# Gravitational Force: Definition, Formula, and Examples (2023)

## What is Gravitational Force?

All objects having mass attract each other with force known as the gravitational force. It is quite noticeable in astronomical objects such as Sun, Earth, and Moon that have enormous masses. The reason is that the force is proportional to the products of the objects’ masses. Gravitational force is responsible for keeping the planets in motion around the Sun and the Moon around the Earth. Even human beings exert a force on each other, but it is insignificant because of relatively low masses.

Gravitational force is non-contact since there is no contact between the objects. It is centripetal since it is directed toward the center of the orbit around which the object moves. It is responsible for keeping the body in orbit. The revolving body feels a tug that is directed away from the center. This tug is called the centrifugal force. The gravitational force is the weakest of all fundamental forces.

Many famous scientists have made significant contributions to the field of gravitation. In the early 17th century, Italian astronomer Galileo Galilei found that all objects accelerate equally toward the center of the Earth. English mathematician Isaac Newton was the first to discover the laws of gravitation in his 1687 seminal work.

## Universal Laws of Gravitation

Also known as Newton’s Law of Universal Gravitation, the law states that all objects with a mass in the universe attract each other with a force that is

• directly proportional to the product of the masses
• inversely proportional to the square of the distance between their centers

These are the two factors that affect the gravitational force. The value is high for massive objects and when the bodies are closer to one another.

General Formula for Gravitational Force

Suppose M1 and M2 be the masses of the two bodies, and R be the distance of separation between their centers. The following equation gives the gravitational force between the two objects.

$F = \frac{GM_1M_2}{d^2} \hspace{2 cm} (1)$

Unit of Gravitational Force: N or Newton

Here, G is called the universal gravitational constant. It is an empirical physical constant with a value of 6.67 X 10-11N.m2/kg2. Its dimensional formula is M-1L-3T-2. By knowing the masses M1 and M2 and their distance of separation d, it is possible to calculate the magnitude of F.

## Properties of the Gravitational Force

Here are some facts and characteristics of gravitational force.

• Attractive
• Non-contact
• Long-range
• It does not require a medium
• Directly proportional to the product of the masses of the objects
• Inversely proportional to the square of the distance of separation between the objects
• A constant value on the surface of the Earth
• Weakest of all fundamental forces
• Acts along the line joining any two bodies

## Examples of Gravitational Force

An example of gravitation force in our daily lives is that when an object is thrown in the air, it returns to the surface due to Earth’s gravitation. Below are some more examples.

(Video) Using the Gravitational Force Formula

### 1. Gravitational Force of the Earth

Earth exerts a gravitational force on every object, a phenomenon known as gravity. Gravity holds us on the surface and does not let us float freely in the air. We exert the same force on Earth that the Earth exerts on us. However, the Earth is so massive that it is unperturbed. An object suspended in air will fall freely towards the center of the Earth when released.

The difference between gravitational force and gravity is that the former is applied to any two objects in the universe. Gravity is the force between Earth and any other object close to Earth, including on its surface.

The force of gravity is given by,

$F = \frac{G\hspace{0.1 cm}M_E\hspace{0.1 cm} m}{R_{E}^2} \hspace{2 cm} (2)$

Where ME is the mass of the Earth, m is the mass of an object, and RE is the Earth’s radius. If the object is at an altitude h above the surface of the Earth, then the equation modifies to

$F = \frac{G\hspace{0.1 cm}M_E\hspace{0.1 cm} m}{(R_{E}+h)^2} \hspace{2 cm} (3)$

From the above equation, it is quite clear that the Earth’s gravitational force vanishes when h →∞, or at large distances from the surface.

According to Newton’s second law of motion, force is given by mass m multiplied by acceleration a. Therefore,

$F = ma \hspace{2 cm} (4)$

Comparing equations (2) and (4),

$a = g = \frac{G\hspace{0.1 cm}M_E\hspace{0.1 cm}}{R_{E}^2} \hspace{2 cm} (5)$

The above term is called acceleration due to gravity. It has a value of 9.81 m/s2 on the surface of the Earth. Multiplying g by the mass of a person gives the weight W of the person.

$W = mg \hspace{2 cm} (6)$

The acceleration due to gravity in space is zero, which is why astronauts feel weightless and float freely.

The following expression gives the work done by Earth’s gravitational force when an object of mass m falls from a height h above the Earth’s surface.

$\text{Work done} = mgh \hspace{2 cm} (7)$

This work is the change in the object’s potential energy as the object falls through the air.

Satellites orbit around the Earth in fixed orbits due to the gravitational pull. Without gravity, the satellites would have been flung away into space.

The gravity in the polar region is higher than that at the equator. The reason is that the poles are closer to the center of the Earth than the equator.

(Video) Calculating the Gravitational Force

#### Gravitational Force Between Earth and Moon

The Moon revolves around the Earth because gravitational forces hold them together. To calculate this force, we put their masses and the distance between their two centers in equation (1).

Mass of the Earth: ME = 6.0 x 1024 kg

Mass of the Moon: MM = 7.35 x 1022 kg

The average distance between the Earth and Moon, REM = 3.844 x 108 m

Universal gravitational constant, G = 6.67 x 10-11 Nm2/kg2

From equation (1),

$F = \frac{G M_E M_M}{R_{EM}^2} \\\Rightarrow F = \frac{6.67 \times 10^{-11} \hspace{0.1 cm} N \cdot m^{2} \cdot kg^{-2} \times 6.0 \times 10^{24} \hspace{0.1 cm} kg \times 7.35 \times 10^{22} \hspace{0.1 cm} kg}{ (3.844 \times 10^{8} \hspace{0.1 cm} m)^2} \\\Rightarrow F = 2 \times 10^{20} \hspace{0.1 cm} N$

Thus, the gravitational force between the Earth and Moon is 2 x 1020 N.

### 2. Gravitational Force of the Sun

The Sun has a gravitational force due to its mass, which is so large that its influence extends vastly. All planets revolve around the Sun in elliptical orbits due to this attractive force. The gravitational force between the Sun and Earth can be calculated using equation (1).

Mass of the Sun: Ms = 2.0 x 1030 kg

Mass of the Earth: ME = 6.0 x 1024 kg

The average distance between the Sun and Earth, RSE = 1.5 x 1011 m

Universal gravitational constant, G = 6.67 x 10-11 Nm2/kg2

From equation (1),

$F = \frac{G M_S M_E}{R_{SE}^2} \\\Rightarrow F = \frac{6.67 \times 10^{-11} \hspace{0.1 cm} N \cdot m^{2} \cdot kg^{-2} \times 2.0 \times 10^{30} \hspace{0.1 cm} kg \times 6.0 \times 10^{24} \hspace{0.1 cm} kg}{ (1.5 \times 10^{11} \hspace{0.1 cm} m)^2} \\\Rightarrow F = 3.5 \times 10^{22} \hspace{0.1 cm} N$

Thus, the gravitational force between the Sun and Earth is 3.5 x 1022 N.

Likewise, the gravitational force between the Sun and other planets will depend upon their masses and distances.

### 3. Gravitational Force of the Planets

All planets of the solar system have their gravitational force. The values of the acceleration due to gravity are given below.

(Video) Gravity, Universal Gravitation Constant - Gravitational Force Between Earth, Moon & Sun, Physics

• Mercury: 3.7 m/s2
• Venus and Uranus: 8.87 m/s2
• Mars: 3.71 m/s2
• Jupiter: 24.79 m/s2
• Saturn: 10.44 m/s2
• Neptune: 11.15 m/s2

Besides, the gravity of the Moon is 1.62 m/s2. When compared to Earth, it is about 1/6th.

The gravitational force has significant importance that has impacted our daily lives. Here are some of its benefits.

• Constant on the surface of the Earth
• It keeps the muscles and bones working
• Allows Earth to retain its atmosphere
• Allows water dams to store energy

Here are some of its disadvantages.

• It makes it difficult to travel to outer space as rockets have to overcome the force of gravity
• It makes us fall and get hurt
• Limits the height of tall buildings during construction
• Hard on the bones and joints as a person ages

## FAQs

Q.1. Is gravitational force conservative?

Ans. Yes. The gravitational force is conservative since the work done by it around a close path is zero.

Q.2. Is there gravitational force in a vacuum?

Ans. Yes. There can be a gravitational force in a vacuum.

Q.3. What is the range of gravitational force?

Ans. The range of the gravitational force is infinite, although it becomes weaker as the distance between objects increases.

Q.4. Which measurement changes based on the strength of gravitational force?

Ans. Weight. A person’s weight on Earth is not the same on the Moon due to the difference in gravitational forces.

Q.5. Which force is stronger? Gravitational or electrical?

Ans. The electrical force is stronger than the gravitational force.

(Video) Gravity Explained Simply

## Gravitational Force Problems and Solutions

Problem 1. What is the gravitational force between two solid objects whose masses are 110 and 130 kgs and whose distance of separation is 80 cm.? Given, G = 6.67 x 10-11 Nm2/kg2.

Solution:

Given

M1 = 110 kg

M2 = 130 kg

d = 80 cm or 0.8 m

F = G M1 M2 / d2

= 6.67 x 10-11 N.m2/kg2 x 110 kg x 130 kg / (0.8)2

= 1.5 X 10-6 N

• References

Article was last reviewed on Friday, February 3, 2023

(Video) Force: Deriving The Formula Of Gravitational Force | Class 10 | Science | CBSE/SEE

## FAQs

### What is the example gravitational force formula? ›

Example: An object of mass 40 Kg experiences a force of 200N towards the center of a planet from a distance of 20Km. Find the mass of the planet. Solution: Let mass of the planet = M, Mass of the object (m) = 40Kg, Distance between both the masses (r) = 20000m, Force due to gravity (F) = 200N.

What is gravitational force definition and examples? ›

The force of attraction on a body by earth is called gravitational force. Example : The leaves and fruits fall from a tree downwards towards the ground, water in a river flows down streams, a ball thrown up goes to a height and then returns back on ground are some examples of motion due to gravitational force.

What is the definition of gravitational force with the formula? ›

The universal law of gravitation states that: Everybody in the universe pulls every other body with a force that is directly proportional to their mass-produced and inversely proportional to the distance square between them. The Gravitational force formula is given by. F = G m 1 m 2 r 2.

What are 2 gravitational force examples? ›

Examples Of Gravity

The force acting between the Sun and the Earth. The force that is responsible for the revolution of the Moon around the Earth. The tides that are caused in the ocean are due to the force from the Moon. The force that is holding all the gases in the Sun.

What is an example of gravitational force for kids? ›

Gravity in our universe

Gravity is what holds the planets in orbit around the sun and what keeps the moon in orbit around Earth. The gravitational pull of the moon pulls the seas towards it, causing the ocean tides. Gravity creates stars and planets by pulling together the material from which they are made.

What is a simple example of gravitational energy? ›

Gravitational energy is the potential energy held by an object because of its high position compared to a lower position. In other words, it is energy associated with gravity or gravitational force. For example, a pen being held above a table has a higher gravitational potential than a pen sitting on the table.

What is an example of gravitational force in a sentence? ›

1. The split rock is slow to fall, the gravitational force being lower and the angle of fall correspondingly sharper. 2. Weight is the gravitational force of attraction exerted on a body.

What is the formula for gravitational force on Earth? ›

Newton's law of gravitation is: F = GMm r2 where the Gravitational Constant G = 6.673 × 10−11Nm2kg−2 (kg−1m3s−2). gravitational force per unit mass = gravitational acceleration g. g is approximately 9.8m/s2 at the surface of the Earth.

What are 4 examples of gravitational energy? ›

Gravitational energy is used in the following ways in everyday life:
• A raised weight.
• A car that is parked at the top of a hill.
• A yoyo before it is released.
• A book on the table before it fails.
• Water flowing from the tap uses gravitational energy.
• We walk, sit and stand comfortably due to gravitational force.

What are the three formulas of gravitation? ›

Important Gravitational Formulas
• Gravitational Force. F = $\frac{Gm_{1}m_{2}}{r^{2}}$ ...
• Gravitational Potential. i) For Point Charge: ...
• Gravitational Acceleration. g = GM / R²
• Variation of g with Depth. ...
• Variation of g with Height. ...
• Effect of Non-Spherical Earth Shape on g. ...
• Effect of Earth Rotation on Apparent Weight.

### What is the gravitational force 4th grade? ›

The gravitational force is a force that attracts any two objects with mass. We call the gravitational force attractive because it always tries to pull masses together, it never pushes them apart. In fact, every object, including you, is pulling on every other object in the entire universe!

What is an example of gravity 5th grade? ›

Gravity on earth pulls objects downward toward the ground. Rain is a good example: the clouds don't "throw" the rain to the ground, but instead when there is so much water that it gets heavy for the cloud to hold, the water then falls to the ground because of gravity.

Why is gravity an example of a force? ›

Newton's Theory of Gravity states that every object in the universe pulls on every other object. Every object feels this force, so it is a universal force. The force is always attractive; it is always a pull, never a push. Picture the force of gravity as the tension in an imaginary rope between two objects.

What is an example of gravitational to kinetic? ›

Gravitational potential energy is transferred to kinetic energy if the object falls towards the ground. An example of this is seen when a book is lifted and placed on a shelf. Work is done against gravity in lifting the book and energy has been transferred to the gravitational potential energy store of the book.

Which is the best example of gravitational potential energy? ›

The correct answer is Water that is behind a dam.

Is gravity a force or an energy? ›

Gravity is a force, so it just provides one way for objects to exchange and transform energy to different states. The kinetic energy that water gains when it falls (and can therefore be converted into electricity by a hydroelectric plant) comes ultimately from sunlight and not from gravity.

What is another word for gravitational force? ›

synonyms: gravitation, gravitational attraction, gravity.

What is an example of gravitational and magnetic force? ›

For example, gravity on Earth that helps us walking on the Earth's surface is the gravitational force. An example of the application of magnetic force is the action of an electric motor.

How do you calculate gravitational force in basic science? ›

To calculate gravitational force (Gf), GF = MG, where M is mass and gravity. F = mg, used for calculation of gravitational force.

How do we use gravitational force in everyday life? ›

Here are 10 uses for gravity that may surprise you.
1. Track Earth's water and ice. Of course we have to begin with this one. ...
2. Provide energy. ...
3. Give a boost to spacecraft. ...
4. Weigh the unweighable. ...
5. Use gravity as a telescope. ...
6. Hunt for planets around other stars. ...
7. Investigate unseen planets. ...
8. Save the Earth.
Sep 30, 2013

### What does gravitational force depend on? ›

The magnitude of this force depends upon the mass of each object and the distance between the centers of the two objects. Mathematically, we say the force of gravity depends directly upon the masses of the objects and inversely upon the distance between the objects squared.

Is gravity an example of energy? ›

Gravity is a form of energy. If there is a gravitational field, then it has energy. There are some well-defined rules in Einstein's theory to calculate the energy per unit volume in a gravitational field.

What is gravitational force in one word? ›

Definitions of gravitational force. (physics) the force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface. synonyms: gravitation, gravitational attraction, gravity.

What is the definition of gravitation? ›

The phenomenon which causes objects to be attracted to each other because they have mass is known as gravitation. All the planets revolve around the sun due to the gravitational force between the sun and the planets.

Is gravitational force a force answer? ›

Gravitational force is a non-contact force. For action of gravitational force, contact with an object is not required. The force of gravity acts on all object at all the time even while not in contact with the earth.

What kind of force is gravity an example of? ›

Gravity is a type of contact force.

What are the types of gravitational force? ›

There is only one type of gravity. There are no other types of gravity present in nature. This means there is only one type of gravitational force that pulls the two bodies together based on their masses and the distance between their centers. Gravity is a type of central force and is the weakest force known in nature.

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