The Complete Guide to Forces, Gravity & the Scientific Revolution

1. The Plague Year

Eighteen months alone in a farmhouse in Lincolnshire.

In 1665 the plague reached Cambridge and the university sent everyone home. A quiet, prickly, twenty-two-year-old undergraduate went back to his mother's farm, where there was nothing to do and nobody to talk to. Over the following year and a half he invented calculus, worked out that white light is a mixture of colours, and had the thought that the force pulling an apple down might be the same force holding the Moon in the sky. He then said nothing about most of it for two decades.

Isaac Newton (1642–1727)

Almost certainly the most powerful scientific mind on record, and difficult company.

A posthumous child, sent away when his mother remarried, Newton grew up solitary and stayed that way. He was secretive, held long and vicious grudges, spent more of his life on alchemy and biblical chronology than on physics, and later ran the Royal Mint with such enthusiasm for prosecuting counterfeiters that he sent several to the gallows. The 'lone genius' cliché exists partly because he really was one.

The problem he inherited was specific. Galileo had shown how things fall on Earth. Kepler had shown that planets move in ellipses, sweeping out equal areas in equal times. Nobody could say why — what kept a planet on its curve, and why that curve rather than another. Most people assumed the heavens simply obeyed different rules from the ground.

Johannes Kepler (1571–1630)

Handed Newton the shape of the problem, and died half a century too early to see it solved.

Kepler spent years forcing Mars into a circular orbit before admitting the data would not allow it, and published three laws describing exactly how planets move. What he could not supply was a cause. He guessed at some magnetic influence radiating from the Sun and knew it was a guess. The gap between his description and its explanation is precisely the space Newton walked into.

Commonly believed: An apple fell on Newton's head and he suddenly understood gravity.

Actually: Newton did tell the apple story himself, late in life, to more than one person — but he described watching an apple fall, not being hit by one, and the thought was a question rather than a revelation: why does it fall straight down, and how far up does that pull reach? Turning that question into a theory took him roughly twenty years of mathematics.

The insight buried in the question is the genuinely radical part. If the same force that drops an apple also holds the Moon, then the heavens are not a separate realm running on different laws. There is one physics, and it applies everywhere. Nobody in Europe had had solid grounds to believe that before.

What just happened

• Plague closed Cambridge in 1665 and Newton worked alone at Woolsthorpe
• In roughly eighteen months he developed calculus, optics and the first idea of gravitation
• The open problem was why planets move as Kepler had described

Newton's real leap was not gravity itself but universality: the assumption that the same laws govern an apple and a moon.

Before the gravity, the motion. Newton first had to say what forces do — and his first law contradicts everything your eyes tell you.

2. Three Laws That Look Obvious and Are Not

What each of Newton's laws actually rules out.

First law: an object continues at rest, or moving in a straight line at constant speed, unless acted on by a resultant force. Read that again, because everyday experience screams that it is false. Push a book across a table and it stops. Stop pedalling and the bike slows. Everything, obviously, needs a push to keep going.

Everything stops because of friction, and friction is a force. Remove it — on ice, in space — and motion continues indefinitely. Aristotle believed motion needed a continuous cause because he never got to see a frictionless case. The first law is the moment physics stops describing what we see and starts describing what is happening underneath it.

Inertia: The resistance of an object to any change in its motion. Mass is the measure of it. This is why a fully loaded shopping trolley is hard to start and, awkwardly, just as hard to stop.

Second law: the resultant force on an object equals its mass times its acceleration — F = ma. It is the workhorse of physics, and note what it means: force does not produce motion, it produces change of motion. Same force, more mass, less acceleration. It also tells you the units: a newton is whatever force accelerates one kilogram at one metre per second squared.

Third law: for every action there is an equal and opposite reaction. The universally misunderstood one. The forces act on different objects, which is why they do not cancel out. You push the ground backwards; the ground pushes you forwards. A rocket does not push against the air — it throws mass out of the back, and the escaping gas pushes the rocket forward. That is why rockets work in a vacuum, and it is why a fire extinguisher would move you across an ice rink.

When you jump, you pull the Earth up towards you with exactly as much force as it pulls you down. F = ma explains why nobody notices: the Earth's mass is about 5.97 × 10²⁴ kg, so its acceleration is a number with more than twenty zeros after the decimal point.

The three laws, in the shortest honest form

• 1. No resultant force, no change in motion — including no change to a straight line at steady speed
• 2. Resultant force = mass × acceleration. Force changes motion, it does not maintain it
• 3. Forces come in pairs, equal and opposite, acting on two different objects

What just happened

• The first law says motion needs no cause; stopping does
• The second law quantifies it: F = ma, force changes motion
• The third law pairs forces on different objects, which is why rockets work in vacuum

These three sentences describe the motion of everything from a dropped pen to a spacecraft, and they replaced two thousand years of confident and wrong physics.

Now the harder question, the one the laws do not answer: what force is holding the Moon?

3. The Force That Reaches Everywhere

One equation for apples, moons, tides and galaxies.

Newton's answer: every object with mass attracts every other object with mass. The strength depends on both masses multiplied together, and falls off with the square of the distance between them. Double the separation and the force drops to a quarter. That is the inverse square law, and it is the shape of the whole theory.

Universal gravitation: F = Gm₁m₂/r². G is the gravitational constant, an astonishingly small number, which is why you feel no attraction to the person next to you and enormous attraction to a planet. The word doing the heavy lifting is universal — the same law, everywhere, for everything.

The test was the Moon. Newton compared the acceleration of a falling apple at the Earth's surface with the acceleration the Moon needs to stay on its curved path, checked the ratio of the distances, and found the inverse square relationship held. One force, one law, from a farmyard to the sky.

Then the same equation started explaining things it had not been designed for. It gave Kepler's ellipses as a mathematical consequence rather than an observed fact. It explained the tides as the Moon and Sun pulling unevenly on different parts of the ocean. It explained why the Earth bulges slightly at the equator. Astronomers later noticed Uranus was not quite where it should be, calculated where an unseen planet would have to be to explain the discrepancy, pointed a telescope there in 1846 and found Neptune. A theory that predicts an unknown planet is doing something remarkable.

Newton published all of this in 1687 in the Principia, essentially because Edmond Halley — of the comet — asked him what curve a planet would follow under an inverse square force, and Newton replied that he had calculated it years earlier and mislaid the paper. Halley then paid for the book's publication out of his own pocket.

Commonly believed: Newton explained what gravity is.

Actually: He explicitly refused to. He could describe gravity's behaviour with extraordinary precision but had no mechanism for how one body pulls another across empty space, and famously declined to invent one — 'I frame no hypotheses'. Physics accepted a law it could not explain because the predictions were perfect. The explanation waited for Einstein, 228 years later.

What just happened

• Newton proposed that all masses attract, with force falling as the inverse square of distance
• The Moon test confirmed the same force acts on falling apples and orbiting bodies
• The theory explained tides, Kepler's laws and eventually predicted Neptune

This is the first time anyone unified the heavens and the Earth in a single mathematical law — the founding achievement of modern physical science.

Two words in that equation get confused constantly, and confusing them is the fastest way to get the physics wrong.

4. Mass Is Not Weight

The distinction that clears up half the confusion in mechanics.

Mass is how much matter an object contains and how strongly it resists being accelerated. It is measured in kilograms and it does not change wherever you take it. Weight is the force gravity exerts on that mass. It is measured in newtons, and it changes with where you are.

The same 60 kg person

Bathroom scales measure force and then divide by g to display a mass, which works fine on Earth and quietly hides the distinction. Take the same scales to the Moon and they would report that you have lost five-sixths of yourself, which you have not — you contain exactly as much matter as before.

There is a deep puzzle hiding here. The mass that resists acceleration (inertial mass) and the mass that responds to gravity (gravitational mass) are conceptually different properties — and every experiment ever done finds them identical to extraordinary precision. Newton could only note the coincidence. Einstein made it the foundation of general relativity.

One more everyday confusion worth killing: heavier objects do not fall faster. A heavier object experiences a bigger gravitational force, but it also has more inertia to overcome, in exactly the same proportion. The two effects cancel, which is why everything accelerates at the same rate in a vacuum — and why the Apollo 15 commander dropped a hammer and a falcon feather on the Moon in 1971 and they hit the surface together.

What just happened

• Mass is quantity of matter in kilograms and does not vary with location
• Weight is a force in newtons and depends on local gravity
• All objects fall at the same rate in the absence of air resistance

Almost every mechanics mistake starts by treating weight as a property of the object rather than a force acting on it.

Which leaves the question everyone asks and almost nobody is told correctly: why do astronauts float?

5. Falling Around the World

Why astronauts float even though gravity has hardly weakened.

The International Space Station orbits about 400 km up. Earth's radius is about 6,400 km, so the station is roughly 6% further from the centre than you are. Put that into the inverse square law and gravity there is around 90% of its strength at the surface. Astronauts are not floating because gravity has stopped. They are falling.

Newton explained it with a thought experiment: imagine a cannon on an impossibly high mountain. Fire the ball gently and it curves down and lands. Fire it harder and it lands further away. Fire it hard enough and the ground curves away beneath it at exactly the rate the ball falls — so it never reaches the surface. It falls forever, in a circle. That is an orbit.

Free fall: Motion under gravity alone, with nothing pushing back. Everything in the station — astronauts, tools, water — is falling around the Earth at the same rate, so nothing presses against anything else. The correct term is microgravity, not zero gravity, and the sensation is exactly what you feel in the first moment of a rollercoaster drop, extended indefinitely.

It also explains why getting to orbit is hard in a way films never convey. The difficulty is not height — a powerful rocket could reach 400 km fairly quickly and would then simply fall back. The difficulty is sideways speed: about 7.7 km per second, roughly 27,700 km per hour. Almost all the fuel is spent going fast horizontally, not going up.

The same maths delivered the Moon landings, and the accuracy is startling. Apollo trajectories were computed with Newtonian mechanics, no relativity required, and they hit a moving target 384,000 km away. The 'wrong' theory is good enough to navigate the solar system, which is why probes still use it today.

Where Newton finally fails is small and specific. Mercury's orbit shifts slightly more per century than his equations allow, by an amount too small to matter for any practical purpose and too consistent to ignore. Astronomers hunted for a hidden planet to explain it. There was none. In 1915 Einstein's general relativity produced Mercury's exact discrepancy as a natural consequence — and gravity stopped being a force at all, becoming instead the curvature of spacetime itself.

What just happened

• Gravity at the space station is about 90% of surface strength; astronauts are in free fall
• Orbiting means falling sideways fast enough to keep missing the ground
• Newtonian mechanics is accurate enough for spaceflight; Mercury's orbit revealed its limit

The cannonball picture is the single most useful mental model in orbital mechanics, and it comes straight from Newton's own book.

Now you know the story

Newton's laws are wrong, strictly speaking: at very high speeds and very strong gravity, Einstein's description takes over. They are also accurate enough to have put people on the Moon, and every spacecraft flying today is navigated with them. That is worth remembering when you meet the word 'wrong' in science — it usually means 'has a known range of validity', which is a different thing entirely.

• State Newton's three laws and say what each one actually rules out
• Explain universal gravitation in plain words, and why 'universal' is the surprising bit
• Distinguish mass from weight without hesitating
• Describe how orbits work — and why astronauts float even though gravity is still pulling on them

Back to Forces, Gravity & the Scientific Revolution →

The assessed treatment is Pearson Edexcel International GCSE Physics Topic 1 (Forces and motion), which requires specific relationships, calculations and a required practical. This course is the story, not the syllabus.