# To describe: The reason for the name "gravity model".

To describe: The reason for the name "gravity model".
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Given: The number of daily phone calls between two cities varies jointly as their populations and varies inversely as the square of the distance between them. The above stated model is called as gravity model.
Definition used:
(1) Joint Variation:Joint variation is a variation in which a variable varies direcly as the product of two or more other variables. Thus, the equation y = kxz, is read y varies jointly as x and z.
(2) Inverse Variation: If a situation is described by an equation in the form $y=\frac{k}{x}$, where k is a nonzero variation constant, then it can be said that y varies inversely as x or y is inversely proportional to x.
Description:
Let the average number of daily phone calls is represented as C and population of two cities are respectively.
The distance between two cities be represented as d.
From definition (1), the given "The C between the two cities varies jointly as the product of their population" can be expressed as,
$C=k{P}_{1}{P}_{2}\left(1\right)$
Similarly by the definition (2) the given "The C varies inversely as the as the square of distance" can be expressed as,
$C=\frac{k}{{d}^{2}}\left(2\right)$
Combine the equation (1) and equation (2) as follows.
$C=\frac{k{P}_{1}{P}_{2}}{{d}^{2}}\left(3\right)$
From equation (3), the given model can be expressed as $C=\frac{k{P}_{1}{P}_{2}}{{d}^{2}}$, where k is the constant of variation.
In general, the newton's formula for gravitation is $F=\frac{G{m}_{1}{m}_{2}}{{d}^{2}},$ where G is the gravitational constant,
The above formula indicates the gravitational force between two objects in the universe. On comparing the gravitational formula with given model, it is observed to be in similar form of joint variation.
Thus, the given model is called as gravity model.