Small g vs Big G – Differences & Similarities in Tabular Form

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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 gBig 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 Nm2/kg2.The value of the Universal Gravitational Constant is 6.67 × 10-11 Nm2/kg2.
7.The S.I. unit of “g” is m/s2.The S.I unit of “G” is Nm2/kg2.
From the above difference between g and G in tabular form, you got the exact overview of these two. However, to know them, let us try to understand both of them in a detailed format. Keep reading!

 

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/s2.

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:

{\displaystyle g={\frac {GM_{\oplus }}{r_{\oplus }^{2}}}.}

where,

G = Universal Gravitational Constant = 6.67 × 10-11 Nm2/kg2

M0 = Mass of the Earth = 5.97 × 1024 Kg

r0 = Radius of the Earth = 6378 Km

On solving, what you get is:

g = 9.81 m/s2

Check Out: Copernican Model of the Universe: Slayer of the Earth-Centered Universe

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.

Editor’s Choice: Centripetal vs Centrifugal Force: How They Affect Motion!!!

 

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 Nm2/kg2.

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:

{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}.}

where,

F = Force of attraction between two bodies

G = Universal Gravitational Constant

m1 = Mass of body 1

m2 = 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:

{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }\,,}

where,

Gμν = Einstein Tensor

Λ = Cosmological Constant

gμν = Metric Tensor

Tμν = Stress-Energy Tensor

k = Constant related to Newtonian Gravitational Constant, where

{\displaystyle \kappa ={\frac {8\pi G}{c^{2}}}\approx 1.866\times 10^{-26}\mathrm {\,m{\cdot }kg^{-1}} .}

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I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my career, and therefore I did my postgraduate degree in physics. Right now I am a loner (as ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every aspect of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

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