Universal gravitation · F = Gm₁m₂/r² · gravitational field g · orbits · weight & weightlessness
An apple falls; the Moon circles; a galaxy holds its stars together. Newton's startling idea was that one law does all three: every mass attracts every other mass with a force F = Gm₁m₂/r² — stronger for bigger masses, weaker the further apart they are. The humble apple and the distant Moon obey exactly the same rule.
This page covers Newton's law of universal gravitation — every mass attracts every other with F = Gm₁m₂/r² — together with the gravitational constant G, gravitational field strength g, the difference between mass and weight, and orbits and weightlessness. By the end you'll be able to:
Every satellite, tide, planet and rocket trajectory obeys it — and "Gravitation" is a core, heavily-tested chapter everywhere. We go beyond the syllabus, but we never skip it:
Searched as: Newton's law of universal gravitation, F = Gm₁m₂/r², gravitational constant G, g = GM/r², mass vs weight, why astronauts are weightless.
Set the central mass and the orbit radius, then watch a satellite circle under gravity. Move it closer or make the planet heavier and the pull — and the orbital speed — climb. Switch to Drop to see that an orbit is just sideways free fall. 🟢 real gravity engine
Set the central mass and orbit radius to see the pull and speed.
In plain terms: every mass pulls on every other mass. The pull is stronger for bigger masses and weaker the further apart they are — and it is the same law for an apple and a planet.
Newton's law of universal gravitation says any two masses attract each other with a force F = Gm₁m₂/r². The force grows with the product of the masses and falls with the square of the distance between their centres. The constant G ≈ 6.67×10⁻¹¹ is astonishingly tiny, which is why gravity is far too weak to feel between everyday objects — only when a mass is astronomical, like the Earth, does the pull become strong.
Near a large body the pull per kilogram is the gravitational field strength g = GM/r², about 9.8 N/kg at Earth's surface. An object's weight is then W = mg. Here is the beautiful part: the acceleration of a falling object is a = F/m = GM/r², which has no m of the falling object in it. So a hammer and a feather fall at exactly the same rate — the heavier one feels more pull, but also needs more force to move.
The playground above puts a satellite into orbit. The Orbit tab shows it circling, with an arrow marking the pull toward the planet's centre; the Force–distance tab plots that pull against distance — a clean inverse-square curve. The satellite is really falling all the time; it just moves sideways fast enough (v = √(GM/r)) that the planet curves away beneath it. Make the planet heavier or the orbit closer and the pull and speed both rise. Switch to Drop and the same gravity pulls it straight in. 🟡 maths of the picture
Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.
The physics is visible in the diagram; the maths usually hides. These little labs make it visible too — drag a slider and watch the force, the field and the curve answer.
A few ideas about gravity are so widespread they feel like facts. Tap a card to flip it and bust the myth.
Thousands of satellites circle the Earth, each held by gravity as the centripetal force — closer ones must move faster (v = √(GM/r)). GPS satellites keep such precise orbits that timing them lets your phone fix its position to a few metres anywhere on the planet.
The Moon pulls a little harder on the near side of the Earth than the far side, and that difference in gravity stretches the oceans into two bulges. As the Earth turns beneath them, every coast rises and falls twice a day — the sea breathing to a rhythm set 380000 km away.
Astronauts float not because gravity is gone — it is nearly as strong up there as on the ground — but because they and their station are falling around the Earth together, over and over. With nothing pushing up on them, there is no weight to feel. It is a dropped lift, made permanent.
Once we could predict the pull, we hung satellites in the sky, found our way by them, and even learned to hear two black holes collide.
Everything pulls — a speck of dust, you, a mountain, a star. Drag from dust to galaxy and watch the same law, F = Gm₁m₂/r², grow from a whisper into the architecture of the cosmos. Gravity isn't mighty because G is big; it becomes mighty because mass becomes enormous.
Gravity is the patience of mass — small mass whispers, great mass gathers worlds.
Physics you can hold. Each project below demonstrates the law you just met — and the measuring is what turns a demo into a science-fair winner. Pick one, build it from things at home, and graph something.
Build: drop a heavy ball and a light ball from the same height at the same instant.
Measure: film them landing in slow-mo — they hit together, because the falling mass cancels out of a = GM/r².
Build: hang a weight on a string of known length and time how long 20 swings take.
Measure: use g = 4π²L/T² to work out your local gravity — you should land near 9.8 N/kg.
Build: stretch fabric over a bowl, drop a heavy ball in the centre to make a well, then roll marbles around it.
Measure: how the marbles spiral and speed up nearer the centre — a hands-on model of orbital motion.
Build: measure a lamp's brightness with a phone light sensor at different distances.
Measure: brightness vs distance follows 1/r² — the very same geometry that makes gravity inverse-square.
Build: shrink the Sun to a beach ball and lay out the planets to scale down a long corridor or street.
Measure: the huge gaps show how gravity reaches across enormous distances, weakening as 1/r².
Build: punch a hole near the base of a paper cup full of water and hold it up — water streams out.
Measure: now drop the cup and watch the stream stop in mid-air — in free fall, nothing has weight to push it out.
Gravity reaches across every distance in the cosmos. Here are the questions that come up most — each answer reads on its own, lifted clean off the page.
Newton's law of universal gravitation states 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 their centres: F = Gm₁m₂/r², where G ≈ 6.67×10⁻¹¹ N·m²/kg². The same single law governs a falling apple and the orbiting Moon — Newton's great unifying insight.
| Feature | Mass | Weight |
|---|---|---|
| What it is | The amount of matter | The gravitational force on it |
| Symbol & unit | m, kilograms (kg) | W, newtons (N) |
| Changes with place? | No — same everywhere | Yes — with local gravity |
| Formula | — | W = mg |
The gravitational constant G is the fixed number that scales Newton's law of gravitation, about 6.67×10⁻¹¹ N·m²/kg². It is the same everywhere, which is why the law is called universal. Because G is so tiny, gravity is extremely weak unless at least one mass is enormous, like a planet — which is why you don't feel pulled toward people standing near you.
A heavier object feels a stronger gravitational pull, but it also has more mass to accelerate, and the two effects cancel exactly. The acceleration is a = force ÷ mass = GM/r², which has no dependence on the falling object's own mass. So a hammer and a feather fall together in a vacuum — famously demonstrated on the airless Moon.
Gravitational field strength, g, is the gravitational force per unit mass at a point: g = GM/r², measured in newtons per kilogram (N/kg). At Earth's surface it is about 9.8 N/kg, which is also the acceleration of free fall. It is weaker higher up and on smaller bodies — only about 1.6 N/kg on the Moon.
Gravity is inverse-square because a mass's influence spreads out evenly over an imaginary sphere around it, and the area of that sphere grows as the square of its radius. So the same pull is shared over an area proportional to r², and the force falls as 1/r². Light intensity and Coulomb's electric force thin out for exactly the same geometric reason.
They are falling — all the time. A satellite moves sideways so fast that, as gravity pulls it down, the curved Earth falls away beneath it just as quickly, so it keeps missing the ground and circles instead. Gravity bends the satellite's path into a circle instead of stopping it. If the satellite slowed down, it would indeed spiral in and fall.
Astronauts are weightless not because gravity has vanished — there is plenty at orbital height — but because they and their spacecraft are in continuous free fall together. Falling at the same rate, the floor no longer pushes up on them, so there is no support force to feel as weight. It is the floating feeling at the top of a dropped lift, made permanent by orbiting.
Newton's gravitation and Coulomb's law of electric force share the same shape: both are inverse-square laws, proportional to the product of the source quantities — masses for gravity, charges for Coulomb — and act along the line joining the bodies. The differences are that gravity only ever attracts, while electric forces can attract or repel, and gravity is vastly weaker, about 10³⁶ times weaker between two protons.
Most marks are lost to a handful of slips. Spot yours here before the exam does.
Seven question formats, the way Beyond Dictionary serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Gravity teaches one quiet truth: distance weakens the pull, but the connection never quite becomes zero.