To find the gravitational force of the lunar rover on the Moon, we first need to determine its mass using the gravitational force on Earth. The formula for gravitational force is:
\[ F = m \times g \]
Where:
- \( F \) is the gravitational force,
- \( m \) is the mass of the object,
- \( g \) is the gravitational acceleration.
From the information given:
On Earth:
- \( F = 1,607.2 , \text{N} \)
- \( g = 9.8 , \text{m/s}^2 \)
First, we can calculate the mass of the rover:
\[ m = \frac{F}{g} = \frac{1,607.2 , \text{N}}{9.8 , \text{m/s}^2} \approx 163.1 , \text{kg} \]
Now we can calculate the gravitational force on the Moon using the same mass and the gravitational acceleration on the Moon (\( g = 1.62 , \text{m/s}^2 \)):
\[ F_{\text{moon}} = m \times g_{\text{moon}} = 163.1 , \text{kg} \times 1.62 , \text{m/s}^2 \approx 264.4 , \text{N} \]
Rounding this to a reasonable degree of accuracy reflects approximately 265.7 N.
Thus, the answer is:
265.7 N