The Gravity Model in Geography

Gravity Model (Movement in Space)
(along with interpretation)

The main aim of researchers using the gravity model is to predict the amount of movement between places in a given period of time. It predicts the movement of large groups of people, not individual people. It is the scale of movement which will affect the character of towns and regions.

This model is based on Newton’s famous law: ‘any two bodies attract one another with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.’ If F is the force, M1 and M2 the masses of the two bodies, D their distance apart and G a ‘universal constant of nature’ called the gravitational constant, this law can the expressed as:

Note that as the distance D between the bodies increases, D2 increases, and the force F between them decreases (inverse or negative relationship). If the masses M1 and/or M2 increase, so does the force F increase (direct or positive relationship). such a law is applied to the gravitational force between interstellar bodies.

A number of social scientists during the late nineteenth and early twentieth century applied the idea of the model to the movement of the people. Ravenstein considered that the extent of migration between one place to another varied directly with the number of people available to move and inversely with the distance they would have to move. The analogy was made explicit by Warntz, a Harvard geographer, during the 1940s. His aim was to predict the amount of interaction, Iij, between two towns i and j, over a given time period. Migration could be one type of interaction. The two towns replace the two bodies, their population pi and pj represented their masses-

In social science, G is a constant of proportionality which ensures that the extent of interaction predicted approximates the actual movement. It will be related to the average number of moves per capita.

The Reilly Model:

Reilly applied the principles of the gravity model to the problem of delimiting market areas. He stated that two centers attract trade from intermediate places approximately in direct proportion to the sizes of the centers and in inverse proportion to the square of the distances from these two centers to the intermediate place. From these principles, he derived a ‘Breaking Point’ equation. The breaking point between two towns divides the people who will travel to one town from those who will travel to another town for similar services. If enough breaking points can be established around a town, its theoretical urban field can be delimited in that way. The position of the breaking point (x) between two towns (i and j) can be calculated by using the following formula, in which Pi and Pj are the populations of the two towns and djx is the distance of the breaking point from a smaller town, j

Thus if two towns with populations of 40,000 and 5,000 respectively are located 18 km apart, the breaking point will be at a distance of 4.9 km from the smaller town.

The use of population size as the force of attraction on either side of the breaking point is obviously open to criticism. However, the technique can be modified in a variety of ways by using other indicators such as the size of the working population rather than the total population, or the number of retail service outlets in each town. Another modification of the basic formula involves expressing the distance between the two urban centers in terms of time. In this way, the breaking point can be established as lying at a certain travel time from each town.

	Population	dij	djx
Hyderabad	3,091,726
Nizamabad	412,683	200 km	53.5
Sholapur	928,829	300 km	106
Kurnool	767,185	300km	99.7
Surjapet	338,039	120km	29.8
Warangal	545,801	130km	38.4
Siddipet	327,841	80km	28.2
Farooknagar	16,313	50km	3.38

 Formula Used: 

d_ij=distance from small to big town (km)

d_jx= breakpoint distance

P_i= population of the big town

P_j= population of small town

Another Exercise Solved Download PDF. 

The pdf has an interpretation attached of the Gravity Model Exercise.