When we talk about the gravitational force i.e. also one of the four fundamental interactions of nature, we cannot afford to forward the discussion without talking about the “small g” and “big G”.

The main difference between g and G in physics is that “small g” is the acceleration due to gravity & “big G” is Universal Gravitational Constant.

The other significant difference between small g and capital G is that “small g” is a vector quantity. And, “big G” is a scalar quantity.

No wonder, there are so many differences as well as similarities between them. But before going ahead, let me give you a brief review of the two in a tabular form. Let’s dive right in…!!!

## Small g vs Big G

Small g | Big G | |

1. | “Small g” stands for acceleration due to gravity. | “Big G” stands for Universal Gravitational Constant. |

2. | Acceleration due to gravity is the net acceleration experienced by a freely falling body due to the gravitational force of the massive body. | Universal Gravitational Constant is the force of gravitation that exists between two bodies with unit mass separated by a unit distance from each other. |

3. | It is a vector quantity. | It is a scalar quantity. |

4. | The value of “small g” varies from place to place. | The value of “big G” is constant throughout the universe. |

5. | It is dependent on the distance between the two bodies. | It is independent of the distance between the two bodies. |

6. | The S.I. unit of “G” is Nm^{2}/kg^{2}. | The value of the Universal Gravitational Constant is 6.67 × 10^{-11} Nm^{2}/kg^{2}. |

7. | The S.I. unit of “g” is m/s^{2}. | The S.I unit of “G” is Nm^{2}/kg^{2}. |

## What is the acceleration due to gravity?

By definition, acceleration due to gravity or “small g” is the net acceleration experienced by a freely falling body due to the gravitational force of the massive body. Its S.I. unit is m/s^{2}.

Since it has both magnitude and direction, acceleration due to gravity is a vector quantity. Just because of the fact that “small g” is dependent on the distance between the two bodies, the magnitude of the acceleration due to gravity varies from place to place.

Mathematically, it is equal to:

where,

G = Universal Gravitational Constant = 6.67 × 10^{-11} Nm^{2}/kg^{2}

M_{0} = Mass of the Earth = 5.97 × 10^{24} Kg

r_{0} = Radius of the Earth = 6378 Km

On solving, what you get is:

g = 9.81 m/s^{2}

**Factors affecting acceleration due to gravity**

There are so many factors that affect the value of acceleration due to gravity, such as:

- Shape
- Latitude
- Altitude
- Dept
- Motion
- Size
- Mass, etc.

**For Example:**

In the case of the earth, the acceleration due to gravity “small g” is minimum at the equator and maximum at the poles. Because the outward centrifugal force produced due to the rotation of the earth is larger at the equator than at the north and south poles.

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## What is Universal Gravitational Constant?

By definition, Universal Gravitational Constant is the force of gravitation that exists between two bodies with unit mass separated by a unit distance from each other. Its S.I. unit is Nm^{2}/kg^{2}.

Since it has only magnitude, the universal Gravitational Constant is a scalar quantity. Just because of the fact that “big G” is independent of the distance between the two bodies, the magnitude of the Gravitational constant remains the same throughout the universe.

Mathematically, it is equal to:

where,

F = Force of attraction between two bodies

G = Universal Gravitational Constant

m_{1} = Mass of body 1

m_{2} = Mass of body 2

r = distance between two bodies

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**Facts about Universal Gravitational Constant**

The above-mentioned definition and mathematical formulation of Gravitational Constant are based on Newtonian Mechanics. There is one more way to define it. That is in terms of Einsteinian Mechanics.

One of the primary differences between Newtonian and Einsteinian Mechanics is that in Newtonian Mechanics, space and time are absolute. Whereas, in Einsteinian Mechanics, space and time are relative, hence also known as Relativistic Mechanics.

As per Einstein’s General Relativity, Universal Gravitational Constant defines the relation between the geometry of spacetime and the energy-momentum tensor. Mathematically, it is equal to:

where,

G_{μν} = Einstein Tensor

Λ = Cosmological Constant

g_{μν} = Metric Tensor

T_{μν} = Stress-Energy Tensor

k = Constant related to Newtonian Gravitational Constant, where

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