Mr. Scandrett's ClassroomOS

Physics · Lesson 07

Universal Gravitation

Gravity Orbits Forces Newton K–12

Every mass in the universe pulls on every other mass — right now. An apple and the Earth are tugging on each other. The Moon and the Earth are tugging on each other. Newton figured out the rule that connects them all with one simple equation.

The Apple and the Idea

Isaac Newton (1643–1727) was an English mathematician and physicist who changed science forever. Around 1666, while sitting in his garden at Woolsthorpe Manor, he allegedly watched an apple fall from a tree. He didn't wonder why it fell — everyone knew things fell. He wondered something far more interesting: is the same force pulling the apple down also pulling the Moon toward the Earth? If so, why doesn't the Moon fall? Newton spent the next twenty years developing the mathematics to answer that question, finally publishing his Law of Universal Gravitation in Principia Mathematica (1687) — one of the most important books in the history of science.

The Big Idea — Every Mass Pulls on Every Other Mass

"Every object in the universe attracts every other object with a gravitational force that depends on their masses and the distance between them."

This is not just about Earth and apples. The Sun pulls on Jupiter. Jupiter pulls on every moon around it. You pull gravitationally on the Andromeda Galaxy (very, very weakly). Gravity has infinite range — it never truly turns off, it only gets weaker with distance.

Think about it: Right now, you and the person sitting next to you are gravitationally attracting each other. The force is unimaginably tiny compared to Earth's pull, but it is absolutely real and non-zero.

The Two Big Questions Newton Answered

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Why does the apple fall?

Earth's mass pulls the apple downward. Because Earth is enormously more massive than the apple, Earth barely moves while the apple accelerates toward it at 9.8 m/s² — what we call g, the gravitational acceleration at Earth's surface.

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Why doesn't the Moon fall?

The Moon is falling — it's just also moving sideways fast enough that the curved Earth keeps "dropping away" beneath it. This is what an orbit is: continuous free-fall while moving sideways. Newton showed these are the same force.

Newton's Law of Universal Gravitation

Reading the Formula

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More mass → stronger pull Double either mass and the force doubles. A planet twice as massive pulls on you twice as hard.
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More distance → weaker pull Double the distance and the force drops to one quarter. This is called an inverse-square law.
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G is tiny on purpose 6.674 × 10⁻¹¹ is an extremely small number — gravity is by far the weakest of the four fundamental forces.
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Forces are equal and opposite Earth pulls the apple down with force F. The apple pulls Earth up with the exact same force F. (Earth barely moves — it's far more massive.)
The inverse-square law: If you move twice as far from Earth's centre, gravity becomes (1/2)² = 1/4 as strong. Three times as far → 1/9 as strong. This pattern appears everywhere in physics — light, sound, electric forces — whenever something spreads out from a point in three dimensions.

Orbit Simulator

Adjust the planet's orbital distance and speed to see how gravity shapes its path around the star.

Orbit Type Circular
Grav. Force 1.00 rel. units
Period 1.00 rel. years

Falling and Orbiting Are the Same Thing

Newton imagined firing a cannonball horizontally from a very tall mountain. If fired slowly, it curves down and hits the ground. Fire it faster and it travels further before hitting. Fire it at exactly the right speed, and the curve of the ball's path perfectly matches the curve of Earth's surface — the ball is always falling but the ground always curves away. That is an orbit.

The International Space Station orbits at ~400 km altitude, moving at about 7,700 m/s (27,700 km/h). At that speed, it falls toward Earth at the same rate that Earth's surface curves away. Astronauts feel weightless not because there is no gravity — Earth's gravity up there is still about 88% of what it is on the surface — but because they and the station are falling together.

Why the Moon Stays in Orbit

The Moon is about 384,400 km from Earth's centre. At that distance, Earth's gravity is much weaker than at the surface — but it is still strong enough to keep the Moon curving around Earth rather than flying off in a straight line. The Moon moves at about 1 km/s, completing one orbit every 27.3 days. Gravity provides the centripetal force that continuously bends the Moon's path into a (nearly) circular orbit.

Newton's genius insight: He calculated how fast something would need to fall over one second to stay in orbit at the Moon's distance. Then he compared it to the Moon's known orbital motion — and they matched perfectly, proving the same gravitational force governs both the apple and the Moon.

Gravity at Work in the Real World

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Satellites & GPS Every GPS satellite, weather satellite, and communication satellite stays in orbit because of the precise balance between its speed and Earth's gravity. Engineers use Newton's formula to calculate exact orbital altitudes.
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Ocean Tides The Moon's gravity pulls on Earth's oceans. The side of Earth facing the Moon has a high tide because water is pulled toward the Moon; the opposite side also bulges because it is pulled least. Two high tides per day.
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Planetary Orbits All eight planets in our solar system orbit the Sun according to this law. Kepler's earlier observational rules about orbits — including the fact that planets move faster when closer to the Sun — are direct mathematical consequences of Newton's equation.
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Space Mission Design NASA engineers used Newton's law to plot trajectories for Apollo missions, Mars rovers, and Voyager probes. "Gravity assists" — using a planet's gravity to slingshot a spacecraft — are pure applied universal gravitation.

Key Vocabulary

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Gravity The attractive force between any two objects with mass. One of the four fundamental forces of nature.
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Inverse-Square Law Force decreases with the square of distance: double the distance, force becomes one-quarter as strong.
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Orbit Continuous free-fall around a massive body where sideways speed prevents the falling object from ever hitting the surface.
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Gravitational Constant (G) 6.674 × 10⁻¹¹ N·m²/kg² — a universal constant of nature, the same everywhere in the universe.
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Surface Gravity (g) The gravitational acceleration at a planet's surface. On Earth: 9.8 m/s². On the Moon: 1.6 m/s². On Jupiter: 24.8 m/s².
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Centripetal Force The inward-directed force needed to keep an object moving in a circle. For orbiting bodies, gravity provides this centripetal force.

Summary

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Universal
Every mass attracts every other mass — no exceptions, everywhere in the universe.
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Inverse-Square
Force weakens with the square of distance. Double the gap → one-quarter the pull.
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Orbits = Falling
The apple and the Moon obey the same law. An orbit is continuous free-fall sideways.

Practice Problems

EasyIf you double the mass of one object in a gravitational pair while keeping everything else the same, what happens to the gravitational force? Enter the multiplier (e.g., enter 2 if it doubles).

Hint: F = G·m₁·m₂/r². If you double m₁, every other term stays the same — so F doubles.

EasyIf you triple the distance between two objects, by what factor does the gravitational force change? (Enter a decimal, e.g. 0.5 for half.)

Hint: Inverse-square law — multiply distance by 3, so force is divided by 3² = 9. Force becomes 1/9 ≈ 0.111.

MediumEarth's surface gravity is about 9.8 m/s². The Moon's radius is about 27% of Earth's radius and its mass is about 1.2% of Earth's mass. Using g = GM/r², calculate the Moon's surface gravity to one decimal place (m/s²).

Hint: g_Moon = g_Earth × (M_Moon/M_Earth) × (R_Earth/R_Moon)² = 9.8 × 0.012 × (1/0.27)² ≈ 9.8 × 0.012 × 13.72 ≈ 1.6 m/s².

HardTwo objects, each with mass 1,000 kg, are separated by 1 metre. G = 6.674 × 10⁻¹¹ N·m²/kg². Calculate the gravitational force between them in scientific notation. Enter the coefficient (e.g. if the answer is 6.674 × 10⁻⁵ N, enter 6.674).

Hint: F = (6.674 × 10⁻¹¹) × 1000 × 1000 / 1² = 6.674 × 10⁻¹¹ × 10⁶ = 6.674 × 10⁻⁵ N. The coefficient is 6.674.