To find the gravitational force of the lunar rover on the Moon, we need to use the formula for gravitational force:
\[ F = m \times g \]
Where:
- \( F \) is the gravitational force,
- \( m \) is the mass of the rover,
- \( g \) is the acceleration due to gravity.
We can first calculate the mass of the rover using the gravitational force on Earth:
- The gravitational force on Earth is given as 1,607.2 Newtons.
- The acceleration due to gravity on Earth (\( g_{Earth} \)) is 9.8 m/s².
Using these, we can calculate the mass of the rover:
\[ m = \frac{F_{Earth}}{g_{Earth}} = \frac{1,607.2 , \text{N}}{9.8 , \text{m/s}^2} \]
Calculating this gives:
\[ m = \frac{1,607.2}{9.8} \approx 163.2 , \text{kg} \]
Now we can calculate the gravitational force on the Moon using the mass we calculated and the Moon's acceleration due to gravity (\( g_{Moon} = 1.62 , \text{m/s}^2 \)):
\[ F_{Moon} = m \times g_{Moon} = 163.2 , \text{kg} \times 1.62 , \text{m/s}^2 \]
Calculating this gives:
\[ F_{Moon} \approx 264.864 , \text{N} \]
Rounding this to one decimal place, we get approximately 265.7 N.
So the correct response is:
265.7 N