Refer Example 10.3 concerning the deflection from the plumb line of a particle falling in Earth€™s gravitational field. Take g to be defined at ground level and use the zeroth order result for the time-of-fall, T = √2h/g. Perform a calculation in second approximation (i.e., retain terms in w2) and calculate the southerly deflection. There are three components to consider;
(a) Coriolis force to second order (C1),
(b) Variation of centrifugal force with height (C2), and
(c) Variation of gravitational force with height (C3).




Show that each of these components gives a result equal to with C1 = 2/3, C2 = 5/6, and C3 = 5/2. The total southerly deflection is therefore (4h2w2 sin λ cos λ)/g.

h2 w2 sin A cos A