Journal of International Economics 53: 1–27.īaldwin, R. The growth of world trade: Tariffs, transport costs, and income similarity. American Economic Review 93: 170–192.īaier, S., and J.H. Gravity with gravitas: A solution to the border puzzle. American Economic Review 69: 106–116.Īnderson, J.A., and E. A theoretical foundation for the gravity equation. Constant-elasticity-of-substitution (CES) preferencesĪnderson, J.A. In addition to explaining the amount of trade, this equation has been applied to foreign direct investment, the volatility of prices, and the impact of currency unions and free trade areas. We review the theoretical and empirical literature on the gravity equation. While it has been in use since the 1960s, its theoretical foundation has been known for a much shorter period, and recent years have seen an large amount of research on its derivation and estimation. The value of g is independent of the mass of the object and only dependent upon location - the planet the object is on and the distance from the center of that planet.The gravity equation explains the amount of trade between countries based on their economic sizes and the distance between them. Yet emerging from Newton's universal law of gravitation is a prediction that states that its value is dependent upon the mass of the Earth and the distance the object is from the Earth's center. The acceleration of gravity of an object is a measurable quantity. Using this equation, the following acceleration of gravity values can be calculated for the various planets. The value of g on any other planet can be calculated from the mass of the planet and the radius of the planet. The same equation used to determine the value of g on Earth' surface can also be used to determine the acceleration of gravity on the surface of other planets. This inverse square relationship is depicted in the graphic at the right. As the distance is tripled, the value of g decreases by a factor of 9. This inverse square relationship means that as the distance is doubled, the value of g decreases by a factor of 4. In fact, the variation in g with distance follows an inverse square law where g is inversely proportional to the distance from earth's center. The table below shows the value of g at various locations from Earth's center.Īs is evident from both the equation and the table above, the value of g varies inversely with the distance from the center of the earth. As shown below, at twice the distance from the center of the earth, the value of g becomes 2.45 m/s 2. For instance, if an object were moved to a location that is two earth-radii from the center of the earth - that is, two times 6.38x10 6 m - then a significantly different value of g will be found. And of course, the value of g will change as an object is moved further from Earth's center. If the value 6.38x10 6 m (a typical earth radius value) is used for the distance from Earth's center, then g will be calculated to be 9.8 m/s 2. 5.98x10 24 kg) and the distance ( d) that an object is from the center of the earth. The above equation demonstrates that the acceleration of gravity is dependent upon the mass of the earth (approx. This leaves us with an equation for the acceleration of gravity. Thus, m can be canceled from the equation. Now observe that the mass of the object - m - is present on both sides of the equal sign. First, both expressions for the force of gravity are set equal to each other. To understand why the value of g is so location dependent, we will use the two equations above to derive an equation for the value of g. As one proceeds further from earth's surface - say into a location of orbit about the earth - the value of g changes still. This would result in larger g values at the poles. They also result from the fact that the earth is not truly spherical the earth's surface is further from its center at the equator than it is at the poles. These variations result from the varying density of the geologic structures below each specific surface location. There are slight variations in the value of g about earth's surface. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s 2. In the first equation above, g is referred to as the acceleration of gravity. Where d represents the distance from the center of the object to the center of the earth. Now in this unit, a second equation has been introduced for calculating the force of gravity with which an object is attracted to the earth. In Unit 2 of The Physics Classroom, an equation was given for determining the force of gravity ( F grav) with which an object of mass m was attracted to the earth F grav = m*g
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