How is Newtonian Mechanics contradictory to Special Relativity at a certain parameter and what conditions must be met for Newtonian Mechanics to be a suitable model for describing systems?
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Newtonian mechanics works fine when dealing with gravitational fields like that of the earth and speeds as fast as an orbiting satellite. Under those conditions, the difference between the predictions of newtonian mechanics and special relativity are very tiny.
I think the parameter you mentioned is called the lorentz factor or gamma, which measures how much difference there would be between these two sets of predictions. Gamma is defined as
gamma = 1/(sqrt(1-v^2/c^2) where
c is the speed of light and v is your velocity. If you are going less than about 25% of the speed of light, gamma is close to 1 and the difference will be small- so in this case, newtonian mechanics is a good approximation.
niels nielsen
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