The full lecture, side by side with a live panel. Read the text on the left; on the right every idea is animated through a real-life picture — an apple and the Moon, a person weighing differently on three worlds, an astronaut floating, Newton's cannon, PAKSAT over Pakistan. Press ▶ and the narration plays straight through, scrolling and animating each section for you.
Newton asked a simple question: if an apple (or a mango in Hyderabad) falls because the Earth pulls it, does that same pull reach all the way to the Moon? His answer became one of the great laws of physics: every body attracts every other body.
The force is always attractive, never repulsive; it is mutual — the apple pulls the Earth with the same force the Earth pulls the apple (Newton's third law) — and it acts centre-to-centre along the line joining the bodies. For uniform spheres the whole mass behaves as if it sits at the centre, so r is measured between centres, in metres.
The 1/r² factor is the heart of the law. Watch the panel: as the masses move apart the force arrow collapses. Double the separation and F drops to a quarter; triple it and F is a ninth.
| Separation | Force |
|---|---|
| r | F |
| 2r | F/4 |
| 3r | F/9 |
| r/2 | 4F |
Newton checked this against the Moon, about 60 Earth-radii away: its falling acceleration should be g/60² ≈ 0.0027 m/s² — exactly what the orbit needs. The apple and the Moon obey the same law.
Your weight on a planet is the gravitational pull of that planet on you. Setting weight equal to the universal force makes the body's own mass cancel:
That is why a stone and a coin land together (with air removed): the m cancels. The panel shows one person on three worlds — the scale changes because g changes.
| World | g (m/s²) | Scale shows |
|---|---|---|
| Moon | 1.6 | about g/6 — astronauts bounce |
| Earth | 9.8 | full weight |
| Jupiter | 24.8 | about 2.5× — you can barely stand |
The newton (N) is the SI unit of weight; mass stays the same everywhere in kilograms, but weight = mg changes with g.
Rearranging g = GM/R² gives the mass of the Earth from three measurable numbers — g, the Earth's radius R, and the constant G that Cavendish's 1798 torsion balance measured. This is why finding G was called "weighing the Earth".
Watch the probe in the panel and the g-meter beside it. Above the surface the distance grows to (R + h), so g falls off by the inverse square; below the surface only the inner sphere pulls, so g shrinks linearly to zero at the centre.
With latitude: the Earth bulges at the equator and spins, so g is smallest at the equator (9.78 m/s²) and largest at the poles (9.83 m/s²) at sea level.
A weighing scale reads the normal reaction it pushes back with — your apparent weight — not the true weight mg. In a lift accelerating up you read m(g + a); accelerating down, m(g − a); and if the cable snaps and a = g, the scale reads zero.
| Lift motion | Apparent weight |
|---|---|
| at rest / uniform velocity | mg (true weight) |
| accelerating up with a | m(g + a) — feel heavier |
| accelerating down with a | m(g − a) — feel lighter |
| free fall (a = g) | 0 — weightless |
An astronaut floating in a satellite is in that snapped-cable lift permanently: capsule, astronaut and water droplets all fall together with the same acceleration, so nothing presses on anything. Gravity at the ISS is still ≈ 8.7 m/s² — weightlessness is not "no gravity", it is apparent weight zero from shared free fall.
Newton's thought experiment, alive in the panel: fire a cannonball horizontally from a high mountain. Faster → it lands farther. Fast enough (7.9 km/s) → the ground curves away exactly as fast as the ball falls. It never lands. A satellite is a projectile that keeps missing the Earth.
For a satellite skimming the surface, gravity supplies the centripetal force, so the orbital speed follows from mg = mv²/R:
Make the period exactly 24 hours, orbit above the equator moving west-to-east, and from the ground the satellite never moves — your TV dish points at it once, forever.