Weight Ratio: Earth vs Moon Explained

The weight of an object depends on its mass and the acceleration due to gravity at its location. The formula for weight (\(W\)) is:

\(W = m \times g\)

Where:

• \(m\) is the mass of the object (constant).
• \(g\) is the acceleration due to gravity.

Calculating Weight on Earth and Moon

Let \(W_e\) be the weight on Earth and \(W_m\) be the weight on the Moon.

• Weight on Earth: \(W_e = m \times g_e\)
• Weight on Moon: \(W_m = m \times g_m\)

Here, \(g_e\) is the acceleration due to gravity on Earth, and \(g_m\) is the acceleration due to gravity on the Moon.

Determining the We/Wm Ratio

To find the ratio \(W_e / W_m\), we divide the weight on Earth by the weight on the Moon:

\( \frac{W_e}{W_m} = \frac{m \times g_e}{m \times g_m} \)

Since the mass (\(m\)) is constant, it cancels out:

\( \frac{W_e}{W_m} = \frac{g_e}{g_m} \)

Gravity Values and Ratio Calculation

The acceleration due to gravity on Earth (\(g_e\)) is approximately \(9.8 \, \text{m/s}^2\). The acceleration due to gravity on the Moon (\(g_m\)) is approximately \(1.62 \, \text{m/s}^2\).

Now, calculate the ratio:

\( \frac{W_e}{W_m} \approx \frac{9.8 \, \text{m/s}^2}{1.62 \, \text{m/s}^2} \approx 6.05 \)

Therefore, the ratio \(W_e / W_m\) is approximately 6.

Conclusion

The ratio of the weight of an object on the Earth to its weight on the Moon (\(W_e/W_m\)) is approximately 6.