Ganymede, one of Jupiter’s moons, is larger than....

Question

Ganymede, one of Jupiter’s moons, is larger than planet Mercury! Its mass is 1.54 x 1023 kg, and its radius is 2.64 x 106 m. What is the escape velocity for a space vehicle trying to leave Ganymede? (ans: 2.79 x 103 m/s)

Answer 1

Use total energy equation:

 

KE + PE = (1/2) mv^2 - GMm/r, where m = mass of spacecraft, M = mass of planet, r = distance from spacecraft to center of planet

 

To find minimum velocity to escape from the surface of the planet, set KE+PE = 0, r = radius of planet = R

 

Note m cancels out, i.e. the answer does not depend on the mass of the spacecraft.

 

(1/2) v^2 - GM/R = 0

 

v = sqrt(2GM/R) = sqrt[2 * (6.67 x 10^-11) * (1.54 x 10^23) / 2.64 x 10^6)] m/s = 2.79 x 10^3 m/s = 2.79 km/s

 

Note answer is of the order of a few km/s, which is a typical planetary escape velocity.