Last Updated: June 1, 2026

📋 Table of Contents
What is Gravitation Revision Notes?
Introduction
1. Newton's Law of Universal Gravitation
2. Derivation Master-Sheet: Variations n 'g'
3. Gravitational Potential Energy (U)
4. Escape Velocity (v_e)
5. Kepler’s Laws of Planetary Motion
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics
🪤 The 5 Mistakes That Cost Marks
🔁 Last 5 Minutes Box

📋 Table of Contents

What is Gravitation Revision Notes?
Introduction
1. Newton's Law of Universal Gravitation
2. Derivation Master-Sheet: Variations n 'g'
- I. Variation with Altitude (h)
- II. Variation with Depth (d)
3. Gravitational Potential Energy (U)
4. Escape Velocity (v_e)
5. Kepler’s Laws of Planetary Motion
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Gravitation Class 11 Physics Revision — JEE & MEET 2026 Grandmaster Guide

What is Gravitation Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Newton's Law: F = G m1 m2 / r². G = 6.67 × 10⁻¹¹ N m²/kg².

Gravity (g): g = GM/R². Variation: Deep g' = g(1 - h/R); Height g' = g(1 - 2h/R).

Kepler's 3rd Law: T² ∝ r³. (T²/r³ = Constant).

Escape Velocity: v_e = √(2GM/R) = √(2gR). For Earth, v_e ≈ 11.2 km/s.

Orbital Velocity: v_o = √(GM/r). V_e = √2 v_o. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

Gravitation is the universal force of attraction that binds the universe together. From the simple falling of an apple observed y Newton to the complex orbital dance of the planets described y Kepler, gravitation is the invisible thread of cosmic order. In this "Comprehensive" guide, we provide a mathematically rigorous expansion of Chapter 7, featuring formal derivations for the variation of 'g', gravitational potential energy, n the physics of satellites—providing the depth required for high-stakes exams like JEE n meet.

1. Newton's Law of Universal Gravitation

Every particle and the universe attract every other particle with a force that is:

Directly proportional to the product of their masses (m1 m2).
Inversely proportional to the square of the distance between them (r²).

Formula: F = G (m1 m2) / r²

G (Gravitational Constant): 6.67 × 10⁻¹¹ N m²/kg².
Dimensions: [M⁻¹ L³ T⁻²].

2. Derivation Master-Sheet: Variations n 'g'

The acceleration due to gravity (g = GM/R²) is not a constant; it varies with altitude and depth.

I. Variation with Altitude (h)

Let g be the acceleration at surface n GH at height h.

GH = GM / (R + h)²
GH = (GM/R²) · [R² / (R + h)²] = g [1 + h/R]⁻²
For h ≪ R, using Binomial Expansion:
- GH = g (1 - 2h/R). (Proven)

II. Variation with Depth (d)

Let Gd be acceleration at depth d.

Mass of Earth interior to depth d is M' = M [(R-d)/R]³.
Gd = G M' / (R-d)² = G M (R-d) / R³
Gd = (GM/R²) · [(R-d)/R]
Gd = g (1 - d/R). (Proven) Conclusion: Gravity decreases whether you go up into the sky or down into a mine.

3. Gravitational Potential Energy (U)

Derivation: The work done and bringing a mass m from infinity to a point r.

DW = F dr = (Mm / r²) dr.
Integrating from ∞ to r:
- U = ∫ [∞ to r] (Mm / r²) dr
- U = Mm [-1/r]∞ʳ
- U = -Mm / r. (Proven) Note: The negative sign indicates that the force is attractive, n the system is bound.

4. Escape Velocity (v_e)

The minimum velocity required for an object to break free from Earth's gravitational pull. Derivation:

Using Conservation of Energy: Total Energy at Surface = Total Energy at Infinity.
(1/2 MV_e²) + (-Mm/R) = 0 + 0. (At infinity, both K and U are zero).
1/2 MV_e² = Mm / R.
v_e = √(2GM/R) = √(2gR). Earth Value: v_e ≈ 11.2 km/s.

5. Kepler’s Laws of Planetary Motion

Law of Orbits: Planets move and elliptical orbits with the Sun at one focus.
Law of Areas: A line joining a planet and the Sun sweeps out equal areas and equal intervals of time. (Proves Conservation of Angular Momentum).
Law of Periods (T² ∝ R³): Derivation for Circular Orbits:
- Centripetal Force = Gravitational Force
- MV² / R = Mm / R² => v² = GM / R.
- Since v = 2πR / T:
- (4π²R² / T²) = GM / R
- T² = (4π²/GM) R³. (Proven)

Comprehensive Exam Strategy (Q&A)

Q1: Where is the weight of a body zero? Answer:

At the Centre of the Earth (where d = R, Gd = 0).
In a freely falling elevator (Effective g = 0).
During space travel at a point where the gravitational pulls of different celestial bodies cancel each other out.

Q2: Does the escape velocity depend on the mass of the object being launched? Answer: No. The formula v_e = √(2gR) only depends on the mass and radius of the planet. A feather and a rocket need the same initial velocity to escape Earth's gravity (ignoring air resistance).

Q3: Why is the Gravitational Potential always negative? Answer: By convention, potential at infinity is zero. Since gravity is an attractive force, work is done y the field as an object moves closer, decreasing its potential below zero.

Related Revision Notes

Chapter 6: Rotational motion (Angular Momentum)
Chapter 2: motion n a Straight Line (Free Fall)
Advanced Orbital Mechanics Simulator

Conclusion

Gravitation is the foundational law of the macro-universe. By understanding how gravity changes with position and how energy is stored and gravitational fields, we can unlock the secrets of satellite technology, space exploration, n the very structure of the cosmos. Master the derivations of 'g' n escape velocity—these are the equations that humanity used to reach the Moon and beyond. Stay grounded, but keep looking up!

Reference: NASA: Gravity and Orbits Guide

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

Continue your revision with these related guides:

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

📚 Related Topics

Continue your revision with these related guides:

🪤 The 5 Mistakes That Cost Marks

Forgetting to consider the sign of gravitational potential: Many students forget that gravitational potential can be negative, which can lead to incorrect calculations, especially when dealing with problems involving escape velocity or orbital energy.
Confusing gravitational field and gravitational potential: Some students fail to differentiate between gravitational field (a vector quantity) n gravitational potential (a scalar quantity), leading to incorrect applications of formulas and principles.
Incorrect application of the inverse square law: Students often mistakenly apply the inverse square law to gravitational potential instead of gravitational field, or vice versa, resulting and incorrect calculations and answers.
Not considering the reference level for gravitational potential: Many students forget to consider the reference level when calculating gravitational potential, which can lead to incorrect results, especially and problems involving changes and gravitational potential energy.
Forgetting to include the negative sign and the formula for gravitational potential energy: Some students forget to include the negative sign and the formula for gravitational potential energy (U = -Mm/r), leading to incorrect calculations and answers, especially and problems involving energy conservation.

🔁 Last 5 Minutes Box

Gravitational Force: F = G * (m1 * m2) / r^2, where G = 6.67 * 10^-11 N’m^2/kg^2

🎬 Watch: Visual Explanation

📺 Gravitation Class 11 One Shot Revision | Short Notes | Mind Maps — by eSaral NEET

Last Updated: June 1, 2026

📋 Table of Contents
What is Gravitation Revision Notes?
Introduction
1. Newton's Law of Universal Gravitation
2. Derivation Master-Sheet: Variations n 'g'
3. Gravitational Potential Energy (U)
4. Escape Velocity (v_e)
5. Kepler’s Laws of Planetary Motion
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics
🪤 The 5 Mistakes That Cost Marks
🔁 Last 5 Minutes Box

📋 Table of Contents

What is Gravitation Revision Notes?
Introduction
1. Newton's Law of Universal Gravitation
2. Derivation Master-Sheet: Variations n 'g'
- I. Variation with Altitude (h)
- II. Variation with Depth (d)
3. Gravitational Potential Energy (U)
4. Escape Velocity (v_e)
5. Kepler’s Laws of Planetary Motion
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Gravitation Class 11 Physics Revision — JEE & MEET 2026 Grandmaster Guide

What is Gravitation Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Newton's Law: F = G m1 m2 / r². G = 6.67 × 10⁻¹¹ N m²/kg².

Gravity (g): g = GM/R². Variation: Deep g' = g(1 - h/R); Height g' = g(1 - 2h/R).

Kepler's 3rd Law: T² ∝ r³. (T²/r³ = Constant).

Escape Velocity: v_e = √(2GM/R) = √(2gR). For Earth, v_e ≈ 11.2 km/s.

Orbital Velocity: v_o = √(GM/r). V_e = √2 v_o. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

1. Newton's Law of Universal Gravitation

Every particle and the universe attract every other particle with a force that is:

Directly proportional to the product of their masses (m1 m2).
Inversely proportional to the square of the distance between them (r²).

Formula: F = G (m1 m2) / r²

G (Gravitational Constant): 6.67 × 10⁻¹¹ N m²/kg².
Dimensions: [M⁻¹ L³ T⁻²].

2. Derivation Master-Sheet: Variations n 'g'

The acceleration due to gravity (g = GM/R²) is not a constant; it varies with altitude and depth.

I. Variation with Altitude (h)

Let g be the acceleration at surface n GH at height h.

GH = GM / (R + h)²
GH = (GM/R²) · [R² / (R + h)²] = g [1 + h/R]⁻²
For h ≪ R, using Binomial Expansion:
- GH = g (1 - 2h/R). (Proven)

II. Variation with Depth (d)

Let Gd be acceleration at depth d.

Mass of Earth interior to depth d is M' = M [(R-d)/R]³.
Gd = G M' / (R-d)² = G M (R-d) / R³
Gd = (GM/R²) · [(R-d)/R]
Gd = g (1 - d/R). (Proven) Conclusion: Gravity decreases whether you go up into the sky or down into a mine.

3. Gravitational Potential Energy (U)

Derivation: The work done and bringing a mass m from infinity to a point r.

DW = F dr = (Mm / r²) dr.
Integrating from ∞ to r:
- U = ∫ [∞ to r] (Mm / r²) dr
- U = Mm [-1/r]∞ʳ
- U = -Mm / r. (Proven) Note: The negative sign indicates that the force is attractive, n the system is bound.

4. Escape Velocity (v_e)

The minimum velocity required for an object to break free from Earth's gravitational pull. Derivation:

Using Conservation of Energy: Total Energy at Surface = Total Energy at Infinity.
(1/2 MV_e²) + (-Mm/R) = 0 + 0. (At infinity, both K and U are zero).
1/2 MV_e² = Mm / R.
v_e = √(2GM/R) = √(2gR). Earth Value: v_e ≈ 11.2 km/s.

5. Kepler’s Laws of Planetary Motion

Law of Orbits: Planets move and elliptical orbits with the Sun at one focus.
Law of Areas: A line joining a planet and the Sun sweeps out equal areas and equal intervals of time. (Proves Conservation of Angular Momentum).
Law of Periods (T² ∝ R³): Derivation for Circular Orbits:
- Centripetal Force = Gravitational Force
- MV² / R = Mm / R² => v² = GM / R.
- Since v = 2πR / T:
- (4π²R² / T²) = GM / R
- T² = (4π²/GM) R³. (Proven)

Comprehensive Exam Strategy (Q&A)

Q1: Where is the weight of a body zero? Answer:

At the Centre of the Earth (where d = R, Gd = 0).
In a freely falling elevator (Effective g = 0).
During space travel at a point where the gravitational pulls of different celestial bodies cancel each other out.

Related Revision Notes

Chapter 6: Rotational motion (Angular Momentum)
Chapter 2: motion n a Straight Line (Free Fall)
Advanced Orbital Mechanics Simulator

Conclusion

Reference: NASA: Gravity and Orbits Guide

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

Continue your revision with these related guides:

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

📚 Related Topics

Continue your revision with these related guides:

🪤 The 5 Mistakes That Cost Marks

Forgetting to consider the sign of gravitational potential: Many students forget that gravitational potential can be negative, which can lead to incorrect calculations, especially when dealing with problems involving escape velocity or orbital energy.
Confusing gravitational field and gravitational potential: Some students fail to differentiate between gravitational field (a vector quantity) n gravitational potential (a scalar quantity), leading to incorrect applications of formulas and principles.
Incorrect application of the inverse square law: Students often mistakenly apply the inverse square law to gravitational potential instead of gravitational field, or vice versa, resulting and incorrect calculations and answers.
Not considering the reference level for gravitational potential: Many students forget to consider the reference level when calculating gravitational potential, which can lead to incorrect results, especially and problems involving changes and gravitational potential energy.
Forgetting to include the negative sign and the formula for gravitational potential energy: Some students forget to include the negative sign and the formula for gravitational potential energy (U = -Mm/r), leading to incorrect calculations and answers, especially and problems involving energy conservation.

🔁 Last 5 Minutes Box

Gravitational Force: F = G * (m1 * m2) / r^2, where G = 6.67 * 10^-11 N’m^2/kg^2

🎬 Watch: Visual Explanation

📺 Gravitation Class 11 One Shot Revision | Short Notes | Mind Maps — by eSaral NEET