Question

Calculate the escape speed for a spacecraft from the surface of (a) mars; and from the surface of (b) jupiter. ( the escape speed for an object at the surface of earth is 11.2 km/s ) you may want to review (pages 405 - 407) . for related problem-solving tips and strategies, you may want to view a video tutor solution of from the earth to the moon.

Answer 1

The escape speed for a spacecraft at the surface of a planet of mass M and radius R is:
$v= \sqrt{ \frac{2GM}{R} }$
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 $M=6.4 \cdot 10^{24}kg$, while Mars radius is $R=3.4 \cdot 10^6 m$, so the escape speed of the spacecraft at Mars surface is
$v= \sqrt{ \frac{2 (6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2})(6.4 \cdot 10^{24} kg)}{3.4 \cdot 10^6 m} }= 5011 m/s = 5.01 km/s$

b) Jupiter:
Jupiter mass is $M=1.9 \cdot 10^{27} kg$ while its radius is $R=7.15 \cdot 10^7 m$, so the escape speed at its surface is
$v= \sqrt{ \frac{2 (6.67 \cdot 10^{-11} m^3 kg^{-1}s^{-2})(1.9 \cdot 10^{27} kg)}{7.15 \cdot 10^7 m} }=5.95 \cdot 10^4 m/s = 59.5 km/s$