MadSci Network: Physics |
Some very simple considerations will sort this one out. The universal law of gravitation gives us the equation F = G*m1*m2/r^2. For an object on the surface of the earth, the value of r is about 6370 km. A 2 km altitude increase means a change in r of +0.03% (3 parts in 10 000) which means a change in gravitational force of -0.06%. This difference is negligible, particularly when you consider that there is a difference of about 1% stronger at the poles than the equator. This is firstly because the poles at the earth's surface are about 25 km closer to the centre of the earth than the equator, and secondly because the centrifugal force of the earth's rotation causes an apparent decrease in gravitational force at the equator, but not at the poles. What about temperature and humidity? Well, I am no great expert on American climatology, but I do not believe that Denver, in spite of its altitude, would be near the American extreme of either. There are low altitude towns that are colder and drier (Edmonton, Canada), warmer and drier (San Diego), colder and wetter (legion) and warmer and wetter (most of the SouthEast US). There is another factor that has been overlooked in your discussion, and I think it is almost certainly the most important one. What about the air pressure? The air presssure at the altitude of Denver (1600 m if "mile high" stadium means what it says) is only about 80% of that at sea level. That 20% difference makes a huge difference to the flight of a ball, in terms of the reduced viscous drag of the air. Firstly, the spin imparted to the ball will not "take" as well in the flight, somewhat defeating the pitcher's wiles. Secondly, the ball itself will fly faster and further, once decently hit, because there will be less friction. Our Australian national rugby football team recently played, effectively for the world championship, in Johannesburg, South Africa. Jo-burg is at a similar altitude to Denver. There were a lot of comments pre-match about the unusual flight of the ball, and certainly our team were soundly defeated when they failed to judge it correctly (or at least, that is a good excuse ;-)
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