The escape speed for a spacecraft at the surface of a planet of mass M and radius R is:
[tex]v= \sqrt{ \frac{2GM}{R} } [/tex]
where G is the gravitational constant. We can use this formula to solve both parts of the problem, using the data of Jupiter and Mars.
a) Mars:
Mars mass is [tex]M=6.4 \cdot 10^{24}kg[/tex], while Mars radius is [tex]R=3.4 \cdot 10^6 m[/tex], so the escape speed of the spacecraft at Mars surface is
[tex]v= \sqrt{ \frac{2 (6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2})(6.4 \cdot 10^{24} kg)}{3.4 \cdot 10^6 m} }= 5011 m/s = 5.01 km/s [/tex]
b) Jupiter:
Jupiter mass is [tex]M=1.9 \cdot 10^{27} kg[/tex] while its radius is [tex]R=7.15 \cdot 10^7 m[/tex], so the escape speed at its surface is
[tex]v= \sqrt{ \frac{2 (6.67 \cdot 10^{-11} m^3 kg^{-1}s^{-2})(1.9 \cdot 10^{27} kg)}{7.15 \cdot 10^7 m} }=5.95 \cdot 10^4 m/s = 59.5 km/s [/tex]
