Gravity Model in AP Human Geography

Step one: borrowing Newton's pull for cities

The model takes its name and logic from Newton's law of gravitation, where two objects pull on each other harder when they have more mass and are closer together. Geographers swapped mass for population and applied the same idea to places.

In AP Human Geography, it's named in Topic 6.4 (The Size and Distribution of Cities) in Unit 6, alongside the rank-size rule, the primate city, and Christaller's central place theory. Together, these concepts help explain city size and distribution. The gravity model specifically helps predict interaction between places. It also puts numbers on two Topic 1.4 spatial concepts, flows and distance decay, which is why it gets tagged across so many units.

Step two: setting up the P1 × P2 ÷ D² formula

The usual version is:

Interaction = (Population 1 × Population 2) ÷ Distance²

Some versions divide by plain distance instead of distance squared. Either way, size sits on top and pushes interaction up, and distance sits on the bottom and drags it down. Squaring the distance makes the distance penalty grow fast, so places far apart lose interaction quickly.

Step three: comparing two city pairs without a calculator

Calculators aren't permitted on this exam, so any numbers you see will be built to work out by hand. Here's the kind of comparison to expect.

Pair 1 is a city of 4 million and a city of 1 million, 200 miles apart. Pair 2 is two cities of 2 million each, 100 miles apart. Use millions for population and hundreds of miles for distance to keep it simple.

• Pair 1: (4 × 1) ÷ 2² = 4 ÷ 4 = 1
• Pair 2: (2 × 2) ÷ 1² = 4 ÷ 1 = 4

Both pairs have the same population product (4), but Pair 2 is half as far apart, so the model predicts four times as much interaction. That's the squared distance at work. On a multiple-choice question, a quantitative stimulus might give you a small table like this and ask which pair has the most migration or trade. Often you can rank the pairs just by spotting which has the biggest populations and the shortest distance.

Step four: where the prediction breaks down

The model assumes distance is the only thing slowing interaction down. Real flows don't always cooperate, and pointing this out is good analysis on a free-response question.

Intervening obstacles from Topic 2.10, such as a national border, a language difference, or a strict immigration policy, can cut flows between two large, close places. Intervening opportunities work too: a city in between can capture migrants who would otherwise go farther. Chain migration can keep a long-distance corridor busy because family networks already exist at the destination.

Time-space compression from Topic 1.4 also weakens the distance penalty. Cheap flights and the internet let far-apart places interact heavily, which ties to the faster cultural contact described in Topic 3.6.

Step five: using size and distance in the stimulus-based FRQs

Free-response questions often draw on more than one unit, so the gravity model fits well in Question 2 (One-stimulus question) or Question 3 (Two-stimuli question). For example, a prompt might show a map of migration flows or a data set of commuting between cities and ask you to explain the pattern.

A top answer names both variables and connects them to the specific flow: "More people move between these two cities because both have large populations and they are relatively close, so the gravity model predicts strong interaction." Then, if the data shows an exception, explain it with a barrier, an intervening opportunity, or time-space compression. Naming the model without tying it to the places in the stimulus usually won't earn the explanation point.

Gravity model vs. distance decay vs. central place theory

Two huge metro areas on opposite coasts can interact more than two small towns an hour apart, and distance decay alone can't explain that. Distance decay is one variable: interaction drops as distance increases. The gravity model includes that but adds population size, so size can outweigh the distance penalty. If an answer choice mentions only distance, think distance decay. If it involves size or population too, think gravity model.

Central place theory is the other trap. It explains the spacing of cities in a hierarchy using threshold and range for goods and services. The gravity model predicts the amount of flow between specific places. And a question about a city's population being tied to its rank is testing the rank-size rule, not gravity.