Is Gravitational Field Strength A Vector: Why, How, Detailed Facts


Gravitational field strength is a mechanism for measuring gravity. It shows the magnitude of gravity at a particular place.

Gravitational field strength is a vector quantity consisting of direction as well as magnitude.

Is gravitational field strength a vector ? Yes, it is, as its formula is gravitational force per unit mass. As gravitational field strength consists of force, and as force is a vector quantity, it naturally makes it a vector quantity.

A scalar quantity will only have magnitude, i.e. a number. For example – 25 metres. It is always one-dimensional.

A vector quantity will have magnitude as well as direction. For example – 25 metres, north. It is multi-dimensional.

What is Gravity?

Gravity is expressed as the force of attraction between any two objects in the universe. It is the weakest force in the universe and has no specific range.

The gravitational force is enormous when the object is heavier. Thus, always the lighter object will be attracted towards the heavier object. Due to this reason, the Earth orbits around the sun, and moon around the Earth.

The exciting fact about gravitation is that all the objects in this universe have their own gravitational field, including humans!

Yes! You read it correctly. But, as gravity is the weakest force, all other gravitation fields are negligible compared to the earth’s gravitational force or, in fact, weaker than any other planet’s gravitational force.

For comparing a human’s gravitational field to that of the Earth’s gravitational field, let us take an example. Say, person A is standing one meter away from person B, who weighs 100 Kg. Earth’s gravitational acceleration will be 1.5 billion times larger than the gravitational acceleration of person B. That is why person A will not gravitate to person B.

Another critical subject heavily affected by gravity is mass and weight. Mass is the quantity of matter available in an object, while weight is the outcome of the force of gravity acting on it. Mass multiplied by gravity gives weight.

w = m x g

Where,w = Weight
 g = Gravitational Field Strength or Gravitational Acceleration
 m = Mass of the object

Gravity is one of the four elemental forces of nature. Gravity affects the solar system or, in fact, any system in the universe. The formation of stars, planets, asteroids, etc., all depends on gravity.

Various scientists like Robert Hooke, Galileo Galilei, Jesuits Grimaldi, Riccioli, Bullialdus, Borelli, etc., put forward different theories on gravitation, and some of which are very similar to each other but still not entirely practically proven. Ancient Greek Philosophers like Archimedes, Roman architect and engineer – Vitruvius, Indian mathematicians and astronomers like Aryabhatta and Brahmagupta also identified Gravity.

But then, one fine day, an apple fell upon Sir Isaac Newton, and he derived the “Newton’s Law of Universal Gravitation” and the world followed it. According to Newton’s theory, the gravitational force is directly proportional to the product of masses and inversely proportional to the square of the distance between them.

The equation for gravitational force is given as:

Fα(m1m2)/r2

To remove the proportionality sign, a constant is added. In this scenario, it is the gravitational constant “G”.

F=G*(m1m2)/r2

Where,F = Gravitational Force
 G = Gravitational Constant = 6.674 x 10-11 N.m2.kg-2
 m1 = Mass of the object 1
m2 = Mass of the object 2
r = Distance between the centre of the objects

Read more on Is Gravity an External Force 

Why is Gravitational Force a Vector Quantity?

Gravitational field strength is a physical quantity according to classical mechanics.

Gravitational field strength is denoted by ‘g’, and its formula is given as force per unit mass.

g=F/m

Where,g = Gravitational Field Strength
 F = Gravitational Force
 m = Mass of the Object

According to this formula, the S. I. Unit of g is N/Kg, and earth’s gravitational field strength is 10 N/Kg. “g” is also referred to as the Gravitational Acceleration, given as 9.8 m/s2 for earth.

As force is a vector quantity, gravitational force will be a vector quantity, making gravitational field strength a vector quantity.

Albert Einstein also put forward his theory for gravitation in his general theory of relativity, and it also has superseded Newton’s theory. Still, it is only used when there is the requirement for extreme accuracy or when dealing with a powerful gravitational field near a super-massive and extremely dense object like the black hole.

is gravitational field strength a vector
Bending of space-time
Image Credits: istockphoto

The bending of space-time is a tricky concept, but it is explained in the general theory of relativity given by Albert Einstein. Here, we only need to understand that it involves the 3-dimensional space and 1-dimensional time, and thus, it is a 4-dimensional flow. So, due to gravity, there is a change in the space-time flow, resulting in different perceptions of observations of an event from different places or observers.

Read more on Is Gravity a Conservative Force

Comparison of Gravitational Acceleration on different planets of our Solar System.

Gravitational acceleration is the speed at which the planet pulls a body. For Earth, its value is 9.8 m / s2. Let’s try to find the acceleration due to gravitation on different planets present in our solar system.

One can detect the gravitational acceleration of any planet using the formula:

g=Gm/r2

Where,g = Gravitational Acceleration 
G = Gravitational Constant = 6.674 x 10-11 N. m2. kg-2 (it will be same everywhere)
 r = radius of the planet
 m = Mass of the Planet
  • Gravitational acceleration on Mercury
For Mercury,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
 r = ~2.4 x 106 m
m = 3.28 x 1023 Kg

Putting all this information in the formula, we get:

g = 3.61 m / s2

  • Gravitational Acceleration on Venus
For Venus,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
r = ~6.07 x 106 m
 m = 4.86 x 1024 Kg

Putting all this information in the formula, we get:

g = 8.83 m / s2

For Mars,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
r = ~3.38 x 106 m
 m = 6.42 x 1023 Kg

Putting all this information in the formula, we get:

g = 3.75 m / s2

  • Gravitational Acceleration on Jupiter
For Jupiter,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
r = ~6.98 x 107 m
 m = 1.90 x 1027 Kg

Putting all this information in the formula, we get:

g = 26.0 m / s2

  • Gravitational Acceleration on Saturn
For Saturn,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
r = ~5.82 x 107 m
 m = 5.68 x 1026 Kg

Putting all this information in the formula, we get:

g = 11.2 m / s2

  • Gravitational Acceleration on Uranus
For Uranus,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
r = ~2.35 x 107 m
 m = 8.68 x 1025 Kg

Putting all this information in the formula, we get:

g = 10.5 m / s2

  • Gravitational Acceleration on Neptune
For Neptune,g = ?
 G = 6.674 x 10-11 N. m2. kg-2
r = ~ 2.27 x 107 m
 m = 1.03 x 1026 Kg

Putting all this information in the formula, we get:

g = 13.3 m / s2

Gravitational Constant vs. Acceleration Gravity

There are innumerable and remarkable differences between the gravitational constant and acceleration gravity. It would be easy to study them in the tabular format.

Gravitational ConstantAcceleration Gravity
It is an empirical physical constant.Acceleration due to gravity on an object under free fall (generally in vacuum).
Also known as “Newtonian Constant of Gravitation” or “Universal Gravitational Constant” or “Cavendish Gravitational Constant.”Also known as “Gravitational Field Strength”.
Denoted by “G”.Denoted by “g”.
The value of the gravitational constant is independent of all factors, and thus, remains the same throughout the universe.The value of acceleration gravity is different on different planets or any other astronomical object.
It is proportionality constant, and thus, it would remain the same anywhere, be it the centre of a planet, outside of it, near the poles, in vacuum, etc., the value of G will remain as it is, without any change.The gravitational acceleration is maximum at the earth’s surface. Gravitational acceleration starts decreasing whether one moves in upward or downward direction.
Gravitational constant is a scalar quantity.Acceleration gravitation is a vector quantity.
Value of gravitational constant is never zero.Value of acceleration gravitation is zero at the centre of the earth.
No formula for G.Formula for finding g = F/m
The relation between G and g can be given as: G=gr2/m G =The relation between G and g can be given as: g = GM/r2
S. I. Unit of G = N. m2 / kg2S. I. Unit of g = m / s2
G = 6.674 x 10-11 N. m2. kg-2Value of gravitational acceleration for earth = g = 9.8 m / s2

Durva Dave

I am Durva Dave, completed my post-graduation in Physics. Physics fascinates me a lot and I like in knowing the ‘Why’ and ‘How’ of everything that unfolds in our universe. I try to write my blogs in simple yet effective language so that it is easier for the reader to understand as well remember. I hope with my curiosity I am able to provide the readers for what their looking for through my blogs. Let’s connect through LinkedIn.

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