Forces · Topic 7 of 17

Universal Gravitation, Mass & Weight

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Physics · gravitation

Every mass attracts every other mass, weaker with distance squared. Weight (w = mg) is that pull on a mass; mass itself never changes.

01 · Inverse square2× the distance → ¼ the force

02 · Mass vs weightMass stays the same; weight can change

03 · Weightw = mg (g = 9.8 m/s² on Earth)

Weight depends on location; mass does not

Orbits: gravity supplies the inward (centripetal) pull

F = G·m₁·m₂ / r² (r = center-to-center distance, in m) must know

Weight w = mg; on Earth g = 9.8 m/s², so 1 kg weighs 9.8 N must know

Moon g = 1.625 m/s² (≈ ⅙ of Earth's): 1 kg weighs ≈ 1.7 N, same mass

Every mass attracts every other mass (universal gravitation) must know

Inverse square: 2× the distance → ¼ the force; 3× → 1/9 must know

Force ∝ each mass: double one mass → 2× the force; both → 4×

36 N, distance ×3 → 36 ÷ 9 = 4 N

60 kg → w = 60 × 9.8 = 588 N; mass stays 60 kg anywhere

Both masses ×2 and distance ×2 → (2×2) ÷ 2² = 1: no change

Mass = amount of matter (kg); weight = gravity's pull on it (N) must know

Commonly confused

	Mass	Weight
What it is	How much matter an object has	The gravitational force on that matter
SI unit	Kilogram (kg)	Newton (N)
Changes with location?	No — same on Earth and the Moon	Yes — depends on local g
How to get it	Measured directly	w = mg (g = 9.8 m/s² on Earth)
1 kg on the Moon	Still 1 kg	About 1.7 N (9.8 N on Earth)

Both objects feel the same size pull — the lighter one moves more

"Weight" in kg is really mass — physics weight is in newtons

"Weightless" astronauts still feel gravity — they are in free fall

Show 3 more facts

G ≈ 6.674 × 10⁻¹¹ N·m²/kg² — gravity is the weakest basic force

Kepler 1: planets orbit the Sun in ellipses (Sun at one focus)

Tides come mainly from the Moon's gravity pulling on Earth's water

Pearl

Distance counts twice: double the gap and the pull drops to a quarter.

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