Physics notes · Chapter 3 of 11
Gravitation
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What is Gravitation? The Big Idea
- Gravitation: the attractive pull every object in the universe feels towards every other; it is always attractive, never repulsive, one of the most basic forces in nature.
- Gravitation acts between any two masses anywhere; gravity is the special pull of a large body (the Earth) on objects near it.
- One force explains a falling fruit, our weight, ocean tides, the Moon orbiting the Earth, planets orbiting the Sun, and satellites.
Check yourself
Define gravitation
The attractive pull every object in the universe feels towards every other object.
Is gravitation ever repulsive?
No — it is always attractive, never repulsive; one of the most basic forces in nature.
Gravitation vs gravity
Gravitation acts between any two masses anywhere; gravity is the special pull of a large body (Earth) on objects near it.
What does one single gravitational force explain?
A falling fruit, our weight, ocean tides, the Moon orbiting Earth, planets orbiting the Sun, and satellites.
History – How We Understood the Sky
- Ptolemy (around 150 AD): the geocentric model, Earth at the centre, later proved wrong.
- Copernicus (1543): the correct heliocentric model, Sun at the centre.
- Tycho Brahe recorded very accurate planetary positions over years, without a telescope; Kepler used his data to work out three laws of planetary motion.
- Astronomers and Their Models
| Scientist | Contribution |
|---|---|
| Ptolemy | Geocentric model (Earth at centre) |
| Copernicus | Heliocentric model (Sun at centre) |
| Tycho Brahe | Accurate planetary observations |
| Kepler | Three laws of planetary motion |
| Galileo | All objects fall at the same rate |
| Newton | Universal Law of Gravitation |
Check yourself
Ptolemy (around 150 AD)
Gave the geocentric model, placing the Earth at the centre — later proved wrong.
Nicolaus Copernicus (1543)
Gave the correct heliocentric model, with the Sun at the centre.
Tycho Brahe
Recorded extremely accurate positions of planets over years, all without a telescope.
Johannes Kepler
Used Brahe's data to work out three precise laws of planetary motion.
Kepler's Three Laws of Planetary Motion
- First law (orbits): every planet moves in an ellipse with the Sun at one focus, not at the centre.
- Second law (areas): the line from planet to Sun sweeps equal areas in equal times, so a planet moves faster near the Sun.
- Third law (periods): T² ∝ r³, the square of the orbital period is proportional to the cube of the average distance.
- Newton later showed all three follow from his law of gravitation.
- Kepler's Three Laws
| Law | Name | What it says |
|---|---|---|
| 1st | Orbits | Orbit is an ellipse, Sun at a focus |
| 2nd | Areas | Equal areas in equal times (faster when near) |
| 3rd | Periods | T² ∝ r³ |
Check yourself
Kepler's 1st Law (Law of Orbits)
Every planet moves around the Sun in an ellipse with the Sun at one focus, not the centre.
Kepler's 2nd Law (Law of Areas)
The line joining a planet to the Sun sweeps out equal areas in equal times — so a planet moves faster when near the Sun.
Kepler's 3rd Law (Law of Periods)
The square of the orbital period ∝ the cube of the average distance — T² ∝ r³.
Who unified Kepler's laws?
Newton later showed all three follow naturally from his law of gravitation.
Newton's Universal Law of Gravitation
- Every object attracts every other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
- F = G m₁m₂ / r², r measured centre to centre; for a sphere like the Earth the whole mass acts as if concentrated at the centre.
- Double a mass and the force doubles; double the distance and it drops to one-fourth.
Check yourself
State the law
Every object attracts every other with a force directly proportional to the product of their masses.
The inverse-square part
The force is inversely proportional to the square of the distance between their centres.
Write it in symbols
F = G m₁m₂ / r², where r is measured centre to centre.
Double a mass? Double the distance?
Double a mass → force doubles; double the distance → force drops to one-fourth.
For a sphere like Earth, where is r measured from?
The whole mass acts as if concentrated at the centre, so r is measured from the centre.
The Gravitational Constant G
- G, the universal gravitational constant, has the same value everywhere: G = 6.67 × 10⁻¹¹ N·m²/kg².
- G is so tiny that everyday gravity between objects is negligible; gravity is huge only between giant bodies such as planets and stars.
- Henry Cavendish (1798) first measured G, with a torsion balance.
- ⚠ Big G vs small g
| Quantity | G (big G) | g (small g) |
|---|---|---|
| Meaning | Gravitational constant | Acceleration due to gravity |
| Value | 6.67 × 10⁻¹¹ N·m²/kg² | 9.8 m/s² (Earth surface) |
| Varies? | Same everywhere | Changes with place |
Check yourself
What is G?
The universal gravitational constant — the same value everywhere in the universe; it never changes.
Value of G
G = 6.67 × 10⁻¹¹ N·m²/kg², an extremely small number.
Why is everyday gravity negligible?
Because G is so tiny — gravity is huge only between giant bodies like planets and stars.
Who first measured G, and how?
Henry Cavendish (1798), using a sensitive torsion balance.
Exam trap: G vs g
G = universal constant, same everywhere; g = acceleration due to gravity, which changes place to place.
Acceleration Due to Gravity (g)
- g: the acceleration of an object falling freely towards the Earth under gravity alone; g = 9.8 m/s² near the surface (often rounded to 10).
- g does not depend on the falling object's mass: the mass cancels out. g = GM / R², with M and R the Earth's mass and radius.
- Galileo: a heavy and a light stone dropped together in a vacuum fall side by side and land together.
Check yourself
Define g
The acceleration an object gains as it falls freely towards the Earth, caused purely by gravity.
Value of g near Earth's surface
g = 9.8 m/s² (often rounded to 10 for quick sums).
Does g depend on the falling object's mass?
No — the mass cancels out.
Relate g to G
g = G M / R², where M and R are Earth's mass and radius. (Newton)
Galileo's discovery
A heavy stone and a light stone dropped together in a vacuum fall side by side and land together.
How g Changes from Place to Place
- The Earth is flattened at the poles, so g is greatest at the poles and least at the equator.
- g decreases with altitude (r increases) and with depth, becoming zero at the Earth's centre.
- The Earth's spin reduces effective g most at the equator; if the Earth spun faster, weight at the equator would decrease.
- On the Moon g is about one-sixth of the Earth's, so objects weigh much less there.
- How g Changes
| Location / change | Effect on g |
|---|---|
| Poles | Maximum |
| Equator | Minimum |
| Higher altitude | Decreases |
| Below surface (depth) | Decreases |
| Centre of Earth | Zero |
| Faster Earth spin | Decreases at equator |
Check yourself
Effect of Earth's shape on g
Earth is flattened at the poles, so g is greatest at the poles and least at the equator.
Effect of altitude on g
g decreases as you go up because r increases.
Effect of depth on g
g decreases below the surface and becomes zero at the centre of the Earth.
Effect of Earth's rotation on g
Earth's spin reduces effective g most at the equator; if Earth spun faster, weight at the equator would decrease.
G on the Moon
About one-sixth of Earth's, so objects weigh much less there.
Free Fall and Equations of Motion
- Free fall: motion under gravity alone, with no other force such as air resistance; the acceleration is always g, downward, whatever the mass.
- In a true vacuum a feather, a rubber ball and a wooden ball fall together and land at the same time.
- Under gravity: v = u + gt, s = ut + ½gt², v² = u² + 2gs.
Check yourself
Define free fall
Motion under gravity alone, with no other force such as air resistance acting.
Acceleration during free fall
Always g, directed downward, regardless of the object's mass.
Feather, rubber ball, wooden ball in a true vacuum
They fall together and reach the ground at the same time.
Motion equations under gravity
v = u + gt; s = ut + ½gt²; v² = u² + 2gs.
Sign of g for an object thrown upward
Negative, because it opposes the upward motion.
Mass and Weight
- Mass: the amount of matter in a body, the same everywhere, in kilograms; a scalar.
- Weight: the force with which the Earth attracts a body, W = mg, in newtons; a vector towards the Earth's centre. It changes from place to place because g changes.
- On the Moon a body weighs about one-sixth of its Earth weight.
- Weightlessness occurs in free fall or in orbit, when there is no support force, even though gravity still acts.
- Mass vs Weight
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter | Force of gravity on body |
| Formula | – | W = mg |
| Unit | kilogram (kg) | newton (N) |
| Varies? | Constant everywhere | Changes with g |
| Type | Scalar | Vector |
Check yourself
Define mass
The amount of matter in a body; constant everywhere, measured in kilograms (kg).
Define weight
The force with which Earth attracts a body — W = mg — measured in newtons (N).
Why does weight change but mass not?
Weight changes from place to place because g changes; mass never changes.
Weight on the Moon
About one-sixth of its Earth weight, since the Moon's g is one-sixth.
Define weightlessness
Occurs in free fall or in orbit, when there is no support force — even though gravity still acts.
Mass and weight: scalar or vector?
Mass is a scalar; weight is a vector directed towards the Earth's centre.
Thrust, Pressure and Buoyancy
- Thrust: force acting perpendicular to a surface. Pressure = thrust per unit area (P = F/A), in pascals (Pa): 1 Pa = 1 N/m².
- A sharp knife cuts easily because the force acts on a tiny area, giving high pressure.
- Buoyancy (upthrust): the upward force a fluid exerts on an object in it, which is why things feel lighter in water. An object floats if its density is less than the fluid's, and sinks if greater.
Check yourself
Thrust vs pressure
Thrust is the force acting perpendicular to a surface; pressure is thrust per unit area (P = F/A).
Why does a sharp knife cut easily?
It exerts high pressure because the force acts over a tiny area.
Define buoyancy (upthrust)
The upward force a fluid exerts on an object placed in it — why things feel lighter in water.
When does an object float or sink?
Floats if its density is less than the fluid's; sinks if greater.
SI unit of pressure
The pascal (Pa), equal to one newton per square metre. (Newton & Pascal)
Archimedes' Principle and Density
- Archimedes' principle: a body in a fluid feels an upward force equal to the weight of fluid it displaces. It explains floating, swimming, ships and submarines.
- Density = mass ÷ volume, in kg/m³. Relative density compares a substance with water and has no unit: below 1 the object floats, above 1 it sinks.
- An iron ship floats because its shape displaces enough water to balance its weight.
Check yourself
State Archimedes' principle
A body immersed in a fluid experiences an upward force equal to the weight of fluid it displaces.
What does it explain?
Floating, swimming, and the working of ships and submarines.
Define density
Mass per unit volume (density = mass / volume), measured in kg/m³.
Define relative density
The density of a substance compared to that of water — it has no unit.
Relative density < 1 or > 1?
Less than 1 → the object floats; more than 1 → it sinks.
Why does an iron ship float?
Its overall shape displaces enough water to balance its weight.
All 11 chapters of Physics notes
- Units, Measurement & Physical Quantities11 sections
- Motion, Laws of Motion & Forces13 sections
- Gravitation11 sections
- Work, Power, Energy & Conservation13 sections
- Properties of Matter & Fluids12 sections
- Heat & Thermodynamics12 sections
- Waves & Sound11 sections
- Light & Optics15 sections
- Current Electricity13 sections
- Magnetism & Electromagnetism15 sections
- Modern & Nuclear Physics16 sections