(a) Explanation The figure 1 shows the three systems of particles (Sun, Earth, and Moon) position along x and y axis. Refer problem 23, by using the situation, placing the sun is at the center of origin and the total mass of the system is approximately equal to the mass of the sun. Write the expression for total mass of the system. M = m Sun + m Earth + m Moon (I) Here, M is the total mass of the system, m Sun is the mass of the Sun, m Earth is the mass of the Earth, and m Moon is the mass of the Moon. This three particle system, the x center of mass is calculated using Equation 10.3. The sun is at the origin so its position is zero. The Earth and the Moon are both at the same x position 1.50 × 10 11 m . Write the expression for center of mass of the Earth-Moon system. x CM = 1 M ( m Earth + m Moon ) x 1 + m Sun x 2 (II) Here, x CM is the center of mass of the system along x axis, x 1 is the position of the Earth-Moon system, and x 2 is the position of the Sun is situated at the origin. Write the expression for y center of mass of the Earth position is zero. y CM = m Earth x 1 + m Sun x 2 + m Moon x 3 M (III) Here, y CM is the center of mass of the system along y axis, x 1 is the position of the Earth, x 2 is the position of the Sun is situated at the origin, and x 3 is the position of the Moon from Earth. Conclusion: Substitute 1.99 × 10 30 kg for m Sun , 5.98 × 10 24 kg for m Earth , and 7.35 × 10 22 kg for m Moon in the equation (I) to find M . M = 1.99 × 10 30 kg + 5.98 × 10 24 kg + 7.35 × 10 22 kg = 1.99 × 10 30 kg + 0.00000598 × 10 30 kg + 0.0000000735 × 10 30 kg = 1.99 × 10 30 kg Substitute 1.99 × 10 30 kg for M , 1.99 × 10 30 kg for m Sun , 5 (b) To determine The dominant mass in the system.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN: 9781133939146

Author: Katz, Debora M.

Publisher: Cengage Learning

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Question

Chapter 10, Problem 24PQ

(a)

To determine

The center of mass of the Earth-Moon system.

(b)

To determine

The dominant mass in the system.

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Chapter 10, Problem 23PQ

Chapter 10, Problem 25PQ

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