10-13. Refer to Example 10.3 concerning the deflection from the plumb line of a particle falling in Earth's gravitationa

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10 13 Refer To Example 10 3 Concerning The Deflection From The Plumb Line Of A Particle Falling In Earth S Gravitationa 1 (202.96 KiB) Viewed 38 times

10-13. Refer to 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 = V2h/g. Perform a calculation in second approximation (i.e., retain terms in wº) and calculate the southerly deflec- tion. There are three components to consider: (a) Coriolis force to second order (C), (b) variation of centrifugal force with height (C2), and (c) variation of gravi- tational force with height (C3). Show that each of these components gives a result equal to h2 C, wº sin cos , 8 with C, = 2/3, C2 = 5/6, and Cg (4h²o2 sin , cos 1)/g. 5/2. The total southerly deflection is therefore