Gravitation
Gravitation is the force of attraction between any two masses in the universe. It is the reason objects fall to the ground, the Moon orbits Earth, and planets orbit the Sun. Understanding gravitation is key to mastering classical mechanics.
This guide covers Newton's Universal Law of Gravitation, the gravitational force formula, weight vs. mass, free fall, and the inverse square law — with clear explanations, worked examples, memory aids, and a practice quiz.
1What Is Gravitation?
Gravitation is the universal force of attraction that acts between any two objects that have mass. Every object in the universe — from tiny atoms to giant stars — exerts a gravitational pull on every other object.
Drop a ball from your hand. It falls straight down toward the ground. Why? Because Earth's enormous mass pulls the ball toward its centre. That invisible pull is gravity — and it works the same way between the Earth and the Moon, the Sun and the planets, and even between you and your desk.
Gravitational Attraction
Why Gravitation Matters
Gravitation is responsible for many everyday and cosmic phenomena:
- Objects falling toward the ground
- The Moon orbiting Earth
- Earth and other planets orbiting the Sun
- Ocean tides caused by the Moon's pull
- Satellites staying in orbit
- The shape and structure of galaxies
Key idea: Gravity is not just something that happens "on Earth." It is a universal force that acts between all masses, everywhere in the universe.
2Key Definitions
Gravitational Force
The attractive force that exists between any two objects with mass. It is always attractive and never repulsive.
Universal Law of Gravitation
Newton's law stating that every object attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravitational Constant (G)
The universal constant in Newton's law of gravitation: G = 6.67 × 10⁻¹¹ N·m²/kg². Its value is the same everywhere in the universe.
Acceleration due to Gravity (g)
The acceleration experienced by an object in free fall near Earth's surface. g ≈ 9.8 m/s². It varies slightly with altitude and latitude.
Mass
The amount of matter in an object, measured in kilograms (kg). Mass is a scalar quantity and remains constant regardless of location.
Weight (W = mg)
The gravitational force acting on an object, measured in Newtons (N). Weight changes with location because g varies.
Free Fall
The motion of an object under the influence of gravitational force alone, with no other forces acting on it. In free fall, all objects accelerate at the same rate regardless of mass (ignoring air resistance).
3Understanding Gravitation
Simple Explanation
Gravity pulls objects toward each other. The bigger the objects, the stronger the pull. Drop a ball and it falls because Earth's gravity pulls it downward. You don't float away because Earth's mass is enormous and you are close to its surface.
Deeper Explanation: Newton's Universal Law
Newton discovered that every object in the universe attracts every other object. The gravitational force between two objects depends on two things:
Masses (m₁ and m₂)
Force is directly proportional to the product of the two masses. More mass = stronger pull.
Distance (r)
Force is inversely proportional to the square of the distance. Greater distance = much weaker pull.
This is the inverse square law: if you double the distance between two objects, the gravitational force becomes one-quarter (not one-half) of what it was. Triple the distance, and the force drops to one-ninth.
Interactive: Inverse Square Law
Drag either ball closer or farther to see how gravitational force changes.
Force
6.04e-7
Newtons
F = G(m1m2) / r²
= 6.67×10⁻¹¹ × 1000×500 / 7.4²
Newton's law explains not only why apples fall from trees, but also why the Moon orbits Earth, why planets orbit the Sun, and why tides rise and fall. The same formula governs them all.
Weight vs. Mass
Mass is how much matter an object contains — it stays the same whether you are on Earth, the Moon, or in deep space. Weight is the gravitational force on that mass: W = mg. Since g is different on the Moon (~1.6 m/s²) than on Earth (~9.8 m/s²), your weight changes even though your mass doesn't.
On Earth
g = 9.8 m/s²
60 kg → 588 N
W = 60 × 9.8
On the Moon
g = 1.6 m/s²
60 kg → 96 N
W = 60 × 1.6
Same mass, different weight — your weight depends on local gravity
"Gravity is the glue of the universe — it holds planets in orbit, keeps your feet on the ground, and shapes the cosmos."
4Important Formulae
These two formulae are the foundation of all gravitation problems. Master them and you can solve any question on this topic.
F = G(m₁m₂) / r²
Newton's Universal Law of Gravitation
F = gravitational force (N), G = 6.67 × 10⁻¹¹ N·m²/kg², m₁ and m₂ = masses (kg), r = distance between centres (m)
W = mg
Weight Formula
W = weight (N), m = mass (kg), g = acceleration due to gravity (9.8 m/s² on Earth)
Don't confuse G (gravitational constant, 6.67 × 10⁻¹¹) with g (acceleration due to gravity, 9.8 m/s²). G is universal and never changes. g depends on the planet and altitude.
5Worked Examples
Example 1: Calculating Weight on Earth
Find the weight of a 5 kg object on Earth's surface (g = 9.8 m/s²).
Given: m = 5 kg, g = 9.8 m/s²
Formula: W = mg
W = 5 × 9.8
W = 49 N
Example 2: Gravitational Force Between Two Masses
Calculate the gravitational force between two 50 kg students standing 2 metres apart.
Given: m₁ = 50 kg, m₂ = 50 kg, r = 2 m
G = 6.67 × 10⁻¹¹ N·m²/kg²
Formula: F = G(m₁m₂) / r²
F = 6.67 × 10⁻¹¹ × (50 × 50) / (2²)
F = 6.67 × 10⁻¹¹ × 2500 / 4
F = 6.67 × 10⁻¹¹ × 625
F = 4.17 × 10⁻⁸ N
This incredibly tiny force explains why we don't feel gravitational attraction to people around us.
Example 3: Inverse Square Law — Tripling Distance
The gravitational force between two objects is 36 N. What happens to the force if the distance between them is tripled?
Original force: F = 36 N
Distance is tripled: r → 3r
F ∝ 1/r², so new F ∝ 1/(3r)² = 1/9r²
New force = F / 9 = 36 / 9
New force = 4 N
Tripling the distance reduces the force to one-ninth of its original value.
Example 4: Mass vs. Weight on the Moon
A person has a mass of 60 kg. Find their weight on Earth (g = 9.8 m/s²) and on the Moon (g = 1.6 m/s²).
Mass on Earth = Mass on Moon = 60 kg (mass doesn't change)
Weight on Earth:
W = mg = 60 × 9.8
W = 588 N
Weight on Moon:
W = mg = 60 × 1.6
W = 96 N
Same person, same mass — but weight on the Moon is roughly one-sixth of weight on Earth because the Moon's gravity is weaker.
6Memory Aids
"Big Mass, Big Pull"
Gravitational force is directly proportional to mass. The greater the mass, the stronger the gravitational attraction.
"Double the distance, quarter the force"
Because force depends on 1/r², doubling distance means 1/(2²) = 1/4 the force. This is the inverse square law.
"FGM over r squared"
F = G(m₁m₂)/r². Say it aloud: "F equals G-M over r-squared." The rhythm helps you remember the structure of Newton's gravitational formula.
7Common Mistakes
Confusing mass and weight
Mass (kg) is the amount of matter and stays constant everywhere. Weight (N) is a force that depends on gravity. A 60 kg person weighs 588 N on Earth but only 96 N on the Moon. Never use kg for weight or N for mass.
Forgetting to square the distance
In F = G(m₁m₂)/r², the distance must be squared. Forgetting r² is one of the most common calculation errors. If the distance doubles, the force doesn't halve — it becomes one-quarter.
Using wrong units for G
The gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg². Its units are very specific. Make sure masses are in kg and distances are in metres before substituting into the formula, otherwise your answer will be completely wrong.
Thinking gravity only exists on Earth
Gravity is a universal force that acts between all masses everywhere in the universe. It is present on the Moon, on Mars, in deep space — everywhere. Astronauts appear "weightless" because they are in free fall, not because gravity is absent.
8Quick Revision Summary
- ✓Gravity is universal — every mass attracts every other mass in the universe.
- ✓F = G(m₁m₂)/r² — gravitational force depends on both masses and the distance between them.
- ✓Force increases with mass (directly proportional to the product of masses).
- ✓Force decreases with distance squared (inverse square law: double distance = quarter force).
- ✓W = mg — weight is the gravitational force on a mass; it changes with location.
- ✓g ≈ 9.8 m/s² on Earth's surface — this is the acceleration due to gravity.
- ✓G = 6.67 × 10⁻¹¹ N·m²/kg² — the universal gravitational constant (don't confuse G with g).
- ✓Mass ≠ Weight — mass is constant (kg); weight depends on local gravity (N).
Frequently Asked Questions
- What is the difference between mass and weight?
- Mass is the amount of matter in an object, measured in kilograms (kg), and remains constant everywhere. Weight is the gravitational force acting on that mass, measured in Newtons (N), and changes with location. Weight depends on the local gravitational field strength: W = mg.
- Why don't we feel gravitational attraction to other people?
- We do experience gravitational attraction to other people, but the force is incredibly tiny because our masses are small compared to Earth. Using F = G(m₁m₂)/r², the force between two 70 kg people standing 1 metre apart is only about 3.3 × 10⁻⁷ N — far too small to notice.
- Is gravity the same everywhere on Earth?
- No, g varies slightly across Earth's surface. It is stronger at the poles (where you are closer to Earth's centre) and weaker at the equator. It is also weaker at higher altitudes. The standard accepted value is 9.8 m/s².
- What happens to gravity in space?
- Gravity never reaches zero — it extends infinitely, though it weakens with distance. Astronauts appear weightless because they are in free fall, continuously falling around Earth in orbit. It is not because gravity is absent; rather, they and their spacecraft accelerate together under gravity.
- How does the Moon cause tides?
- The Moon's gravitational pull is stronger on the side of Earth nearest to it, creating a bulge of water (high tide). A second bulge occurs on the far side of Earth due to inertia — the water there is pulled less strongly than the solid Earth beneath it, so it "lags behind." As Earth rotates, coastlines move through these bulges, producing two high tides per day.
Practice Quiz
Test your understanding — select the correct answer for each question.
1.The gravitational force between two objects depends on:
2.What happens to gravitational force if the distance between two objects is doubled?
3.What is the value of g on Earth's surface?
4.Calculate the weight of a 2 kg mass on Earth.
5.Which statement about gravity is correct?
Final Study Advice
- 1.Always write down the formula before substituting values — this avoids silly mistakes.
- 2.Remember the difference between G (constant) and g (acceleration) — they are very different quantities.
- 3.Practice inverse square law questions — "what happens when distance doubles/triples?" questions appear frequently in exams.
- 4.Always check your units: mass in kg, distance in metres, force in Newtons.
- 5.Draw diagrams showing the two masses and the force arrows — visualising helps you set up problems correctly.