The Gravity Model of Interaction

Borrowed straight from physics, the gravity model says interaction between two places works like gravitational pull: bigger masses attract more, and pulling apart weakens the attraction fast. In geography, population stands in for mass. The formula is interaction = (population 1 x population 2) / distance^2. Multiply the two populations first, since a huge city paired with a tiny town still generates a lot of potential interaction. Then divide by distance squared, not just distance, because the squaring makes far-apart places drop off in interaction much faster than near ones. That squared term is why a city 900 km away loses out so badly to one only 400 km away, even if the far one is bigger.

The model is used to predict things like migration flows, commuting, phone calls, trade, or shopping trips between city pairs. It does not give a real count of trips or dollars; it gives a comparative score, useful for ranking which pair interacts more than another. Planners and geographers use it alongside distance decay, the general idea that interaction fades as distance grows, and it pairs naturally with central place theory: bigger places with more services pull in surrounding populations the way the gravity model predicts.

This connects back to the three urban models and Christaller's hexagons earlier in the unit, since all of them are about how city size and spacing shape interaction and service areas. The gravity model gives that intuition a number. Changing the exponent on distance, from 1 to 2 or higher, shows how sensitive the model is to how sharply we assume interaction decays with distance.