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### Calculation of Weight on the Moon

**Problem**:  
The Moon’s mass is 1/80 that of Earth, and the lunar radius is 1/4 Earth’s radius. Based on these figures, calculate the total weight on the Moon of a 100-kg astronaut with a 50-kg spacesuit and backpack, relative to his or her weight on Earth.

#### Step-by-Step Solution:

1. **Understanding the Figures**:  
    - Mass of the Moon \(M_{\text{Moon}} = \frac{1}{80} \times M_{\text{Earth}}\)
    - Radius of the Moon \(R_{\text{Moon}} = \frac{1}{4} \times R_{\text{Earth}}\)

2. **Gravitational Force Formula**:  
    The weight of an object is determined by the gravitational force, which is given by the formula:
    \[
    F = \frac{G \times m_1 \times m_2}{r^2}
    \]
    Here, \(F\) is the gravitational force, \(G\) is the universal gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between the centers of the two objects (the radius of the planet in this case).

3. **Setting Up the Weight Comparison**:
    We need to compare weights on Earth and the Moon. Since \(G\), the astronaut's mass (\(m\)), and the mass of the equipment (\(m_{\text{equipment}}\)) are constants, we can use:
    \[
    \frac{W_{\text{Moon}}}{W_{\text{Earth}}} = \frac{M_{\text{Moon}}}{M_{\text{Earth}}} \times \left(\frac{R_{\text{Earth}}}{R_{\text{Moon}}}\right)^2
    \]

4. **Substitute Known Values**:
    \[
    W_{\text{Moon}} = W_{\text{Earth}} \times \left(\frac{1/80}{1} \times \left(\frac{4}{1}\right)^2\right)
    \]
    Simplify the equation:
    \[
    W_{\text{Moon}} = W_{\text{Earth}} \times \left(\frac{1}{80} \times
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Transcribed Image Text:### Calculation of Weight on the Moon **Problem**: The Moon’s mass is 1/80 that of Earth, and the lunar radius is 1/4 Earth’s radius. Based on these figures, calculate the total weight on the Moon of a 100-kg astronaut with a 50-kg spacesuit and backpack, relative to his or her weight on Earth. #### Step-by-Step Solution: 1. **Understanding the Figures**: - Mass of the Moon \(M_{\text{Moon}} = \frac{1}{80} \times M_{\text{Earth}}\) - Radius of the Moon \(R_{\text{Moon}} = \frac{1}{4} \times R_{\text{Earth}}\) 2. **Gravitational Force Formula**: The weight of an object is determined by the gravitational force, which is given by the formula: \[ F = \frac{G \times m_1 \times m_2}{r^2} \] Here, \(F\) is the gravitational force, \(G\) is the universal gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between the centers of the two objects (the radius of the planet in this case). 3. **Setting Up the Weight Comparison**: We need to compare weights on Earth and the Moon. Since \(G\), the astronaut's mass (\(m\)), and the mass of the equipment (\(m_{\text{equipment}}\)) are constants, we can use: \[ \frac{W_{\text{Moon}}}{W_{\text{Earth}}} = \frac{M_{\text{Moon}}}{M_{\text{Earth}}} \times \left(\frac{R_{\text{Earth}}}{R_{\text{Moon}}}\right)^2 \] 4. **Substitute Known Values**: \[ W_{\text{Moon}} = W_{\text{Earth}} \times \left(\frac{1/80}{1} \times \left(\frac{4}{1}\right)^2\right) \] Simplify the equation: \[ W_{\text{Moon}} = W_{\text{Earth}} \times \left(\frac{1}{80} \times
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