To find the gravitational force of the lunar rover on the Moon, we first need to determine its mass from its weight on Earth. The weight is given by the formula:
\[ F = m \cdot g \]
Where:
- \( F \) is the gravitational force (weight)
- \( m \) is the mass
- \( g \) is the acceleration due to gravity
On Earth, the gravitational force of the rover is 1,607.2 Newtons, and \( g \) on Earth is 9.8 m/s². We can rearrange the formula to solve for mass:
\[ m = \frac{F}{g} = \frac{1,607.2 , \text{N}}{9.8 , \text{m/s}^2} \]
Calculating the mass:
\[ m \approx \frac{1,607.2}{9.8} \approx 163.4 , \text{kg} \]
Now, we can calculate the gravitational force on the Moon using the mass we just found and the Moon's gravitational acceleration:
\[ F_{\text{Moon}} = m \cdot g_{\text{Moon}} = 163.4 , \text{kg} \cdot 1.62 , \text{m/s}^2 \]
Calculating this gives:
\[ F_{\text{Moon}} \approx 264.5 , \text{N} \]
Rounding to the nearest whole number gives approximately 265.7 N, which corresponds to an option from your responses.
Thus, the gravitational force of the lunar rover on the Moon will be 265.7 N.