Gravity Model

What is the gravity model? A model that holds that the potential use of a service at a particular location is directly related to the number of people in a location and inversely related to the distance people must travel to reach the service. It can be put into a formula: Population 1 X Population 2 distance 2

What does the gravity model do? It predicts spatial interaction. Spatial interaction: Daily commuting, e-mail, travel, international trade. Remember Ullman’s theory

Ullman’s Theory Chicago Travel Patterns: shows 96% of all trips. What factors influence and create these patterns of interaction?

Edward Ullman’s Theory Spatial Interaction is controlled by three flow-determining factors. Complementarity Transferability Intervening Opportunity Travel patterns for purchase of clothing and yard goods. A) Canadian rural cash-economy. B) Canadian older Mennonite sect. A – Canadian rural cash economy B – Canadian older Mennonite sect

What does the Gravity Model Illustrate? It illustrates that spatial interaction in not based solely upon distance because it also incorporates population as a factor as well.

What kind of model is the Gravity Model? It is a mathematical model. Interaction between two places is directly proportional to the sizes of their populations and inversely proportional to the distance separating them.

What kind of model? Mathematical. Interaction between two places is directly proportional to the sizes of their populations and inversely proportional to the distance separating them.

Illustrate the gravity model… Home J The shorter the distance between two objects the greater the mass of either (or both) objects, the greater the gravitational pull between the objects

Which has a greater bond? NYC and Los Angeles or El Paso and Tucson. Use the gravity model.

Population 1 X Population 2 Example: El Paso, Texas and Tucson, Arizona. El Paso population 703,127. Tucson population 790,755. Population 1 X Population 2 distance 2

Population 1 X Population 2 Example: El Paso, Texas and Tucson, Arizona. El Paso population 703,127. Tucson population 790,755. The distance between the two is 263 miles Population 1 X Population 2 distance 2

Population 1 X Population 2 Example: El Paso, Texas and Tucson, Arizona. El Paso population 703,127. Tucson population 790,755. Equals 556,001,190,885. The distance between the two is 263 miles. 263 miles squared = 69,169 Population 1 X Population 2 distance 2

Population 1 X Population 2 Example: Population - Equals 556,001,190,885. The distance between the two is 263 miles. 263 miles squared = 69,169 Population 1 X Population 2 distance 2 The math works out to 8,038,300 El Paso (Texas) and Tucson (Arizona). We multiply their populations (703,127 and 790,755) to get 556,001,190,885 and then we divide that number by the distance (263 miles) squared (69,169) and the result is 8,038,300. Therefore, the bond between New York and Los Angeles is greater than that of El Paso and Tucson!

Population 1 X Population 2 Example: NYC metropolitan population 20,124,377. LA metro population 15,781,273. Distance 2462 miles. Population 1 X Population 2 distance 2 Do the math… Thus, if we compare the bond between the New York and Los Angeles metropolitan areas, we first multiply their 1998 populations (20,124,377 and 15,781,273, respectively) to get 317,588,287,391,921 and then we divide that number by the distance (2462 miles) squared (6,061,444). The result is 52,394,823. We can shorten our math by reducing the numbers to the millions place - 20.12 times 15.78 equals 317.5 and then divide by 6 with a result of 52.9.

Example: NYC metropolitan population 20,124,377. LA metro population 15,781,273. Distance 2462 miles. 317,588,287,391,921 6,061,444 Do the math… Thus, if we compare the bond between the New York and Los Angeles metropolitan areas, we first multiply their 1998 populations (20,124,377 and 15,781,273, respectively) to get 317,588,287,391,921 and then we divide that number by the distance (2462 miles) squared (6,061,444). The result is 52,394,823. We can shorten our math by reducing the numbers to the millions place - 20.12 times 15.78 equals 317.5 and then divide by 6 with a result of 52.9.

Which has the great pull? Example: NYC metropolitan population 20,124,377. LA metro population 15,781,273. Distance 2462 miles. 317,588,287,391,921 6,061,444 The result is 52,394,823 Which has the great pull? Thus, if we compare the bond between the New York and Los Angeles metropolitan areas, we first multiply their 1998 populations (20,124,377 and 15,781,273, respectively) to get 317,588,287,391,921 and then we divide that number by the distance (2462 miles) squared (6,061,444). The result is 52,394,823. We can shorten our math by reducing the numbers to the millions place - 20.12 times 15.78 equals 317.5 and then divide by 6 with a result of 52.9. NYC and LA

Questions…. 1. If you were fitting a gravity model for Federal Express package flows between cities, which of the following would be best to substitute for total city population in the gravity model formula? number of elderly and children in the city square miles covered by the city annual steel production of the entire city total employment in offices in the entire city

Questions…. If you were fitting a gravity model for Federal Express package flows between cities, which of the following would be best to substitute for total city population in the gravity model formula? number of elderly and children in the city square miles covered by the city annual steel production of the entire city total employment in offices in the entire city

Questions… Using the graphic and the concepts of the gravity model to answer the question. Bob is considering selling his house and moving, which of the following cities is he most likely going to move to? City A, B or C?

Questions… Using the graphic and the concepts of the gravity model to answer the question. Bob is considering selling his house and moving, which of the following cities is he most likely going to move to? City C

Questions… 3. Applying the gravity model to services you would see: A) Services located inverse to population and directly to distance B) Services located directly to population and inversely to distance C) Services located directly to population and directly to distance

Questions… 3. Applying the gravity model to services you would see: A) Services located inverse to population and directly to distance B) Services located directly to population and inversely to distance C) Services located directly to population and directly to distance