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Which approximation replaces the distance from the Earth's centre by a constant?

  • A.The shallow atmosphere approximation
  • B.The traditional approximation, which discards the cosine terms of the Coriolis force in the equations
  • C.The hydrostatic approximation
  • D.The Boussinesq approximation, in which density is held constant except where it multiplies gravity

Answer: A

Since the atmosphere is only about ten kilometres deep against an Earth radius of six thousand four hundred kilometres, replacing the radial distance by the mean radius introduces an error of well under one per cent. The approximation is applied together with the traditional approximation to preserve conservation of angular momentum and energy. Hydrostatic and Boussinesq approximations concern the vertical momentum equation and the treatment of density respectively.

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