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The mass of the earth is 6×10^24kg and that of the moon is 7.4×10^23kg. If the distance between the earth and the moon is 3.84×10^5, calculate the force exerted by the earth on the moon.Take G=6.67×10^-11 Nm^2/kg^2.?
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The mass of the earth is 6×10^24kg and that of the moon is 7.4×10^23kg...
To calculate the gravitational force exerted by the Earth on the Moon, we can use Newton's law of universal gravitation, which is given by the formula:
F = G * (m1 * m2) / r²
Where:
- **F** is the gravitational force between the two masses.
- **G** is the gravitational constant (6.67 × 10^-11 Nm²/kg²).
- **m1** is the mass of the Earth (6 × 10²⁴ kg).
- **m2** is the mass of the Moon (7.4 × 10²³ kg).
- **r** is the distance between the two masses (3.84 × 10⁵ m).
Step-by-step Calculation
1. **Substituting known values into the formula**:
F = (6.67 × 10^-11) * (6 × 10²⁴) * (7.4 × 10²³) / (3.84 × 10⁵)²
2. **Calculating the denominator**:
- r² = (3.84 × 10⁵)² = 1.47456 × 10¹¹ m²
3. **Calculating the numerator**:
- m1 * m2 = (6 × 10²⁴) * (7.4 × 10²³)
= 44.4 × 10⁴⁷ kg²
4. **Putting it all together**:
F = (6.67 × 10^-11) * (44.4 × 10⁴⁷) / (1.47456 × 10¹¹)
5. **Final computation**:
F ≈ (2.96468 × 10³7) / (1.47456 × 10¹¹) ≈ 2.01 × 10² N
Conclusion
The gravitational force exerted by the Earth on the Moon is approximately 2.01 × 10² N. This demonstrates the significant gravitational interaction between these two celestial bodies.
F = G * (m1 * m2) / r²
Where:
- **F** is the gravitational force between the two masses.
- **G** is the gravitational constant (6.67 × 10^-11 Nm²/kg²).
- **m1** is the mass of the Earth (6 × 10²⁴ kg).
- **m2** is the mass of the Moon (7.4 × 10²³ kg).
- **r** is the distance between the two masses (3.84 × 10⁵ m).
Step-by-step Calculation
1. **Substituting known values into the formula**:
F = (6.67 × 10^-11) * (6 × 10²⁴) * (7.4 × 10²³) / (3.84 × 10⁵)²
2. **Calculating the denominator**:
- r² = (3.84 × 10⁵)² = 1.47456 × 10¹¹ m²
3. **Calculating the numerator**:
- m1 * m2 = (6 × 10²⁴) * (7.4 × 10²³)
= 44.4 × 10⁴⁷ kg²
4. **Putting it all together**:
F = (6.67 × 10^-11) * (44.4 × 10⁴⁷) / (1.47456 × 10¹¹)
5. **Final computation**:
F ≈ (2.96468 × 10³7) / (1.47456 × 10¹¹) ≈ 2.01 × 10² N
Conclusion
The gravitational force exerted by the Earth on the Moon is approximately 2.01 × 10² N. This demonstrates the significant gravitational interaction between these two celestial bodies.
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The mass of the earth is 6×10^24kg and that of the moon is 7.4×10^23kg. If the distance between the earth and the moon is 3.84×10^5, calculate the force exerted by the earth on the moon.Take G=6.67×10^-11 Nm^2/kg^2.?
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