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Class 11 Chapter 7

Class 11 Physics Chapter 7: Gravitation

Gravitation is one of the most fundamental chapters in Class 11 Physics, explaining the universal force of attraction between masses. The chapter covers Newton's Universal Law of Gravitation, gravitational field, gravitational potential, acceleration due to gravity, escape velocity, orbital motion, satellites, and Kepler's Laws of Planetary Motion. These concepts are frequently tested in JEE Main, JEE Advanced, NEET, and CBSE Board examinations.

At ALLEN, Chapter 7: Gravitation study resources are prepared by experienced faculty to help students master gravitational concepts through concise explanations, important formulas, solved examples, previous years' question analysis, and exam-oriented tips. Whether you are preparing for school examinations or competitive entrance exams, these notes offer a quick and effective way to revise one of the highest-scoring chapters in mechanics.

1.0Chapter Snapshot

Parameter	Details
Difficulty Level	Moderate
JEE Main Weightage	Moderate to High (1–2 Questions)
JEE Advanced Weightage	High
Key Concepts Covered	Universal Law of Gravitation, Gravitational Field, Potential, Escape Velocity, Satellites, Kepler's Laws

2.0Chapter 7 Smart Study Material by ALLEN Experts: Download PDFs

Continue your preparation after completing Gravitation with these additional study resources.

Practice Resources

Resource	Access
Chapter Mock Test Paper
Chapter Mock Test Solutions

Test your Knowledge

question 1 of 5

According to Newton’s law of universal gravitation, the gravitational force between two bodies is proportional to:

1.The sum of their masses and inversely proportional to distance

2.The product of their masses and inversely proportional to the square of distance

3.The difference of their masses and directly proportional to distance

4.The product of their masses and directly proportional to the square of distance

Must-Revise Concepts

Black hole

Difference between mass and weight

Hydroelectric Energy Advantages And Disadvantages

Kepler's Laws of Planetary Motion

Motion of celestial objects in space

Universal Law of Gravitation

Gravitation: Download Important IIT JEE & NEET Questions

Gravitation is a fundamental force of nature that governs the motion of objects throughout the universe. It is the attractive force that draws two bodies toward one another, resulting in a pull that depends on their masses and the distance separating them. This force not only keeps us anchored to the Earth but also plays a vital role in the movement of celestial bodies, such as planets, moons, and stars.

The understanding of gravitation has significantly evolved over the centuries. In the late 17th century, Sir Isaac Newton was among the first to mathematically describe this force through his Universal Law of Gravitation.

1.0Newton Law of Gravitation

Gravitation is the property of matter due to which two bodies always attract each other.
It states that every particle in the universe attracts all other particles with a force which is directly commensurate to the product of their masses and is inversely commensurate to the square of the distance between them.
This formula is given for point masses. For spherical objects (planets), the distance between centres is taken.

$F_{g} = G \frac{m _{1} m _{2}}{r ^{2}}$

G=universal Gravitational Constant,Its value is the same throughout the universe; G independent of the nature and size of the bodies; it does not depend even upon the nature of the medium between the bodies.
Value of G in $SI = 6.67 \times 1 0^{- 11} Nm^{2} kg^{- 2} or CG.S = 6.67 \times 1 0^{- 8} dyne cm^{2} g^{- 2}$
Dimension of $G = [M^{- 1} L^{3} T^{- 2}]$
Forces due to Multiple Particles is given as, $F_{n e t} = F_{1} + F_{2} + F_{3} + \dots\dots$

Law of Gravitation in Vector Form

$F_{12} = - G \frac{m _{1} m _{2}}{r ^{2}} \overset{r}{^}$

Related Video:

1.0Gravitational Field

It is the region around a mass where its gravitational effects can be observed. The gravitational field due to a body extends till infinity.
Strength of the gravitational field decreases on moving away from a body.

(i) In an infinite gravitational field, the acceleration is zero.

(ii) Gravitational field ∝ mass

Gravitational field is conservative in nature.
There are two ways to measure the strength of the gravitational field.

(i) Gravitational field intensity.

(ii) Gravitational potential

Gravitational Field Intensity

It is defined as gravitational force exerted on a unit mass positioned in a gravitational field.
It is a vector quantity.Its direction is same as that of gravitational force.
$I = \frac{F}{m} \Rightarrow Unit - N / K g$
Dimensional Formula $- [M^{0} L^{1} T^{- 2}]$
Gravitational Field Intensity owed to a point mass,is given as,

$I = \frac{GM}{r ^{2}} (- \overset{r}{^})$

Negative sign indicates that the force due to the gravitational field is attractive in nature.
Gravitational Field Intensity due to multiple particles,

$I_{n e t} = I_{1} + I_{2} + I_{3} + \dots\dots\dots\dots\dots$

A. Solid Sphere

Outside the Sphere (r>R)

$I_{out} = \frac{GM}{r ^{2}} (- \overset{r}{^})$

At the Surface (r=R)

Gravitational field intensity at the surface of sphere

$I_{surface} = \frac{GM}{R ^{2}} (- r)$

Inside the Sphere (r<R)

Gravitational Field Intensity Inside the Sphere

$I_{in} = \frac{GM r}{r ^{3}} (- \overset{r}{^})$

Graph between $I$ and r for a solid sphere

Graph between gravitational field intensity and r

B. Hollow Sphere

Outside the Shell (r>R)

Gravitational Field Intensity Outside the Shell

$I_{out} = \frac{GM}{r ^{2}} (- \overset{r}{^})$

At the Surface (r=R)

Gravitational field intensity at the surface

$I_{surface} = \frac{GM}{R ^{2}} (- \overset{r}{^})$

Inside the Shell (r<R) I=0

Gravitational field intensity in the inside of the shell

Graph between $I$ and r for Hollow sphere

Graph between gravitational field intensity and r for a hollow sphere

2.0Acceleration Due to Gravity

If a body is placed inside a gravitational field having intensity I, gravitational force applied on it is, F=m I
Earth also pulls every object towards its center with force F=mg

On comparing both the equations we get $g = ∣ I ∣$

Where g = acceleration due to gravity I is intensity of gravitational field due to Earth.

Assuming Earth to be a Solid Sphere

$g_{s} = \frac{GM}{R _{e}^{2}} \Rightarrow 9.81 m / s^{2}$ , Same formula can be used to find acceleration due to gravity at the surface of any planet.

In terms of density $(ρ) : g = \frac{GM}{R ^{2}}$

$mass = density \times Volume$

$M = ρ \times \frac{4}{3} π R^{3}$

$g = \frac{G ( \frac{4}{3} π R ^{3} )}{R ^{2}} = \frac{4}{3} π GRρ$

Variation in acceleration due to gravity with height

Variation in acceleration due to gravity with height

$g_{h} = g [1 - \frac{2 h}{R _{e}}]$ , This formula is valid if h is upto 5% of earth's radius (320 km from earth's surface)

If h is greater than 5% earth's radius we use, $g_{h} = \frac{G M _{e}}{( R _{e} + h ) ^{2}}$

Variation in acceleration due to gravity with depth

$g_{d} = g_{s} (1 - \frac{d}{R})$ , For any depth below Earth's Surface

Note:

Valid for small or large depth.
Fractional change in value of $g \to \frac{Δ g}{g} = \frac{d}{R}$
At any depth, $g_{d} < g_{s}$
Another form that can be used $g_{d} = \frac{GM}{R ^{3}} r \to g_{d} = g_{s} \frac{r}{R}$

Graph

For (r<R)

$g = \frac{GM}{R ^{3}} r \to g = g_{s} \frac{r}{R}$

For $(r \geq R)$

$g = \frac{GM}{r ^{2}} \to g = g_{s} \frac{R ^{2}}{r ^{2}}$

Value of g is maximum at Earth's surface

Variation in acceleration due to gravity with depth

Variation in value of 'g' due to rotation of earth

Variation in value of acceleration due to gravity due to rotation of earth

$N = M g_{e ff} = M g - M ω^{2} R_{e} Cos^{2} λ$ , As one moves towards pole, apparent weight increases

$λ : Angle of Latitude$

$For Poles λ = 9 0^{\circ}$

$For Equator λ = 0^{\circ}$

$g =$ acceleration due to gravity without considering rotation of Earth

$g_{eff} =$ acceleration due to gravity considering rotation of Earth

Variation in value of "g" due to shape of Earth

Variation in value of acceleration due to gravity due to shape of Earth

$Δ g = g_{e} - g_{p} \approx 0.02 m / s^{2}$ , Earth is not a perfect sphere

$g_{surface} = \frac{GM}{R ^{2}}$

$g_{p} > g_{eq’}$ (as surface is close to center of Earth near pole as compared to equator )

3.0Gravitational Potential

It is defined as amount of work done by external agent against gravitational pull in conveying a unit mass from infinity to that point without changing its kinetic energy

$V_{P} = \frac{W _{\infty \to p}}{m}$

Motion of unit mass is considered slowly, so that no energy is spent to change the kinetic energy of the system.
At infinity, Gravitational Potential is assumed to be ZERO.

Also Read : Difference Between Mass and Weight

Gravitational Potential Due To a Point Mass:

$V = \frac{W _{e x t}}{m} = - \frac{GM}{r}$ (Negative sign in potential indicates attractive nature of force. )

Relation between Potential and Intensity

$I = - \frac{d V}{d r}$

If V is constant in a region, I = 0
This relation is valid for all conservative fields.

Standard results to remember:

Spherical shell (M, R)

Case 1. Outside the Shell $(r > R), V_{out} = - \frac{GM}{r}$

Case 2. On the Surface $(r = R), V_{Surface} = - \frac{GM}{R}$

Case 3. Inside the Shell $(r < R), V_{I n} = - \frac{GM}{R}$ , (Potential is same everywhere and is equal to its value at the surface.)

Solid sphere(M, R)

Case 1. Outside the Sphere $(r > R), V_{out} = - \frac{GM}{r}$

Case 2. On the Surface $(r = R), V_{Surface} = - \frac{GM}{R}$

Case 3. Inside the Sphere $(r < R), V_{I n} = - \frac{GM}{2 R ^{3}} (3 R^{2} - r^{2})$ , (Potential is same everywhere and is equal to its value at the surface.)

4.0Gravitational Potential Energy

The gravitational potential energy of a particle situated at a point in some gravitational field is defined as the amount of work required to bring it from infinity to that point without changing its kinetic energy.

$U = - G \frac{m _{1} m _{2}}{r}$ , negative sign shows the boundedness of the two bodies

It is a scalar quantity.
It's SI unit is joule and Dimensions are [M¹L²T^–2]
The gravitational potential energy of a particle of mass 'm' placed on the surface of earth of mass 'M' , radius 'R' is given by : $U = - G \frac{m _{1} m _{2}}{R}$

Gravitational Potential Energy for Three Particle System

If there are more than two particles in a system, then the net gravitational potential energy of the whole system is the sum of gravitational potential energies of all the possible pairs in that system.

$U_{System} = (G \frac{m _{1} m _{2}}{r _{1}}) + (G \frac{m _{2} m _{3}}{r _{2}}) + (G \frac{m _{1} m _{3}}{r _{3}})$

$= - G \frac{m _{1} m _{2}}{r _{1}} - G \frac{m _{2} m _{3}}{r _{2}} - G \frac{m _{1} m _{3}}{r _{3}}$

If Gravitational Potential at a point P is V_P
Then GPE of a particle of mass m placed at P is :U_P = m(V_P)

Note: At infinity, $V_{\infty} = 0 \Rightarrow U_{\infty} = 0$

5.0Escape Velocity

It is the minimum velocity required for an object located at the planet's surface so that it just escapes the planet's gravitational field

$V_{e} = \frac{2 GM}{R _{e}}$

$V_{e} = 2 g_{s} R_{e} = 11.2 km / s . R_{e} = 6400 km$

Escape speed depends on :

Mass (M), radius (R) of the planet
Position from where the particle is projected.

Escape speed does not depend on :

Mass (m) of the body which is projected
Angle of projection.
If a body is thrown from the Earth's surface with escape speed, it goes out of earth's gravitational field and never returns back to the earth's surface.

Escape velocity from a point other than surface

1. Total energy is zero at any point when particle start moving with escape velocity,T E=0

2. If given point is at distance r (>R) from center of Earth, $P E_{Out} = - \frac{G M _{e} m}{r}$

3. If given point is at distance r (<R) from the center of Earth, $P E_{I n} = - \frac{GM ( 3 R ^{2} - r ^{2} )}{2 R ^{3}} \times m$

6.0Escape Energy-Binding Energy

Minimum energy given to a particle in the form of kinetic energy so that it can just escape the Earth's gravitational field.
Magnitude of escape energy = $G \frac{M m}{R}$
(–ve of PE on the Earth's surface)
Escape energy = Kinetic Energy corresponding to the escape velocity

$G \frac{M m}{R} = \frac{1}{2} m v_{e}^{2}$

KE < Escape Energy v_o < v_e Body returns to Earth surface
KE = Escape Energy v_o = v_e Body comes to rest at infinity
KE > Escape Energy v_o > v_e Body has residual velocity at infinity

Binding energy:

Total energy of a particle near Earth.

BE < 0 Particles cannot escape the gravitational field of Earth.
BE ≥ 0 Particles can escape the gravitational field of Earth.

7.0Kepler’s Law

Kepler's $1^{s t}$ Law: Each planet moves in an elliptical revolution, with the sun at one focus of the ellipse.

Kepler's $2^{n d}$ Law: A line joining any planet to the Sun glides out equal areas in equal intervals of time, i.e. the areal velocity of the planet remains constant.

Kepler's $3^{r d}$ Law: The square of the period of revolution of any planet around the Sun is directly relationall to the cube of the semi-major axis of its elliptical orbit.

$T^{2} \propto a^{3}$

a : average distance of the planet from Sun

$a = \frac{r _{m a x} + r _{m i n}}{2}$

8.0Satellite Motion

A light body revolving around a heavier planet due to gravitational attraction, is called a satellite. Moon is a natural satellite of Earth.

Essential conditions for satellite motion:

The centre of the satellite's orbit should coincide with the centre of Earth
Plane of the orbit of the satellite should pass through the centre of Earth.

It follows that a satellite can revolve around the earth only in those circular orbits whose centres coincide with the centre of earth. Circles drawn on a globe with centres coincident with earth are known as 'great circles'. Therefore, a satellite revolves around the earth along circles concentric with great circles.

Also Read : Earth Satellites

9.0Orbital Velocity (V_o)

$V_{o} = \frac{G M _{e}}{R _{e}} \approx 8.1 km / s$

Time period of orbital motion:

$T = 2 π \frac{R _{e}^{3}}{G M _{e}} \approx 84 min$

Satellite motion - Energy Analysis

1.Kinetic energy of satellite

$K E = \frac{G M _{e} m}{2 r}$

2.Potential energy of satellite

$PE = - \frac{G M _{e} m}{r}$

Total Energy = Kinetic Energy + Potential Energy

$TE = - \frac{G M _{e} m}{2 r}$

$K E = - TE = - \frac{PE}{2} = - \frac{G M _{e} m}{2 r}$

As total energy of a satellite is negative, it is called as bounded system

Also Read : Kepler's Law of Planetary Motion

10.0Binding Energy

Minimum energy required to break a bounded system.
$BE + TE = 0 \Rightarrow BE = - TE$
$BE = ∣ TE ∣ \Rightarrow BE = \frac{G M _{e} m}{2 r}$

Note:

$TE = - \frac{G M _{e} m}{2 r}$
$PE = - \frac{G M _{e} m}{r}$
$K E = \frac{G M _{e} m}{2 r}$
$V_{0} = \frac{G M _{e}}{r}$

$\Rightarrow T \propto R^{3/2}$

So, If the radius of the orbit of the satellite is increased,

KE will decrease, TE will increase, PE will increase, Orbital velocity will decrease, and Time period will increase.

11.0Work Done to Shift Orbit of Satellite

$W_{E x t} = Δ TE$

$w_{E x t} = \frac{G M _{ε} m}{2} (\frac{1}{r _{1}} - \frac{1}{r _{2}})$

Essential conditions for satellite motion

The Center of the satellite's orbit coincides with the center of Earth.
Plane of orbit of the satellite is passing through the center of Earth.

There are two stable orbits for a satellite

Equatorial orbit
Polar orbit

Any satellite is projected as near to the equator as possible as-

g is minimum near the equator, less fuel
Easier to set the satellite in any orbit

12.0Polar Satellite

It rotates in the Polar plane.

Its height from Earth's surface is 500 km ~ 600 km.
Its time period is 100 min.
Used for weather data collection

Note: Any satellite is said to be in a condition of freely falling on Earth. (as the only force acting on it is the force of gravity). Hence, the apparent weight of any object in a satellite is always ZERO.

Related Video:

Also Read:

Escape Velocity	Gravitational Potential Energy	Potential Energy
Kepler's Law of Planetary Motion	Acceleration Due To Gravity	Kinetic Energy
Vectors in Physics	Centre of Mass And Collision	Elastic Collision

1.0Learning Outcomes

After studying these revision notes, you will be able to:

Apply Newton's Universal Law of Gravitation to solve numerical problems.
Calculate gravitational force between two bodies.
Understand gravitational field intensity and gravitational potential.
Determine the variation of acceleration due to gravity with height and depth.
Solve problems involving escape velocity and orbital velocity.
Apply Kepler's Laws of Planetary Motion.
Analyze the motion of artificial satellites.
Strengthen concepts used in advanced mechanics and astronomy-related questions.

2.05-Minute Quick Revision

If you have only 5 minutes before your exam, revise these important concepts and formulas.

Must-Revise Concepts

Universal Law of Gravitation
Gravitational Constant (G)
Gravitational Field
Gravitational Potential
Potential Energy
Acceleration Due to Gravity
Variation of g with Height
Variation of g with Depth
Escape Velocity
Orbital Velocity
Geostationary Satellites
Kepler's Laws of Planetary Motion

Important Formula Recall

Quickly revise these formulas before solving numerical questions:

Newton's Law of Gravitation
Gravitational Field Intensity
Gravitational Potential
Potential Energy
Acceleration Due to Gravity
Escape Velocity
Orbital Velocity
Time Period of Satellite
Kepler's Third Law
Relation Between Orbital Speed and Radius

3.0High Weightage Topics

Topic	Focus Area
Universal Law of Gravitation	Numerical Problems
Gravitational Field & Potential	Conceptual Questions
Variation of g	Formula-Based Questions
Escape Velocity	JEE Numerical Problems
Orbital Velocity	Satellite Motion
Kepler's Laws	Conceptual Applications
Artificial Satellites	Mixed Numerical Problems
Energy of Satellites	Advanced JEE Questions

4.0Formula Handbook

The following formulas are essential for solving numerical and conceptual questions from Gravitation in JEE Main, JEE Advanced, NEET, and CBSE examinations.

5.0Common Mistakes & JEE Tips

Gravitation is a formula-rich chapter, but most mistakes occur because students confuse similar formulas or use the wrong radius in calculations.

Common Mistake	Correct Approach
Using Earth's radius instead of orbital radius	For satellites, always use the distance from Earth's centre.
Confusing escape velocity with orbital velocity	Escape velocity is (\sqrt{2}) times the orbital velocity at the same point.
Ignoring negative signs in potential energy	Gravitational potential and potential energy are always negative (taking infinity as reference).
Mixing mass and weight	Weight depends on (g), whereas mass remains constant.
Applying the wrong formula for variation of (g)	Use separate formulas for height and depth.
Forgetting units of the gravitational constant	Revise the SI unit and dimensions of (G).
Confusing gravitational field with gravitational potential	Field is a vector quantity, while potential is a scalar quantity.
Using Kepler's laws without understanding assumptions	Remember that Kepler's laws apply to planetary motion under gravitational force.

6.0ALLEN Faculty Tips

Memorize all satellite-related formulas together for quick revision.
Learn the derivation of escape velocity to strengthen conceptual understanding.
Practice questions on the variation of (g) with height and depth.
Understand the relationship between orbital velocity, escape velocity, and total energy.
Draw neat diagrams while solving satellite motion problems.
Revise Kepler's Laws along with their practical applications.
Solve Previous Years' Questions to improve accuracy in formula-based problems.
Keep a separate formula sheet for gravitation as many expressions look similar.

7.0PYQ Trend Analysis

Gravitation is a consistently scoring chapter in JEE Main and JEE Advanced. Questions are commonly asked from satellite motion, escape velocity, gravitational potential, and Kepler's Laws.

Note: The trend below is based on the analysis of previous years' JEE Main and JEE Advanced question papers. The exact number of questions may vary each year.

Concept	Questions Asked (Last 5 Years)	Average Difficulty
Universal Law of Gravitation	2–3	Easy
Gravitational Field & Potential	2–3	Moderate
Variation of (g)	2–3	Easy–Moderate
Escape Velocity	3–4	Moderate
Orbital Motion & Satellites	4–5	Moderate
Kepler's Laws	2–3	Moderate

Most Common Question Types

Numerical problems based on Newton's Universal Law of Gravitation.
Escape velocity and orbital velocity calculations.
Variation of acceleration due to gravity with height and depth.
Energy of artificial satellites.
Conceptual questions based on Kepler's Laws.
Gravitational field and potential comparison questions.
Assertion–Reason and statement-based conceptual MCQs.

8.0Smart Revision Strategy

Revise this chapter in the following sequence for maximum retention:

Universal Law of Gravitation
Gravitational Field and Potential
Variation of (g)
Escape Velocity
Orbital Velocity
Artificial Satellites
Kepler's Laws
Formula Revision
PYQs from JEE Main & Advanced
Mixed Numerical Practice

Class 11 Physics Chapters List:- JEE & NEET Revision Notes

Chapter 1 Units and Measurements

Chapter 2 Motion in a Straight Line

Chapter 3 Motion in a Plane

Chapter 4 Laws of Motion

Chapter 5 Work, Energy and Power

Chapter 6 System of Particles and Rotational Motion

Chapter 7 Gravitation

Chapter 8 Mechanical Properties of Solids

Chapter 9 Mechanical Properties of Fluids

Chapter 10 Thermal Properties of Matter

Chapter 11 Thermodynamics

Chapter 12 Kinetic Theory

Chapter 13 Oscillations

Chapter 14 Waves

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Class 11 Physics Chapter 7: Gravitation

Gravitation is one of the most fundamental chapters in Class 11 Physics, explaining the universal force of attraction between masses. The chapter covers Newton's Universal Law of Gravitation, gravitational field, gravitational potential, acceleration due to gravity, escape velocity, orbital motion, satellites, and Kepler's Laws of Planetary Motion. These concepts are frequently tested in JEE Main, JEE Advanced, NEET, and CBSE Board examinations.

At ALLEN, Chapter 7: Gravitation study resources are prepared by experienced faculty to help students master gravitational concepts through concise explanations, important formulas, solved examples, previous years' question analysis, and exam-oriented tips. Whether you are preparing for school examinations or competitive entrance exams, these notes offer a quick and effective way to revise one of the highest-scoring chapters in mechanics.

1.0Chapter Snapshot

Parameter	Details
Difficulty Level	Moderate
JEE Main Weightage	Moderate to High (1–2 Questions)
JEE Advanced Weightage	High
Key Concepts Covered	Universal Law of Gravitation, Gravitational Field, Potential, Escape Velocity, Satellites, Kepler's Laws

2.0Chapter 7 Smart Study Material by ALLEN Experts: Download PDFs

Continue your preparation after completing Gravitation with these additional study resources.

Practice Resources

Resource	Access
Chapter Mock Test Paper
Chapter Mock Test Solutions

Gravitation: Download Important IIT JEE & NEET Questions

Gravitation is a fundamental force of nature that governs the motion of objects throughout the universe. It is the attractive force that draws two bodies toward one another, resulting in a pull that depends on their masses and the distance separating them. This force not only keeps us anchored to the Earth but also plays a vital role in the movement of celestial bodies, such as planets, moons, and stars.

The understanding of gravitation has significantly evolved over the centuries. In the late 17th century, Sir Isaac Newton was among the first to mathematically describe this force through his Universal Law of Gravitation.

1.0Newton Law of Gravitation

Gravitation is the property of matter due to which two bodies always attract each other.
It states that every particle in the universe attracts all other particles with a force which is directly commensurate to the product of their masses and is inversely commensurate to the square of the distance between them.
This formula is given for point masses. For spherical objects (planets), the distance between centres is taken.

$F_{g} = G \frac{m _{1} m _{2}}{r ^{2}}$

G=universal Gravitational Constant,Its value is the same throughout the universe; G independent of the nature and size of the bodies; it does not depend even upon the nature of the medium between the bodies.
Value of G in $SI = 6.67 \times 1 0^{- 11} Nm^{2} kg^{- 2} or CG.S = 6.67 \times 1 0^{- 8} dyne cm^{2} g^{- 2}$
Dimension of $G = [M^{- 1} L^{3} T^{- 2}]$
Forces due to Multiple Particles is given as, $F_{n e t} = F_{1} + F_{2} + F_{3} + \dots\dots$

Law of Gravitation in Vector Form

$F_{12} = - G \frac{m _{1} m _{2}}{r ^{2}} \overset{r}{^}$

Related Video:

1.0Gravitational Field

It is the region around a mass where its gravitational effects can be observed. The gravitational field due to a body extends till infinity.
Strength of the gravitational field decreases on moving away from a body.

(i) In an infinite gravitational field, the acceleration is zero.

(ii) Gravitational field ∝ mass

Gravitational field is conservative in nature.
There are two ways to measure the strength of the gravitational field.

(i) Gravitational field intensity.

(ii) Gravitational potential

Gravitational Field Intensity

It is defined as gravitational force exerted on a unit mass positioned in a gravitational field.
It is a vector quantity.Its direction is same as that of gravitational force.
$I = \frac{F}{m} \Rightarrow Unit - N / K g$
Dimensional Formula $- [M^{0} L^{1} T^{- 2}]$
Gravitational Field Intensity owed to a point mass,is given as,

$I = \frac{GM}{r ^{2}} (- \overset{r}{^})$

Negative sign indicates that the force due to the gravitational field is attractive in nature.
Gravitational Field Intensity due to multiple particles,

$I_{n e t} = I_{1} + I_{2} + I_{3} + \dots\dots\dots\dots\dots$

A. Solid Sphere

Outside the Sphere (r>R)

$I_{out} = \frac{GM}{r ^{2}} (- \overset{r}{^})$

At the Surface (r=R)

$I_{surface} = \frac{GM}{R ^{2}} (- r)$

Inside the Sphere (r<R)

$I_{in} = \frac{GM r}{r ^{3}} (- \overset{r}{^})$

Graph between $I$ and r for a solid sphere

B. Hollow Sphere

Outside the Shell (r>R)

$I_{out} = \frac{GM}{r ^{2}} (- \overset{r}{^})$

At the Surface (r=R)

$I_{surface} = \frac{GM}{R ^{2}} (- \overset{r}{^})$

Inside the Shell (r<R) I=0

Graph between $I$ and r for Hollow sphere

2.0Acceleration Due to Gravity

If a body is placed inside a gravitational field having intensity I, gravitational force applied on it is, F=m I
Earth also pulls every object towards its center with force F=mg

On comparing both the equations we get $g = ∣ I ∣$

Where g = acceleration due to gravity I is intensity of gravitational field due to Earth.

Assuming Earth to be a Solid Sphere

$g_{s} = \frac{GM}{R _{e}^{2}} \Rightarrow 9.81 m / s^{2}$ , Same formula can be used to find acceleration due to gravity at the surface of any planet.

In terms of density $(ρ) : g = \frac{GM}{R ^{2}}$

$mass = density \times Volume$

$M = ρ \times \frac{4}{3} π R^{3}$

$g = \frac{G ( \frac{4}{3} π R ^{3} )}{R ^{2}} = \frac{4}{3} π GRρ$

Variation in acceleration due to gravity with height

$g_{h} = g [1 - \frac{2 h}{R _{e}}]$ , This formula is valid if h is upto 5% of earth's radius (320 km from earth's surface)

If h is greater than 5% earth's radius we use, $g_{h} = \frac{G M _{e}}{( R _{e} + h ) ^{2}}$

Variation in acceleration due to gravity with depth

$g_{d} = g_{s} (1 - \frac{d}{R})$ , For any depth below Earth's Surface

Note:

Valid for small or large depth.
Fractional change in value of $g \to \frac{Δ g}{g} = \frac{d}{R}$
At any depth, $g_{d} < g_{s}$
Another form that can be used $g_{d} = \frac{GM}{R ^{3}} r \to g_{d} = g_{s} \frac{r}{R}$

Graph

For (r<R)

$g = \frac{GM}{R ^{3}} r \to g = g_{s} \frac{r}{R}$

For $(r \geq R)$

$g = \frac{GM}{r ^{2}} \to g = g_{s} \frac{R ^{2}}{r ^{2}}$

Value of g is maximum at Earth's surface

Variation in value of 'g' due to rotation of earth

$N = M g_{e ff} = M g - M ω^{2} R_{e} Cos^{2} λ$ , As one moves towards pole, apparent weight increases

$λ : Angle of Latitude$

$For Poles λ = 9 0^{\circ}$

$For Equator λ = 0^{\circ}$

$g =$ acceleration due to gravity without considering rotation of Earth

$g_{eff} =$ acceleration due to gravity considering rotation of Earth

Variation in value of "g" due to shape of Earth

$Δ g = g_{e} - g_{p} \approx 0.02 m / s^{2}$ , Earth is not a perfect sphere

$g_{surface} = \frac{GM}{R ^{2}}$

$g_{p} > g_{eq’}$ (as surface is close to center of Earth near pole as compared to equator )

3.0Gravitational Potential

It is defined as amount of work done by external agent against gravitational pull in conveying a unit mass from infinity to that point without changing its kinetic energy

$V_{P} = \frac{W _{\infty \to p}}{m}$

Motion of unit mass is considered slowly, so that no energy is spent to change the kinetic energy of the system.
At infinity, Gravitational Potential is assumed to be ZERO.

Also Read : Difference Between Mass and Weight

Gravitational Potential Due To a Point Mass:

$V = \frac{W _{e x t}}{m} = - \frac{GM}{r}$ (Negative sign in potential indicates attractive nature of force. )

Relation between Potential and Intensity

$I = - \frac{d V}{d r}$

If V is constant in a region, I = 0
This relation is valid for all conservative fields.

Standard results to remember:

Spherical shell (M, R)

Case 1. Outside the Shell $(r > R), V_{out} = - \frac{GM}{r}$

Case 2. On the Surface $(r = R), V_{Surface} = - \frac{GM}{R}$

Case 3. Inside the Shell $(r < R), V_{I n} = - \frac{GM}{R}$ , (Potential is same everywhere and is equal to its value at the surface.)

Solid sphere(M, R)

Case 1. Outside the Sphere $(r > R), V_{out} = - \frac{GM}{r}$

Case 2. On the Surface $(r = R), V_{Surface} = - \frac{GM}{R}$

Case 3. Inside the Sphere $(r < R), V_{I n} = - \frac{GM}{2 R ^{3}} (3 R^{2} - r^{2})$ , (Potential is same everywhere and is equal to its value at the surface.)

4.0Gravitational Potential Energy

The gravitational potential energy of a particle situated at a point in some gravitational field is defined as the amount of work required to bring it from infinity to that point without changing its kinetic energy.

$U = - G \frac{m _{1} m _{2}}{r}$ , negative sign shows the boundedness of the two bodies

It is a scalar quantity.
It's SI unit is joule and Dimensions are [M¹L²T^–2]
The gravitational potential energy of a particle of mass 'm' placed on the surface of earth of mass 'M' , radius 'R' is given by : $U = - G \frac{m _{1} m _{2}}{R}$

Gravitational Potential Energy for Three Particle System

If there are more than two particles in a system, then the net gravitational potential energy of the whole system is the sum of gravitational potential energies of all the possible pairs in that system.

$U_{System} = (G \frac{m _{1} m _{2}}{r _{1}}) + (G \frac{m _{2} m _{3}}{r _{2}}) + (G \frac{m _{1} m _{3}}{r _{3}})$

$= - G \frac{m _{1} m _{2}}{r _{1}} - G \frac{m _{2} m _{3}}{r _{2}} - G \frac{m _{1} m _{3}}{r _{3}}$

If Gravitational Potential at a point P is V_P
Then GPE of a particle of mass m placed at P is :U_P = m(V_P)

Note: At infinity, $V_{\infty} = 0 \Rightarrow U_{\infty} = 0$

5.0Escape Velocity

It is the minimum velocity required for an object located at the planet's surface so that it just escapes the planet's gravitational field

$V_{e} = \frac{2 GM}{R _{e}}$

$V_{e} = 2 g_{s} R_{e} = 11.2 km / s . R_{e} = 6400 km$

Escape speed depends on :

Mass (M), radius (R) of the planet
Position from where the particle is projected.

Escape speed does not depend on :

Mass (m) of the body which is projected
Angle of projection.
If a body is thrown from the Earth's surface with escape speed, it goes out of earth's gravitational field and never returns back to the earth's surface.

Escape velocity from a point other than surface

1. Total energy is zero at any point when particle start moving with escape velocity,T E=0

2. If given point is at distance r (>R) from center of Earth, $P E_{Out} = - \frac{G M _{e} m}{r}$

3. If given point is at distance r (<R) from the center of Earth, $P E_{I n} = - \frac{GM ( 3 R ^{2} - r ^{2} )}{2 R ^{3}} \times m$

6.0Escape Energy-Binding Energy

Minimum energy given to a particle in the form of kinetic energy so that it can just escape the Earth's gravitational field.
Magnitude of escape energy = $G \frac{M m}{R}$
(–ve of PE on the Earth's surface)
Escape energy = Kinetic Energy corresponding to the escape velocity

$G \frac{M m}{R} = \frac{1}{2} m v_{e}^{2}$

KE < Escape Energy v_o < v_e Body returns to Earth surface
KE = Escape Energy v_o = v_e Body comes to rest at infinity
KE > Escape Energy v_o > v_e Body has residual velocity at infinity

Binding energy:

Total energy of a particle near Earth.

BE < 0 Particles cannot escape the gravitational field of Earth.
BE ≥ 0 Particles can escape the gravitational field of Earth.

7.0Kepler’s Law

Kepler's $1^{s t}$ Law: Each planet moves in an elliptical revolution, with the sun at one focus of the ellipse.

Kepler's $2^{n d}$ Law: A line joining any planet to the Sun glides out equal areas in equal intervals of time, i.e. the areal velocity of the planet remains constant.

Kepler's $3^{r d}$ Law: The square of the period of revolution of any planet around the Sun is directly relationall to the cube of the semi-major axis of its elliptical orbit.

$T^{2} \propto a^{3}$

a : average distance of the planet from Sun

$a = \frac{r _{m a x} + r _{m i n}}{2}$

8.0Satellite Motion

A light body revolving around a heavier planet due to gravitational attraction, is called a satellite. Moon is a natural satellite of Earth.

Essential conditions for satellite motion:

The centre of the satellite's orbit should coincide with the centre of Earth
Plane of the orbit of the satellite should pass through the centre of Earth.

It follows that a satellite can revolve around the earth only in those circular orbits whose centres coincide with the centre of earth. Circles drawn on a globe with centres coincident with earth are known as 'great circles'. Therefore, a satellite revolves around the earth along circles concentric with great circles.

Also Read : Earth Satellites

9.0Orbital Velocity (V_o)

$V_{o} = \frac{G M _{e}}{R _{e}} \approx 8.1 km / s$

Time period of orbital motion:

$T = 2 π \frac{R _{e}^{3}}{G M _{e}} \approx 84 min$

Satellite motion - Energy Analysis

1.Kinetic energy of satellite

$K E = \frac{G M _{e} m}{2 r}$

2.Potential energy of satellite

$PE = - \frac{G M _{e} m}{r}$

Total Energy = Kinetic Energy + Potential Energy

$TE = - \frac{G M _{e} m}{2 r}$

$K E = - TE = - \frac{PE}{2} = - \frac{G M _{e} m}{2 r}$

As total energy of a satellite is negative, it is called as bounded system

Also Read : Kepler's Law of Planetary Motion

10.0Binding Energy

Minimum energy required to break a bounded system.
$BE + TE = 0 \Rightarrow BE = - TE$
$BE = ∣ TE ∣ \Rightarrow BE = \frac{G M _{e} m}{2 r}$

Note:

$TE = - \frac{G M _{e} m}{2 r}$
$PE = - \frac{G M _{e} m}{r}$
$K E = \frac{G M _{e} m}{2 r}$
$V_{0} = \frac{G M _{e}}{r}$

$\Rightarrow T \propto R^{3/2}$

So, If the radius of the orbit of the satellite is increased,

KE will decrease, TE will increase, PE will increase, Orbital velocity will decrease, and Time period will increase.

11.0Work Done to Shift Orbit of Satellite

$W_{E x t} = Δ TE$

$w_{E x t} = \frac{G M _{ε} m}{2} (\frac{1}{r _{1}} - \frac{1}{r _{2}})$

Essential conditions for satellite motion

The Center of the satellite's orbit coincides with the center of Earth.
Plane of orbit of the satellite is passing through the center of Earth.

There are two stable orbits for a satellite

Equatorial orbit
Polar orbit

Any satellite is projected as near to the equator as possible as-

g is minimum near the equator, less fuel
Easier to set the satellite in any orbit

12.0Polar Satellite

It rotates in the Polar plane.

Its height from Earth's surface is 500 km ~ 600 km.
Its time period is 100 min.
Used for weather data collection

Note: Any satellite is said to be in a condition of freely falling on Earth. (as the only force acting on it is the force of gravity). Hence, the apparent weight of any object in a satellite is always ZERO.

Related Video:

Also Read:

Escape Velocity	Gravitational Potential Energy	Potential Energy
Kepler's Law of Planetary Motion	Acceleration Due To Gravity	Kinetic Energy
Vectors in Physics	Centre of Mass And Collision	Elastic Collision

1.0Learning Outcomes

After studying these revision notes, you will be able to:

Apply Newton's Universal Law of Gravitation to solve numerical problems.
Calculate gravitational force between two bodies.
Understand gravitational field intensity and gravitational potential.
Determine the variation of acceleration due to gravity with height and depth.
Solve problems involving escape velocity and orbital velocity.
Apply Kepler's Laws of Planetary Motion.
Analyze the motion of artificial satellites.
Strengthen concepts used in advanced mechanics and astronomy-related questions.

2.05-Minute Quick Revision

If you have only 5 minutes before your exam, revise these important concepts and formulas.

Must-Revise Concepts

Universal Law of Gravitation
Gravitational Constant (G)
Gravitational Field
Gravitational Potential
Potential Energy
Acceleration Due to Gravity
Variation of g with Height
Variation of g with Depth
Escape Velocity
Orbital Velocity
Geostationary Satellites
Kepler's Laws of Planetary Motion

Important Formula Recall

Quickly revise these formulas before solving numerical questions:

Newton's Law of Gravitation
Gravitational Field Intensity
Gravitational Potential
Potential Energy
Acceleration Due to Gravity
Escape Velocity
Orbital Velocity
Time Period of Satellite
Kepler's Third Law
Relation Between Orbital Speed and Radius

3.0High Weightage Topics

Topic	Focus Area
Universal Law of Gravitation	Numerical Problems
Gravitational Field & Potential	Conceptual Questions
Variation of g	Formula-Based Questions
Escape Velocity	JEE Numerical Problems
Orbital Velocity	Satellite Motion
Kepler's Laws	Conceptual Applications
Artificial Satellites	Mixed Numerical Problems
Energy of Satellites	Advanced JEE Questions

4.0Formula Handbook

The following formulas are essential for solving numerical and conceptual questions from Gravitation in JEE Main, JEE Advanced, NEET, and CBSE examinations.

5.0Common Mistakes & JEE Tips

Gravitation is a formula-rich chapter, but most mistakes occur because students confuse similar formulas or use the wrong radius in calculations.

Common Mistake	Correct Approach
Using Earth's radius instead of orbital radius	For satellites, always use the distance from Earth's centre.
Confusing escape velocity with orbital velocity	Escape velocity is (\sqrt{2}) times the orbital velocity at the same point.
Ignoring negative signs in potential energy	Gravitational potential and potential energy are always negative (taking infinity as reference).
Mixing mass and weight	Weight depends on (g), whereas mass remains constant.
Applying the wrong formula for variation of (g)	Use separate formulas for height and depth.
Forgetting units of the gravitational constant	Revise the SI unit and dimensions of (G).
Confusing gravitational field with gravitational potential	Field is a vector quantity, while potential is a scalar quantity.
Using Kepler's laws without understanding assumptions	Remember that Kepler's laws apply to planetary motion under gravitational force.

6.0ALLEN Faculty Tips

Memorize all satellite-related formulas together for quick revision.
Learn the derivation of escape velocity to strengthen conceptual understanding.
Practice questions on the variation of (g) with height and depth.
Understand the relationship between orbital velocity, escape velocity, and total energy.
Draw neat diagrams while solving satellite motion problems.
Revise Kepler's Laws along with their practical applications.
Solve Previous Years' Questions to improve accuracy in formula-based problems.
Keep a separate formula sheet for gravitation as many expressions look similar.

7.0PYQ Trend Analysis

Gravitation is a consistently scoring chapter in JEE Main and JEE Advanced. Questions are commonly asked from satellite motion, escape velocity, gravitational potential, and Kepler's Laws.

Note: The trend below is based on the analysis of previous years' JEE Main and JEE Advanced question papers. The exact number of questions may vary each year.

Concept	Questions Asked (Last 5 Years)	Average Difficulty
Universal Law of Gravitation	2–3	Easy
Gravitational Field & Potential	2–3	Moderate
Variation of (g)	2–3	Easy–Moderate
Escape Velocity	3–4	Moderate
Orbital Motion & Satellites	4–5	Moderate
Kepler's Laws	2–3	Moderate

Most Common Question Types

Numerical problems based on Newton's Universal Law of Gravitation.
Escape velocity and orbital velocity calculations.
Variation of acceleration due to gravity with height and depth.
Energy of artificial satellites.
Conceptual questions based on Kepler's Laws.
Gravitational field and potential comparison questions.
Assertion–Reason and statement-based conceptual MCQs.

8.0Smart Revision Strategy

Revise this chapter in the following sequence for maximum retention:

Universal Law of Gravitation
Gravitational Field and Potential
Variation of (g)
Escape Velocity
Orbital Velocity
Artificial Satellites
Kepler's Laws
Formula Revision
PYQs from JEE Main & Advanced
Mixed Numerical Practice

Test your Knowledge

question 1 of 5

According to Newton’s law of universal gravitation, the gravitational force between two bodies is proportional to:

Frequently Asked Questions

Which Gravitation topic is the most scoring in JEE?

How can I remember the difference between orbital and escape velocity?

Are Kepler's Laws important for competitive exams?

What is the biggest mistake students make in Gravitation?

Which chapter should I revise along with Gravitation?

Join ALLEN!

Class 11 Physics Chapter 7: Gravitation

1.0Chapter Snapshot

2.0Chapter 7 Smart Study Material by ALLEN Experts: Download PDFs

Practice Resources

Test your Knowledge

question 1 of 5

According to Newton’s law of universal gravitation, the gravitational force between two bodies is proportional to:

Gravitation: Download Important IIT JEE & NEET Questions

1.0Newton Law of Gravitation

1.0Learning Outcomes

2.05-Minute Quick Revision

Must-Revise Concepts

3.0High Weightage Topics

4.0Formula Handbook

5.0Common Mistakes & JEE Tips

6.0ALLEN Faculty Tips

7.0PYQ Trend Analysis

Most Common Question Types

8.0Smart Revision Strategy

Frequently Asked Questions

Which Gravitation topic is the most scoring in JEE?

How can I remember the difference between orbital and escape velocity?

Are Kepler's Laws important for competitive exams?

What is the biggest mistake students make in Gravitation?

Which chapter should I revise along with Gravitation?

Join ALLEN!

Class 11 Physics Chapter 7: Gravitation

1.0Chapter Snapshot

2.0Chapter 7 Smart Study Material by ALLEN Experts: Download PDFs

Practice Resources

Gravitation: Download Important IIT JEE & NEET Questions

1.0Newton Law of Gravitation

1.0Learning Outcomes

2.05-Minute Quick Revision

Must-Revise Concepts

3.0High Weightage Topics

4.0Formula Handbook

5.0Common Mistakes & JEE Tips

6.0ALLEN Faculty Tips

7.0PYQ Trend Analysis

Most Common Question Types

8.0Smart Revision Strategy