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Olympic Physics: Air Density and Bob Beamon’s Crazy-Awesome Long Jump

• http://www.wired.com, By Rhett Allain

First, let’s look at gravity. On the surface of the Earth, the usual model for gravitational force is the object’s mass times the gravitational field (represented by g) where g is about 9.8 Newtons per kilogram. So, a 1 kg object would have a gravitational force of 9.8 Newtons (directed down).

However, this model doesn’t work if you get too far from the surface. Really, the gravitational force is an interaction between two objects with mass, and the magnitude of this force decreases as the two objects get farther away.

 

In this expression, G is the gravitational constant (not to be confused with “g”). ME an RE are the mass and radius of the Earth and h is the height above the surface.

 

Which gets you back to the gravitational force being “mg.” Also, since the radius of the Earth is around 6,000 km, a height of 100 meters above the surface doesn’t change the force too much. But what about a place like Mexico City with an elevation of 2,240 meters above sea level? With that value for h, an object would have weight that is 99.93% the weight of the object at sea level. Not a big difference, no. But is it a big enough difference to mean a new world-record long jump? 

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