The apple and the Moon
The story goes that Isaac Newton saw an apple fall and wondered: does the same force that pulls the apple down reach all the way up to the Moon? It was a daring thought. For thousands of years, people believed the heavens followed completely different rules from things on Earth.
Newton's answer was yes — one law of gravity for everything. The apple falls and the Moon orbits for exactly the same reason. But then why doesn't the Moon fall down?
It does. It's falling right now. It just keeps missing.
Newton's cannon
Newton imagined a cannon on top of an enormously tall mountain, firing horizontally. A slow shot curves down and lands nearby. A faster shot lands farther away. But the Earth is round — so the ground curves away beneath a fast shot. Fire fast enough, and the ground curves away exactly as fast as the cannonball falls. It falls forever, never landing. That's an orbit.
Newton's cannon: a cannon on a mountain on Earth fires a ball horizontally. Set the launch speed and press Fire. Slow shots fall back to the ground; at about 7.9 km/s the ball falls around the Earth in an orbit; faster shots make wider orbits or escape. Readings show the altitude and speed.
Newton's cannon
InteractiveThe math, with your numbers
Try this
- →Fire at 4 km/s, then 6 km/s. Each shot lands farther around the curve of the Earth.
- →Find the speed that makes a perfect circle (≈ 7.7 km/s — the ISS's real speed).
- →Fire at 9 km/s, then 11 km/s. What shape does the orbit become? When does it never come back?
The law of universal gravitation
Newton worked out exactly how strong gravity is between any two objects. Every mass in the universe pulls on every other mass:
Say it out loud: “the gravity force equals G times the two masses multiplied together, divided by the distance between them squared.”
Gravitational force· measured in N
The pull each object feels toward the other (equal and opposite — Newton's 3rd law!).
The two masses· measured in kg
Double either mass → double the force.
Distance· measured in m
Between the centres of the two objects.
Gravitational constant· measured in N·m²/kg²
6.674 × 10⁻¹¹ — a tiny number. That's why you don't feel your desk pulling on you.
The most striking part is the on the bottom. Go twice as far away, and gravity becomes four times weaker. Three times as far: nine times weaker.
Lines of force spreading out from a source. As the distance slider increases, the same lines spread over a larger sphere, so each patch of area gets fewer of them: twice as far means one quarter as strong.
Why 1/r²? Spreading out
InteractiveThe math, with your numbers
Newton's great test: the Moon
Newton checked his idea with a beautiful calculation. Here's a simplified version you can follow:
Is the Moon's 'fall' really caused by Earth's gravity?
Step 1 of 4- 1The Moon is about 60 Earth-radii away from Earth's centre. An apple is 1 Earth-radius away.
Make a prediction first
How fast must something move to orbit just above Earth's surface (ignoring air)?
Think about it, then click to reveal the answer.
Make a prediction first
How fast must something move to orbit just above Earth's surface (ignoring air)?
Think about it, then click to reveal the answer.
For a circular orbit, gravity must supply exactly the acceleration needed to curve: . So m/s — about 7.9 km/s, or 28,000 km/h. A low orbit takes about 90 minutes. (In the simulation, the ISS altitude gives 7.67 km/s.)
Wrap-up
Key ideas to remember
- An orbit is falling while moving sideways so fast that you keep missing the ground.
- Every mass attracts every other: .
- Gravity weakens with the square of distance, because its influence spreads over a sphere.
- “Weightless” astronauts are in free fall, not free of gravity.
Check your understanding
Sources & further reading
Everything in this lesson agrees with these references. They're all free to read.