Meanings of the J terms

# Meanings of the J terms - Meanings of the J terms The Ji...

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Meanings of the J terms The J i terms are dimensionless constants showing the relative sizes of the terms in the latitudinal expansion of the geopotential in Legendre Polynomials. Basically, the i denotes how many maxima the (axially symmetric) term has, as shown here: Note that this is the relative size of the geopotential term, it is not necessarily the shape of the body - a density variation can cause these variations in the geopotential without the body being mis-shapen at all. (Gnereally it will be a mixture of shape and density variations.) Earth Tides We can look at the deformation of a primary body being acted upon by a secondary:

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The gravitational attraction at A due to M depends on R'. The acceleration due to the moon, g A , is (g Ar ,g Ap ) in the r and psi directions shown on the diagram. Now if P is the angle psi shown on the diagram, and P' the angle psi-dashed: g Ar = (GM/R' 2 ) cos P' g Ap = -(GM/R' 2 ) sin P' and the Tidal Acceleration is the difference between the acceleration of the point A and the
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## This note was uploaded on 12/15/2011 for the course AST AST1002 taught by Professor Emilyhoward during the Fall '10 term at Broward College.

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Meanings of the J terms - Meanings of the J terms The Ji...

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