Gravity Model

The gravity model is a simple mathematical formulation used to model the interaction between two locations. It has been used to account for a wide variety of interactions such as telephone calls, automobile trips, and migration and merchandise flows. The model takes the form

where Iij is the interaction between places i and j, k is an empirically determined constant, Pi and Pj are measures of the importance (or mass) of i and j (e.g., their populations), dij is the distance between i and j, and b is the friction of distance, an empirically derived parameter that represents the difficulty or cost of moving between i and j.

The gravity model is based on the law of physical gravitation, expressed as

where Fij is the gravitational attraction between two objects with masses Mi and Mj separated by a distance of dij and G is the gravitational constant. The gravity model is an example of a model from the social physics school. The proponents of these models attempted to adapt the ideas and concepts of physical science, especially those of Newtonian physics and Darwinian ecology, to explain human patterns and processes. E. G. Ravenstein, writing about migration during the late 19th century, often is credited with being the first person to apply the gravity concept to social science when he observed that more migrants travel short distances than travel long distances and that long-distance migrants tended to move to large centers.

The basic gravity model was incorporated into a variety of more complicated and sophisticated formulations used to describe the spatial extent of markets, the geographic distribution of demand, and transportation flows. W. J. Reilly used the gravity concept in the development of his “law of retail gravitation” that, among other things, delimited the market boundaries between cities. J. Q. Stewart and others developed potential models that characterized the interaction of a place with all other places. The results of these calculations typically were represented as potential surfaces that displayed the potential of all places in the study area simultaneously. That is, place i's population potential is calculated as

where Mj is the population of j, dij is the distance between i and j, and x is the friction of distance. Other potential surfaces can be created to describe the spatial distribution of other phenomena. For example, by substituting a measure of disposable income or retail expenditures for population, market potential, an estimate of the spatial distribution of demand, can becalculated.

Today the gravity model is used most commonly in transportation geography and planning. Its flexibility and adaptability allow it to provide an accurate fit to data from a wide variety of situations and problems. Some have criticized the gravity model because they see little connection between the model's theoretical rationale and the problems to which it is applied. Critics also note that use of the model tends to support the status quo and the distribution of resources at the time the model is applied.