Explanation Calculation: Write the equation of acceleration of moon: a n = v 2 r (1) Write the Equation of attraction force between earth and moon. F = m a n (2) Here, m is the mass of moon. Find the mass of earth ( M ): Consider the Newton’s law of universal gravitation: F = G M m r 2 (3) Here, F is the attraction force, G is the universal constant, M is the mass of earth, and m is the mass of moon. Substitute Equation (2) in Equation (3). F = G M m r 2 m a n = G M m r 2 a n = G M r 2 (4) Substitute Equation (1) in Equation (4). v 2 r = G M r 2 G M = r v 2 v 2 = G M r (5) Write the equation for mass of planet: G M = g R 2 (6) Substitute Equation (6) in Equation (5). v 2 = g R 2 r v = R g r (7) Write the equation of velocity of earth: v = 2 π r Γ Γ = 2 π r v (8) Substitute Equation (7) in Equation (8). Γ = 2 π r R g r Γ 2 = 4 π 2 r 2 R 2 ( g r ) Γ 2 = 4 π 2 r 3 R 2 g r 3 = g Γ 2 R 2 4 π 2 r = [ g Γ 2 R 2 4 π 2 ] 1 3 (9) Find the radius of the moon’s orbit in SI units using Equation (9). r = [ g Γ 2 R 2 4 π 2 ] 1 3 Substitute 9

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ISBN: 9781260804638

Author: BEER

Publisher: MCG

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Chapter 12.2, Problem 12.81P

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Show that the radius r of the moon’s orbit can be determined from the radius (R) of the earth, the acceleration of gravity (g) at the surface of the earth, and the time (Γ) in SI and U.S Customary units.

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Chapter 12.2, Problem 12.80P

Chapter 12.2, Problem 12.82P

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Show that the radius r of the moon’s orbit can be determined from the radius ( R ) of the earth, the acceleration of gravity ( g ) at the surface of the earth, and the time ( Γ ) in SI and U.S Customary units.

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Show that the radius r of the moon’s orbit can be determined from the radius (R) of the earth, the acceleration of gravity (g) at the surface of the earth, and the time (Γ) in SI and U.S Customary units.

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Chapter 12 Solutions