Classical Dynamics of Particles and Systems · Problem 5-17

Calculus of Variations — Marion & Thornton

Physics — Mechanics · tidal-height-newtons-model

Problem

Newton's model of the tidal height, using the two water wells dug to the center of Earth, used the fact that the pressure at the bottom of the two wells should be the same. Assume water is incompressible and find the tidal height difference hh, Equation 5.55, due to the Moon using this model. (Hint: ∫0ymax⁡ρgy dy=∫0xmax⁡ρgx dx\int_0^{y_{\max}} \rho g_y\, dy = \int_0^{x_{\max}} \rho g_x\, dx; h=xmax⁡−ymax⁡h = x_{\max} - y_{\max}, where xmax+ymax=2Rearthx_{max} + y_{max} = 2R_{\text{earth}}, and RearthR_{\text{earth}} is Earth's median radius.)

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