Grade 12 Physics · Little g from big G
Three symbols, three animals
score 0

Three symbols, three animals

Put a mass mm on a planet of mass MM and radius rr, then write the same force twice: GMmr2=mg\dfrac{GMm}{r^2} = mg. The little mass cancels off both sides — which is why a hammer and a feather land together — and what survives is g=GMr2g = \dfrac{GM}{r^2}, read aloud g equals big G M over r squared. Here gg is the gravitational field strength in m/s2\mathrm{m/s^2} (equivalently newtons per kilogram — the same unit wearing two hats), MM is the mass of the world making the field in kilograms, and rr is the distance from that world's centre in metres — its radius, if you are standing on it.

Keep the three symbols apart, because an exam will absolutely try to blur them. Big G is the universal constant, 6.67×10116.67 \times 10^{-11}, identical everywhere. Little g is local: 9.81 here, 1.62 on the Moon, and smaller still the moment you climb. Weight, W=mgW = mgW equals m g, with WW a force in newtons and mm the object's mass in kilograms — belongs to one particular object standing in one particular field. Your mass is your business; your weight is a negotiation with a planet.