1.3 An object tuat is falling freely on the planet Mars experiences an gravitational acceleration with a magnitude of \( 3.8 \mathrm{~m} \cdot \mathrm{~s}^{-2} \). The mass of the Mars is \( 6,4 \times 10^{23} \mathrm{~kg} \). Calculate the radius of the planet Mars in metres formula \( f=\frac{G m_{1}}{r^{2}} \)

To calculate the radius of Mars using the given gravitational acceleration, we can rearrange the formula for gravitational force \( f = \frac{G m_{1}}{r^{2}} \). Here, \( f \) is the gravitational acceleration (3.8 m/s²), \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \mathrm{m}^3/\mathrm{kg} \cdot \mathrm{s}^2 \)), and \( m_{1} \) is the mass of Mars (\( 6.4 \times 10^{23} \, \mathrm{kg} \)). Rearranging the formula gives us \( r = \sqrt{\frac{G m_{1}}{f}} \). Plugging in the values: \[ r = \sqrt{\frac{(6.674 \times 10^{-11}) (6.4 \times 10^{23})}{3.8}} \approx \sqrt{1.10 \times 10^{13}} \approx 3.32 \times 10^{6} \, \mathrm{m} \] Thus, the radius of Mars is approximately \( 3,320,000 \) meters! Mars may not have the gravitational pull of Earth, but it surely has its own charm! Did you know that despite being only about half of Earth's diameter, Mars holds the title for the tallest volcano in the solar system? Olympus Mons stands at a whopping 22 km high—nearly three times the height of Mount Everest! It's a fascinating reminder of the diverse geological features found across our cosmic neighborhood. If you ever find yourself in a predicament while solving physics problems like this, remember to always check your units and calculations twice! Many learners trip up when misremembering the gravitational constant or converting units improperly. A great practice is to create a checklist for each problem, ensuring that all variables are correctly identified and that you're using standard units! Happy problem-solving, future physicists!