What is the Relation between G and g? (original) (raw)

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.

Table of Content

What is g?
Relation between G and g
Derivation of Relation Between G and g
Difference between G and g

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 = Gm 1 m 2 /r 2

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

The value of G is 6.67408 x 10 -11 m 3 kg -1 s -2.
The dimensional formula of G is **[M -1 L 3 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/s 2 ).
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/s 2.
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/r _**2_

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:

_F is the gravitational force between the masses,
_G is the gravitational constant,
_m 1 and _m _2_ are the masses of the objects,
_r is the distance between the centers of the two masses.

Let us consider _m _1_ as the mass of the Earth (_M), _m _2_ 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/ r 2

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

**g **= **GM/r **2

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) :

Feature	_G (Gravitational Constant)	_g (Acceleration due to Gravity)
**Definition	_G 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.
**Symbol	_G	_g
**Value	Constant, 6.67430 × 10-11 m3kg-1s-2	Varies, e.g., ~9.81 m/s2 on Earth
**Unit	Cubic meters per kilogram per second squared	Meters per second squared
**Application	Used 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.
**Constancy	_G 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.