Question

4. (10 points) Tidal force According to Taylor, the tidal force on Earth's ocean due to the moon is given by Eq. (9.12) (a) What is the physical meaning of the two terms in this equation? (b) If the Law of Gravitation is given by Gm,m, where r, is the distance between m ,and m2. 12 then what is the modified formula for the tidal force?

Answer 1

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(a) We know that tidal force is difference between the gravitational force at two different distances from question F_tid = -G M_m m d^^/d^2 + G M_m m d^^_0/d^2_0 In this expression first term is Gravitational force at outer surface of the mass Second term rightarrow Gravitational force at the center of mass (b) From Law of Gravitation Vertical-bar F vector Vertical-bar = G m_1 m_2/r^2_12 r^2_12 = (r_12 + Delta r)^2, n^^_12 = r vector_12/r_12 F vector = G m_1 m_2/r^2_12 rightarrow due of center of mass = G m_1 m_2/(r_12 + Delta r)^2 rightarrow due to outer surface of mass Therefore F_tidal = G m_1 m_2 r^^_12 {1/r^2_12 - 1/r_12 + Delta r)^2} = G m_1 m_2 r^^_12 {r_12 + Delta r)^2 - r^2_12/r^2_12 (r_12 + Delta r)^2} Delta r < < r_12 = G m_1 m_2 r_12 {2 r_12 Delta r/r^4_12 + 2 r^3_12 Delta r + r^2_12 Delta r^2} Since Delta r < < r_12