Gravity's Long Reach

Why it matters

The apple falling and the Moon orbiting are the SAME event — one law, F = Gm₁m₂/d², runs both. And on the Moon, your bathroom scale becomes a flatterer.

The idea in plain words

The law and the local rate. Tap the terms.

F = G m₁m₂ / d²

g on Jupiter ≈ 24.8 m/s². Weight of the 60 kg astronaut there?

1488 N — two and a half Earth-weights, same person

• the constant: G — 6.67 × 10⁻¹¹ N·m²/kg² — universal, tiny, the same everywhere
• the shape: inverse square — double the distance, quarter the pull
• the exam table: mass vs weight — mass: kg, scalar, constant · weight: N, vector, = mg, changes by planet and even by latitude
• fine print: g variations — slightly more at the poles than the equator; less up a mountain
• W = mg = 60 × 24.8

Predict first

A 60 kg astronaut goes to the Moon (g = 1.6 m/s²). There, her…

Mass is her matter — luggage that never changes. Weight = mg is gravity's local opinion of it: 60 × 1.6 = 96 N, versus 588 N at home.

• mass stays 60 kg; weight drops to 96 N — correct
• mass drops to 10 kg
• mass and weight both stay the same

What you do

Carry the same 60 kg from Moon to Jupiter — the mass card never flinches, the weight card can't sit still.

Check yourself

Halve the distance between two masses; the gravitational force becomes…

F ∝ 1/d²: (½)² in the denominator = ×4 force.

A beam balance and a spring balance on the Moon…

The beam compares your mass against standard masses — gravity cancels. The spring feels the pull directly.

You 'weigh' 588 N on Earth. Your mass is…

m = W/g = 588/9.8 = 60 kg — the number the Moon can't change.

• four times — correct
• double
• half
• beam reads the same as Earth (compares masses); spring reads less (measures weight) — correct
• both read less
• both read the same
• 60 kg — correct
• 588 kg
• 5880 kg