Chapter 7, Problem 57P

a.

To determine

To find: The location of center of mass.

Answer to Problem 57P

  $x=4.66\times {10}^6$ m

So the CM of the system is at a distance of 4.66×10⁶m from the earth , towards the moon.

Explanation of Solution

Given:

Masses of Earth and Moon are 5.98×10²⁴kg and 7.35×10²²kg.

Their centers are separated by 3.84×10⁸m.

Formula used:

  $x=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

Here, m₁ and m₂ are the masses of Earth and Moon respectively.

Calculation:

Let the earth is the origin

Then x₁₌0, x₂= 3.84×10⁸m

m₁= 5.98×10²⁴kg and m₂= 7.35×10²²kg

  $x=\frac{0+\left(7.35\times {10}^{22}\times 3.84\times {10}^8\right)}{5.98\times {10}^{24}+7.35\times {10}^{22}}$

  $x=\frac{28.224\times {10}^{30}}{598\times {10}^{22}+7.35\times {10}^{22}}$

  $x=\frac{28.224\times {10}^{30}}{605.35\times {10}^{22}}$

  $x=0.0466\times {10}^8$

  $x=4.66\times {10}^6$ m

So the CM of the system is at a distance of 4.66×10⁶m from the earth , towards the moon.

b.

To determine

To explain: The information about the motion of Earth Moon system about the sun, and of the earth and moon separately about the sun.

Explanation of Solution

Introduction:

Earth is in orbit moves around the Sun and Moon orbit around the Earth. Earth’s rotation takes place in 24 hours. Earth takes one year to complete one orbit around the Sun.

It is known that Earth rotates on its axis and also revolve around the Sun. The Earth-Moon system revolve around the Sun, then solar eclipse is produced.

When Earth revolve around the sun, it produces different seasons and leap year. Moon takes 29 days to reach the same position with respect to the sun.