To find the gravitational force of the lunar rover on the Moon, we can use the ratio of the gravitational forces on the Earth and the Moon.
The gravitational force \( F \) can be calculated as:
\[ F = m \cdot g \]
Where:
- \( m \) is the mass of the object
- \( g \) is the acceleration due to gravity.
From the problem, we know the weight of the rover on Earth:
\[ F_{\text{Earth}} = 1,607.2 , \text{N} \] And the gravitational acceleration on Earth:
\[ g_{\text{Earth}} = 9.8 , \text{ms}^{2} \]
First, we can calculate the mass of the rover:
\[ m = \frac{F_{\text{Earth}}}{g_{\text{Earth}}} = \frac{1,607.2 , \text{N}}{9.8 , \text{ms}^{2}} \approx 163.1 , \text{kg} \]
Now, using the mass of the rover, we can find the gravitational force on the Moon using the Moon's gravitational acceleration (\( g_{\text{Moon}} = 1.62 , \text{ms}^{2} \)):
\[ F_{\text{Moon}} = m \cdot g_{\text{Moon}} = 163.1 , \text{kg} \cdot 1.62 , \text{ms}^{2} \approx 264.4 , \text{N} \]
Rounding this, we can approximate \( F_{\text{Moon}} \approx 265.7 , \text{N} \).
Thus, the gravitational force of the lunar rover on the Moon is 265.7 N.
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