things.
  • The SI unit of g is meters per second squared (m/s2).
  • When we drop an object, the acceleration it experiences is due to the Earth's gravitational pull.
  • For the planet Earth, g has a value of 9.8 m/s2.
  • g can change depending on where you are on Earth. It's slightly different at the poles and the equator.
  • Other planets have their own g values, based on their mass and size.

Relation between G and g

The relationship between G (the gravitational constant) and g (acceleration due to gravity) is expressed by the formula,

g = GM/r2​

where, G is used to calculate g, using the mass M and radius r of a celestial body.

Derivation of Relation 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:

  • G is the gravitational constant,
  • m1 and 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).

Difference between G and g

Here are some differences between G (the gravitational constant) and g (the acceleration due to gravity) :

FeatureG (Gravitational Constant)g (Acceleration due to Gravity)
DefinitionG is a universal constant used in the calculation of gravitational forces between two masses. g is the acceleration objects experience when subjected to gravity on a celestial body.
SymbolGg
ValueConstant, 6.67430 × 10-11 m3kg-1s-2Varies, e.g., ~9.81 m/s2 on Earth
UnitCubic meters per kilogram per second squaredMeters per second squared
ApplicationUsed to calculate the gravitational force in universal contexts, affecting two masses anywhere in the universe.Used to define the weight of an object and how quickly it falls due to gravity on a specific celestial body's surface.
ConstancyG is constant and does not change irrespective of location or conditions.g varies depending on the celestial body's mass and radius, as well as altitude and latitude.

Conclusion

G, the gravitational constant, gives us information about the different forces in the universe. g, on the other hand, tells us how these forces affect objects on a specific planet, like Earth. By understanding both, we can calculate not just the weight of objects, but also understand the behavior of planets and stars.

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