Physics › 🌌 Astrophysics & Space

Gravitation & Newton's Law

The same tug that pulls an apple to the ground is pulling on the Moon right now — one law, one force, reaching across every distance in the universe.

High schoolUni Year 1
💡
The big idea: Every object with mass attracts every other object with mass — a falling apple and an orbiting Moon obey the identical rule. That rule weakens with the square of the distance between the objects, which is why gravity feels overwhelming right next to a planet but is nearly nothing between two people standing in a room. Understanding this one equation unlocks weight, orbits, and why nothing in space ever truly "falls" the way we imagine.
🎯 By the end, you'll be able to
  • State Newton's law of universal gravitation and identify what each symbol represents.
  • Explain why gravitational force follows an inverse-square relationship with distance.
  • Distinguish between mass and weight, and calculate weight using local gravitational field strength g.
  • Explain why the Moon continuously orbits Earth instead of flying off or crashing down.
📎 You should already know
  • Newton's Laws of Motion
  • Basic algebra and exponents
  • Force, mass, and acceleration basics

The Same Force, Everywhere

Drop an apple, and it falls. Look up at night, and the Moon hangs there, quietly circling Earth once a month. For most of history these seemed like two completely unrelated things — one an everyday accident, the other a cosmic mystery. Newton's great insight was that they are exactly the same phenomenon: the very force pulling the apple down is pulling on the Moon right now, bending its path from a straight line into a curve.

This is universal gravitation — every object with mass pulls on every other object with mass, from apples to planets to galaxies, using one single, elegant rule.

🔑 Newton's Law of Universal Gravitation

Any two masses attract each other with a force that depends on how much mass each one has and how far apart they are. More mass means a stronger pull. More distance means a weaker pull — and the distance effect is far more dramatic than most people expect.

\[ F = G\dfrac{m_1 m_2}{r^2} \]
F is the attractive force between masses \(m_1\) and \(m_2\), separated by distance \(r\) (measured center to center). \(G = 6.674\times10^{-11}\ \text{N·m}^2/\text{kg}^2\) is the gravitational constant — the same tiny number everywhere in the universe.
\[ g = \dfrac{GM}{r^2} \]
Apply the same law to one large mass \(M\) (like a planet) acting on a much smaller test object at distance \(r\) from its center. The result, \(g\), is the gravitational field strength — the acceleration any object feels near that mass, no matter how big or small that object is.
\[ W = mg \]
Weight is simply the force gravity exerts on a mass sitting inside a field of strength \(g\). Mass (\(m\), in kg) measures how much matter you have and never changes. Weight (\(W\), in newtons) measures how hard gravity pulls on that mass, and it changes depending on where you stand.
🎮 Interactive: Feel the Inverse-Square Law LIVE
Drag the masses closer together or farther apart and watch the force arrows respond. Notice how sharply the pull grows as objects approach each other, and how quickly it fades as they separate — that's the inverse-square law in action.
📝 Worked example: A 70 kg astronaut stands on Earth's surface (g = 9.8 m/s²), then later stands on the Moon's surface (g = 1.62 m/s²). Find her weight in each location.
  1. Weight follows W = mg, where m is mass (the same everywhere) and g is the local gravitational field strength.
  2. On Earth: W = 70 kg × 9.8 m/s² = 686 N.
  3. On the Moon: W = 70 kg × 1.62 m/s² = 113.4 N.
  4. Her mass is 70 kg in both places — it never changed — but her weight dropped to roughly one-sixth, because the Moon's gravity is much weaker.
✓ 686 N on Earth; about 113 N on the Moon — same mass, very different weight.
📝 Worked example: Two identical satellites orbit at distance r from Earth's center and feel gravitational force F. A third identical satellite orbits at distance 3r. How does its gravitational force compare to F?
  1. Gravitational force follows F = Gm₁m₂/r², so force is proportional to 1/r².
  2. Tripling the distance means the new separation is 3r, so the new denominator is (3r)² = 9r².
  3. The new force is F_new = Gm₁m₂/(9r²) = F/9.
  4. So a satellite three times farther away feels only one-ninth the gravitational pull — not one-third.
✓ F/9 — one-ninth of the original force, because gravity falls off with the square of distance, not the distance itself.
✨ Why Doesn't the Moon Fall Into Earth?

It is falling — that's the whole point. The Moon moves sideways very fast (roughly 1 km every second), and Earth's gravity is constantly pulling it toward Earth's center. Left alone with no gravity, its inertia would carry it off in a straight line forever. Instead, gravity continuously bends that straight-line path into a curve — and the Moon's sideways speed is exactly enough that its curving path falls away from a straight line at the same rate gravity pulls it inward, so it keeps missing Earth instead of spiraling into it. The result: it falls forever without ever getting closer. An orbit is really a continuous, endless fall that keeps missing.

⚠️ Mass Is Not Weight — and "Zero Gravity" Is a Myth

Astronauts aboard the International Space Station look weightless, but gravity up there is only about 10% weaker than on Earth's surface — nowhere near zero. What they're actually experiencing is free fall: the station and everything inside it, astronauts included, are continuously falling around Earth together, so nothing presses against anything else. It feels weightless, but the gravitational field is very much still doing its job.

Keep mass and weight straight: mass (kg) is how much matter you have and never changes; weight (N) is the force gravity exerts on that mass, and it changes depending on where you are.

Check your understanding

1. According to Newton's law of universal gravitation, what happens to the force between two objects if you double the mass of one of them?
Force is directly proportional to each mass in F = Gm₁m₂/r², so doubling one mass doubles the force.
2. A 60 kg person stands on a planet where g = 4 m/s². What is their weight there?
Weight is W = mg = 60 kg × 4 m/s² = 240 N.
3. If the distance between two masses is tripled, what happens to the gravitational force between them?
Gravity follows an inverse-square law: force is proportional to 1/r². Tripling r makes the denominator 9 times larger, so force drops to 1/9.
4. Why do astronauts aboard the ISS appear weightless?
Gravity at ISS altitude is still about 90% as strong as at the surface. The floating sensation comes from free fall, not an absence of gravity.
✅ Key takeaways
  • Every pair of masses attracts each other with force F = Gm₁m₂/r² — the same rule for apples, planets, and galaxies.
  • Gravity is an inverse-square force: double the distance and force drops to a quarter; triple it and force drops to a ninth.
  • Weight (W = mg) depends on location and changes from planet to planet, while mass never changes.
  • The Moon orbits because it is continuously falling toward Earth while moving sideways fast enough to keep missing — that endless fall is what an orbit is.