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

A – Canadian rural cash economyB – 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?

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…

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

Example:

• El Paso, Texas and Tucson, Arizona.

• El Paso population 703,127.

• Tucson population 790,755.

Population 1 X Population 2 distance 2

Example:• El Paso, Texas and Tucson,

Arizona.• El Paso population

703,127.• Tucson population

790,755.• The distance between the

two is 263 milesPopulation 1 X Population 2

distance 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

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

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…

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…

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?

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?

A. number of elderly and children in the city

B. square miles covered by the city

C. annual steel production of the entire city

D. total employment in offices in the entire city

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?

A. number of elderly and children in the city

B. square miles covered by the city

C. annual steel production of the entire city

D. total employment in offices in the entire city

Questions…

2. 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…

2. 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 distanceB) Services located directly to population and inversely to distanceC) 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 distanceB) Services located directly to population and inversely to distanceC) Services located directly to population and directly to distance